Properties

Label 731.2.a.a
Level 731
Weight 2
Character orbit 731.a
Self dual Yes
Analytic conductor 5.837
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(5.83706438776\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - 3q^{8} - 2q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - 3q^{8} - 2q^{9} - q^{10} - 6q^{11} - q^{12} + q^{13} - q^{15} - q^{16} - q^{17} - 2q^{18} - 2q^{19} + q^{20} - 6q^{22} + 2q^{23} - 3q^{24} - 4q^{25} + q^{26} - 5q^{27} + 6q^{29} - q^{30} + 2q^{31} + 5q^{32} - 6q^{33} - q^{34} + 2q^{36} - 3q^{37} - 2q^{38} + q^{39} + 3q^{40} - 4q^{41} - q^{43} + 6q^{44} + 2q^{45} + 2q^{46} + 13q^{47} - q^{48} - 7q^{49} - 4q^{50} - q^{51} - q^{52} + q^{53} - 5q^{54} + 6q^{55} - 2q^{57} + 6q^{58} - 3q^{59} + q^{60} - 7q^{61} + 2q^{62} + 7q^{64} - q^{65} - 6q^{66} - 9q^{67} + q^{68} + 2q^{69} + 11q^{71} + 6q^{72} - 7q^{73} - 3q^{74} - 4q^{75} + 2q^{76} + q^{78} - 8q^{79} + q^{80} + q^{81} - 4q^{82} - 9q^{83} + q^{85} - q^{86} + 6q^{87} + 18q^{88} + 2q^{89} + 2q^{90} - 2q^{92} + 2q^{93} + 13q^{94} + 2q^{95} + 5q^{96} + 10q^{97} - 7q^{98} + 12q^{99} + O(q^{100}) \)

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 1.00000 −1.00000 −1.00000 1.00000 0 −3.00000 −2.00000 −1.00000
\(n\): 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
\(17\) \(1\)
\(43\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(731))\).