Properties

Label 1155.2.a.e
Level 1155
Weight 2
Character orbit 1155.a
Self dual Yes
Analytic conductor 9.223
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1155.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(9.22272143346\)
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

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

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 3.00000 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
\(3\) \(1\)
\(5\) \(-1\)
\(7\) \(1\)
\(11\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\):

\( T_{2} + 1 \)
\( T_{13} + 2 \)
\( T_{17} + 6 \)