Properties

Label 5610.2.a.l
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

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

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 −3.00000 −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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5610))\):

\( T_{7} + 3 \)
\( T_{13} - 1 \)
\( T_{19} + 3 \)
\( T_{23} + 1 \)