Properties

Label 5610.2.a.bb
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

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

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 −2.00000 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5610))\):

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