Properties

 Level 102 Weight 2 Character $\chi_{102}(1, \cdot)$ Label 102.2.1.c Dimension of Galois orbit 1 Twist info Is minimal CM No Atkin-Lehner eigenvalues $\omega_{ 17 }$ : -1 $\omega_{ 2 }$ : -1 $\omega_{ 3 }$ : -1

Related objects

Show commands for: SageMath
magma: S := CuspForms(102,2);
magma: N := Newforms(S);
sage: N = Newforms(102,2,names="a")
sage: f = N[2]

q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field
$q$ $\mathstrut+$ $q^{2}$ $\mathstrut+$ $q^{3}$ $\mathstrut+$ $q^{4}$ $\mathstrut-$ $2q^{5}$ $\mathstrut+$ $q^{6}$ $\mathstrut+$ $q^{8}$ $\mathstrut+$ $q^{9}$ $\mathstrut+O(q^{10})$

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

$p$ 5 7
$\alpha_{p}$ $-0.447213595499958 + 0.894427190999916i$ $1.00000000000000i$
$\theta_{p}$ $2.03444393579570$ $1.57079632679490$

Further Properties

The database contains the coefficients of $q^n$ for $0 \le n\le 124$.
 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 124)