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

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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
\(q \) \(\mathstrut-\) \(2q^{2} \) \(\mathstrut-\) \(3q^{3} \) \(\mathstrut+\) \(4q^{4} \) \(\mathstrut+\) \(6q^{5} \) \(\mathstrut+\) \(6q^{6} \) \(\mathstrut-\) \(16q^{7} \) \(\mathstrut-\) \(8q^{8} \) \(\mathstrut+\) \(9q^{9} \) \(\mathstrut+O(q^{10}) \)

(To download coefficients, see below.)

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

Download this Newform

The database contains the coefficients of \(q^n\) for \(0 \le n\le 999 \).
Choose format to download:
Download coefficients of \(q^n\) for \(0\le n\le \) (maximum 999)