Properties

Label 114.2.a.a
Level 114
Weight 2
Character orbit 114.a
Self dual Yes
Analytic conductor 0.910
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 114.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.910294583043\)
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

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

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 0 1.00000 4.00000 −1.00000 1.00000 0
\(n\): 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
\(2\) \(1\)
\(3\) \(1\)
\(19\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(114))\):

\( T_{5} \)
\( T_{7} - 4 \)