# Properties

 Level 37 Weight 2 Character $\chi_{37}(1, \cdot)$ Label 37.2.1.b Dimension of Galois orbit 1 Twist info Is minimal CM No Atkin-Lehner eigenvalues $\omega_{ 37 }$ : -1

# Related objects

Show commands for: SageMath
magma: S := CuspForms(37,2);
magma: N := Newforms(S);
sage: N = Newforms(37,2,names="a")
sage: f = N[1]

## q-expansion

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

### 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
$\alpha_{p}$ $1.00000000000000i$ $0.288675134594813 + 0.957427107756338i$ $1.00000000000000i$ $-0.188982236504614 + 0.981980506061966i$
$\theta_{p}$ $1.57079632679490$ $1.27795355506632$ $1.57079632679490$ $1.76092193014136$

## Further Properties

The database contains the coefficients of $q^n$ for $0 \le n\le 99$.
 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 99)