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

Learn more about

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
\(q \) \(\mathstrut-\) \(2q^{2} \) \(\mathstrut-\) \(q^{3} \) \(\mathstrut+\) \(2q^{4} \) \(\mathstrut+\) \(q^{5} \) \(\mathstrut+\) \(2q^{6} \) \(\mathstrut-\) \(2q^{7} \) \(\mathstrut-\) \(2q^{9} \) \(\mathstrut+O(q^{10}) \)

(To download coefficients, see below.)

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

Download this Newform

The database contains the coefficients of \(q^n\) for \(0 \le n\le 999 \).
Choose format to download:
Download coefficients of \(q^n\) for \(0\le n\le \) (maximum 999)