Properties

Level 17
Weight 2
Character $\chi_{17}(1, \cdot)$
Label 17.2.1.a
Dimension of Galois orbit 1
Twist info Is minimal
CM No
Atkin-Lehner eigenvalues \( \omega_{ 17 } \) : -1

Related objects

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Show commands for: SageMath

magma: S := CuspForms(17,2);
magma: N := Newforms(S);
sage: N = Newforms(17,2,names="a")
sage: f = N[0]

q-expansion

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

(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
\(\alpha_{p}\) \( -0.353553390593274 + 0.935414346693485i \) \( 1.00000000000000i \) \( -0.447213595499958 + 0.894427190999916i \) \( 0.755928946018455 + 0.654653670707977i \)
\(\theta_{p}\) \( 1.93216345070160 \) \( 1.57079632679490 \) \( 2.03444393579570 \) \( 0.713724378944766 \)

Further Properties

Download this Newform

The database contains the coefficients of \(q^n\) for \(0 \le n\le 999 \).
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Download coefficients of \(q^n\) for \(0\le n\le \) (maximum 999)