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

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

(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 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

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)