Properties

Label 17.2.a.a
Level 17
Weight 2
Character orbit 17.a
Self dual Yes
Analytic conductor 0.136
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 17.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.135745683436\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - q^{4} - 2q^{5} + 4q^{7} + 3q^{8} - 3q^{9} + O(q^{10}) \) \( q - q^{2} - q^{4} - 2q^{5} + 4q^{7} + 3q^{8} - 3q^{9} + 2q^{10} - 2q^{13} - 4q^{14} - q^{16} + q^{17} + 3q^{18} - 4q^{19} + 2q^{20} + 4q^{23} - q^{25} + 2q^{26} - 4q^{28} + 6q^{29} + 4q^{31} - 5q^{32} - q^{34} - 8q^{35} + 3q^{36} - 2q^{37} + 4q^{38} - 6q^{40} - 6q^{41} + 4q^{43} + 6q^{45} - 4q^{46} + 9q^{49} + q^{50} + 2q^{52} + 6q^{53} + 12q^{56} - 6q^{58} - 12q^{59} - 10q^{61} - 4q^{62} - 12q^{63} + 7q^{64} + 4q^{65} + 4q^{67} - q^{68} + 8q^{70} - 4q^{71} - 9q^{72} - 6q^{73} + 2q^{74} + 4q^{76} + 12q^{79} + 2q^{80} + 9q^{81} + 6q^{82} - 4q^{83} - 2q^{85} - 4q^{86} + 10q^{89} - 6q^{90} - 8q^{91} - 4q^{92} + 8q^{95} + 2q^{97} - 9q^{98} + O(q^{100}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
−1.00000 0 −1.00000 −2.00000 0 4.00000 3.00000 −3.00000 2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

\( p \) Sign
\(17\) \(-1\)

Hecke kernels

There are no other newforms in \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\).