Properties

 Level 17 Weight 2 Character $\chi_{17}(1, \cdot)$ Label 17.2.1.a Dimension of Galois orbit 1 Twist info Is minimal CM No Atkin-Lehner eigenvalues $\omega_{ 17 }$ : -1

Related objects

Show commands for: SageMath
magma: S := CuspForms(17,2);
magma: N := Newforms(S);
sage: N = Newforms(17,2,names="a")
sage: f = N[0]

q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field
$q$ $\mathstrut-$ $q^{2}$ $\mathstrut-$ $q^{4}$ $\mathstrut-$ $2q^{5}$ $\mathstrut+$ $4q^{7}$ $\mathstrut+$ $3q^{8}$ $\mathstrut-$ $3q^{9}$ $\mathstrut+O(q^{10})$

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
$\alpha_{p}$ $-0.353553390593274 + 0.935414346693485i$ $1.00000000000000i$ $-0.447213595499958 + 0.894427190999916i$ $0.755928946018455 + 0.654653670707977i$
$\theta_{p}$ $1.93216345070160$ $1.57079632679490$ $2.03444393579570$ $0.713724378944766$

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)