Properties

 Level 36 Weight 2 Character $\chi_{36}(1, \cdot)$ Label 36.2.1.a Dimension of Galois orbit 1 Twist info not available CM Yes Atkin-Lehner eigenvalues $\omega_{ 2 }$ : -1 $\omega_{ 3 }$ : 1

Related objects

Show commands for: SageMath
magma: S := CuspForms(36,2);
magma: N := Newforms(S);
sage: N = Newforms(36,2,names="a")
sage: f = N[0]

q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field
$q$ $\mathstrut-$ $4q^{7}$ $\mathstrut+O(q^{10})$

Coefficient field

sage: K = f.hecke_eigenvalue_field() # note that sage often uses an isomorphic number field
The coefficient field is $\Q$

Detailed data

The first few Satake parameters $\alpha_p$ and angles $\theta_p = \textrm{Arg}(\alpha_p)$ are

$p$ 5 7
$\alpha_{p}$ $1.00000000000000i$ $-0.755928946018455 + 0.654653670707977i$
$\theta_{p}$ $1.57079632679490$ $2.42786827464503$

This cusp form can be expressed as an eta product $\eta^4(6z)=q\prod_{n=1}^\infty(1-q^{6n})^4$, where $q=e^{2\pi iz}$.

Further Properties

The database contains the coefficients of $q^n$ for $0 \le n\le 99$.
 Choose format to download: .sage file (contains more information) .sobj file for sage (only coefficients) text file of the algebraic coefficients in a table text file of the complex coefficients in double precision text file of the q-expansion Download coefficients of $q^n$ for $0\le n\le$ (maximum 99)