Properties

Label 5390.2.a.h
Level 5390
Weight 2
Character orbit 5390.a
Self dual Yes
Analytic conductor 43.039
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5390.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(43.0393666895\)
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

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

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 −1.00000 −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
\(2\) \(1\)
\(5\) \(-1\)
\(7\) \(-1\)
\(11\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5390))\):

\( T_{3} + 1 \)
\( T_{13} + 2 \)
\( T_{17} + 3 \)
\( T_{19} - 7 \)
\( T_{31} - 7 \)