# Properties

 Level 24 Weight 4 Character $\chi_{24}(1, \cdot)$ Label 24.4.1.a Dimension of Galois orbit 1 Twist info not available CM No Atkin-Lehner eigenvalues $\omega_{ 2 }$ : -1 $\omega_{ 3 }$ : -1

# Related objects

Show commands for: SageMath
magma: S := CuspForms(24,4);
magma: N := Newforms(S);
sage: N = Newforms(24,4,names="a")
sage: f = N[0]

## q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field
$q$ $\mathstrut+$ $3q^{3}$ $\mathstrut+$ $14q^{5}$ $\mathstrut-$ $24q^{7}$ $\mathstrut+$ $9q^{9}$ $\mathstrut+O(q^{10})$

### 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
$\alpha_{p}$ $0.626099033699941 + 0.779743547584717i$ $-0.647939096587247 + 0.761692147204960i$
$\theta_{p}$ $0.894256109100503$ $2.27567194851327$

## Further Properties

The database contains the coefficients of $q^n$ for $0 \le n\le 119$.
 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 119)