Properties

Label 354.2.a.c
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

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

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 −1.00000 −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
\(2\) \(1\)
\(3\) \(-1\)
\(59\) \(1\)

Hecke kernels

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

\( T_{5} \)
\( T_{7} + 1 \)
\( T_{11} - 3 \)