# Properties

 Level 24 Weight 12 Character $\chi_{24}(1, \cdot)$ Label 24.12.1.b 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(24,12);
magma: N := Newforms(S);
sage: N = Newforms(24,12,names="a")
sage: f = N[1]

## q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field
$q$ $\mathstrut-$ $243q^{3}$ $\mathstrut+$ $1190q^{5}$ $\mathstrut+$ $18480q^{7}$ $\mathstrut+$ $59049q^{9}$ $\mathstrut+O(q^{10})$

### 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
$\alpha_{p}$ $0.0851494685831920 + 0.996368188974337i$ $0.207793879372003 + 0.978172634914478i$
$\theta_{p}$ $1.48554362596852$ $1.36147725843771$

## Further Properties

The database contains the coefficients of $q^n$ for $0 \le n\le 314$.
 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 314)