# Properties

 Level 6 Weight 4 Character $\chi_{6}(1, \cdot)$ Label 6.4.1.a Dimension of Galois orbit 1 Twist info Is minimal CM No Atkin-Lehner eigenvalues $\omega_{ 2 }$ : 1 $\omega_{ 3 }$ : 1

# Related objects

Show commands for: SageMath
magma: S := CuspForms(6,4);
magma: N := Newforms(S);
sage: N = Newforms(6,4,names="a")
sage: f = N[0]

## q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field
$q$ $\mathstrut-$ $2q^{2}$ $\mathstrut-$ $3q^{3}$ $\mathstrut+$ $4q^{4}$ $\mathstrut+$ $6q^{5}$ $\mathstrut+$ $6q^{6}$ $\mathstrut-$ $16q^{7}$ $\mathstrut-$ $8q^{8}$ $\mathstrut+$ $9q^{9}$ $\mathstrut+O(q^{10})$

### 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
$\alpha_{p}$ $0.268328157299975 + 0.963327566303384i$ $-0.431959397724831 + 0.901893052815688i$
$\theta_{p}$ $1.29913920311732$ $2.01746051519443$

# eta-product

This cusp form has an eta product $\eta(z)^2\eta(2z)^2\eta(3z)^2\eta(6z)^2=q\prod_{n=1}^\infty (1-q^n)^2(1-q^{2n})^2 (1-q^{3n})^2(1-q^{6n})^2$ where $q=\exp(2\pi i z)$.

## 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)