# Properties

 Level 11 Weight 2 Character $\chi_{11}(1, \cdot)$ Label 11.2.1.a Dimension of Galois orbit 1 Twist info Is minimal CM No Atkin-Lehner eigenvalues $\omega_{ 11 }$ : -1

# Related objects

Show commands for: SageMath
magma: S := CuspForms(11,2);
magma: N := Newforms(S);
sage: N = Newforms(11,2,names="a")
sage: f = N[0]

## q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field
$q$ $\mathstrut-$ $2q^{2}$ $\mathstrut-$ $q^{3}$ $\mathstrut+$ $2q^{4}$ $\mathstrut+$ $q^{5}$ $\mathstrut+$ $2q^{6}$ $\mathstrut-$ $2q^{7}$ $\mathstrut-$ $2q^{9}$ $\mathstrut+O(q^{10})$

### 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

$p$ 2 3 5 7
$\alpha_{p}$ $-0.707106781186548 + 0.707106781186547i$ $-0.288675134594813 + 0.957427107756338i$ $0.223606797749979 + 0.974679434480896i$ $-0.377964473009227 + 0.925820099772551i$
$\theta_{p}$ $2.35619449019234$ $1.86363909852347$ $1.34528292089677$ $1.95839301345008$

# eta-product

This cusp form can be expressed as an eta product $\eta(z)^2\eta(11z)^2=q\prod_{n=1}^\infty (1-q^n)^2 (1-q^{11 n})^2$, where $q=\exp(2 \pi i z)$.

## Further Properties

The database contains the coefficients of $q^n$ for $0 \le n\le 999$.
 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 999)