Properties

Label 354.2.a.e
Level 354
Weight 2
Character orbit 354.a
Self dual Yes
Analytic conductor 2.827
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 354.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(2.82670423155\)
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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + 4q^{11} - q^{12} + 4q^{13} + q^{16} + 6q^{17} + q^{18} - 4q^{19} + 4q^{22} - 4q^{23} - q^{24} - 5q^{25} + 4q^{26} - q^{27} + 2q^{31} + q^{32} - 4q^{33} + 6q^{34} + q^{36} - 8q^{37} - 4q^{38} - 4q^{39} + 6q^{41} + 4q^{43} + 4q^{44} - 4q^{46} - 4q^{47} - q^{48} - 7q^{49} - 5q^{50} - 6q^{51} + 4q^{52} + 4q^{53} - q^{54} + 4q^{57} - q^{59} + 2q^{62} + q^{64} - 4q^{66} - 16q^{67} + 6q^{68} + 4q^{69} - 14q^{71} + q^{72} + 2q^{73} - 8q^{74} + 5q^{75} - 4q^{76} - 4q^{78} - 8q^{79} + q^{81} + 6q^{82} - 4q^{83} + 4q^{86} + 4q^{88} + 14q^{89} - 4q^{92} - 2q^{93} - 4q^{94} - q^{96} - 10q^{97} - 7q^{98} + 4q^{99} + O(q^{100}) \)

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 0 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
\(2\) \(-1\)
\(3\) \(1\)
\(59\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(354))\):

\( T_{5} \)
\( T_{7} \)
\( T_{11} - 4 \)