Properties

Label 7406.2.a.a
Level 7406
Weight 2
Character orbit 7406.a
Self dual Yes
Analytic conductor 59.137
Analytic rank 2
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 7406 = 2 \cdot 7 \cdot 23^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 7406.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(59.137207737\)
Analytic rank: \(2\)
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

\(f(q)\) \(=\) \( q - q^{2} - 2q^{3} + q^{4} + 2q^{6} - q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - 2q^{3} + q^{4} + 2q^{6} - q^{7} - q^{8} + q^{9} - 2q^{12} - 4q^{13} + q^{14} + q^{16} - 6q^{17} - q^{18} - 2q^{19} + 2q^{21} + 2q^{24} - 5q^{25} + 4q^{26} + 4q^{27} - q^{28} - 6q^{29} - 4q^{31} - q^{32} + 6q^{34} + q^{36} - 2q^{37} + 2q^{38} + 8q^{39} + 6q^{41} - 2q^{42} - 8q^{43} - 12q^{47} - 2q^{48} + q^{49} + 5q^{50} + 12q^{51} - 4q^{52} - 6q^{53} - 4q^{54} + q^{56} + 4q^{57} + 6q^{58} - 6q^{59} - 8q^{61} + 4q^{62} - q^{63} + q^{64} + 4q^{67} - 6q^{68} - q^{72} + 2q^{73} + 2q^{74} + 10q^{75} - 2q^{76} - 8q^{78} - 8q^{79} - 11q^{81} - 6q^{82} + 6q^{83} + 2q^{84} + 8q^{86} + 12q^{87} + 6q^{89} + 4q^{91} + 8q^{93} + 12q^{94} + 2q^{96} + 10q^{97} - q^{98} + O(q^{100}) \)

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 −2.00000 1.00000 0 2.00000 −1.00000 −1.00000 1.00000 0
\(n\): 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
\(2\) \(1\)
\(7\) \(1\)
\(23\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7406))\):

\( T_{3} + 2 \)
\( T_{5} \)
\( T_{11} \)