Properties

Label 5610.2.a.y
Level 5610
Weight 2
Character orbit 5610.a
Self dual Yes
Analytic conductor 44.796
Analytic rank 0
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: \(0\)
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

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

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 −1.00000 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5610))\):

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