Properties

Level 36
Weight 2
Character $\chi_{36}(1, \cdot)$
Label 36.2.1.a
Dimension of Galois orbit 1
Twist info not available
CM Yes
Atkin-Lehner eigenvalues \( \omega_{ 2 } \) : -1
\( \omega_{ 3 } \) : 1

Related objects

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Show commands for: SageMath

magma: S := CuspForms(36,2);
magma: N := Newforms(S);
sage: N = Newforms(36,2,names="a")
sage: f = N[0]

q-expansion

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

(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
\(\alpha_{p}\) \( 1.00000000000000i \) \( -0.755928946018455 + 0.654653670707977i \)
\(\theta_{p}\) \( 1.57079632679490 \) \( 2.42786827464503 \)

This cusp form can be expressed as an eta product $\eta^4(6z)=q\prod_{n=1}^\infty(1-q^{6n})^4$, where $q=e^{2\pi iz}$.

Further Properties

Download this Newform

The database contains the coefficients of \(q^n\) for \(0 \le n\le 99 \).
Choose format to download:
Download coefficients of \(q^n\) for \(0\le n\le \) (maximum 99)