Properties

Label 354.2.a.f
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

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

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 4.00000 −1.00000 0 1.00000 1.00000 4.00000
\(n\): 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
\(2\) \(-1\)
\(3\) \(1\)
\(59\) \(1\)

Hecke kernels

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

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