Properties

Level 7
Weight 3
Character $\chi_{7}(6, \cdot)$
Label 7.3.6.a
Dimension of Galois orbit 1
Twist info Is minimal
CM Yes
Atkin-Lehner eigenvalues \( \omega_{ 7 } \) : -3

Related objects

Learn more about

Show commands for: SageMath

magma: D := FullDirichletGroup(7);
magma: c := D![3];
magma: S:= CuspForms(c,3);
magma: N := Newforms(S);
sage: D = DirichletGroup(7)
sage: c = D.Element(D,vector([3]))
sage: N = Newforms(c,3,names="a")
sage: f = N[0]

q-expansion

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

(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

\( p \) 2 3 5
\(\alpha_{p}\) \( -0.750000000000000 + 0.661437827766148i \) \( -1.00000000000000 \) \( -1.00000000000000 \)
\(\theta_{p}\) \( 2.41885840577638 \) \( 3.14159265358979 \) \( 3.14159265358979 \)

This cusp form has an eta product $\eta(z)^3\eta(7z)^3=q\prod_{n=1}^\infty (1-q^n)^3(1-q^{7n})^3$, where $q=\exp(2\pi i z)$.

Further Properties

Download this Newform

The database contains the coefficients of \(q^n\) for \(0 \le n\le 499 \).
Choose format to download:
Download coefficients of \(q^n\) for \(0\le n\le \) (maximum 499)