Properties

Label 5610.2.a.bk
Level 5610
Weight 2
Character orbit 5610.a
Self dual Yes
Analytic conductor 44.796
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5610.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(44.7960755339\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 4q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 4q^{7} + q^{8} + q^{9} + q^{10} + q^{11} + q^{12} - 2q^{13} - 4q^{14} + q^{15} + q^{16} - q^{17} + q^{18} - 2q^{19} + q^{20} - 4q^{21} + q^{22} - 6q^{23} + q^{24} + q^{25} - 2q^{26} + q^{27} - 4q^{28} - 2q^{29} + q^{30} - 8q^{31} + q^{32} + q^{33} - q^{34} - 4q^{35} + q^{36} - 6q^{37} - 2q^{38} - 2q^{39} + q^{40} + 4q^{41} - 4q^{42} + 8q^{43} + q^{44} + q^{45} - 6q^{46} + 4q^{47} + q^{48} + 9q^{49} + q^{50} - q^{51} - 2q^{52} - 12q^{53} + q^{54} + q^{55} - 4q^{56} - 2q^{57} - 2q^{58} - 12q^{59} + q^{60} - 6q^{61} - 8q^{62} - 4q^{63} + q^{64} - 2q^{65} + q^{66} + 6q^{67} - q^{68} - 6q^{69} - 4q^{70} - 4q^{71} + q^{72} - 2q^{73} - 6q^{74} + q^{75} - 2q^{76} - 4q^{77} - 2q^{78} - 10q^{79} + q^{80} + q^{81} + 4q^{82} + 8q^{83} - 4q^{84} - q^{85} + 8q^{86} - 2q^{87} + q^{88} - 10q^{89} + q^{90} + 8q^{91} - 6q^{92} - 8q^{93} + 4q^{94} - 2q^{95} + q^{96} - 12q^{97} + 9q^{98} + q^{99} + O(q^{100}) \)

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 −4.00000 1.00000 1.00000 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
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(-1\)
\(11\) \(-1\)
\(17\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5610))\):

\( T_{7} + 4 \)
\( T_{13} + 2 \)
\( T_{19} + 2 \)
\( T_{23} + 6 \)