## Experimental Mathematics

- Experiment. Math.
- Volume 11, Issue 3 (2002), 407-426.

### Hecke Eigenvalues for Real Quadratic Fields

#### Abstract

We describe an algorithm to compute the trace of Hecke operators acting on the space of Hilbert cusp forms defined relative to a real quadratic field with class number greater than one. Using this algorithm, we obtain numerical data for eigenvalues and characteristic polynomials of the Hecke operators. Within the limit of our computation, the conductors of the orders spanned by the Hecke eigenvalue for any principal split prime ideal contain a nontrivial common factor, which is equal to a Hecke {\small$L$}-value.

#### Article information

**Source**

Experiment. Math., Volume 11, Issue 3 (2002), 407-426.

**Dates**

First available in Project Euclid: 9 July 2003

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1057777431

**Mathematical Reviews number (MathSciNet)**

MR1959751

**Zentralblatt MATH identifier**

1117.11304

**Subjects**

Primary: 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]

Secondary: 11F60: Hecke-Petersson operators, differential operators (several variables) 11F72: Spectral theory; Selberg trace formula 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]

**Keywords**

Hilbert cusp form Hecke operator eigenvalue trace formula L-value

#### Citation

Okada, Kaoru. Hecke Eigenvalues for Real Quadratic Fields. Experiment. Math. 11 (2002), no. 3, 407--426. https://projecteuclid.org/euclid.em/1057777431