Properties

Label 14.4.a.b
Level 14
Weight 4
Character orbit 14.a
Self dual Yes
Analytic conductor 0.826
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 14.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.82602674008\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 7q^{7} \) \(\mathstrut +\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 7q^{7} \) \(\mathstrut +\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 24q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut +\mathstrut 56q^{13} \) \(\mathstrut +\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 24q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 46q^{18} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 48q^{20} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut +\mathstrut 96q^{22} \) \(\mathstrut -\mathstrut 120q^{23} \) \(\mathstrut -\mathstrut 16q^{24} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut +\mathstrut 112q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 28q^{28} \) \(\mathstrut -\mathstrut 54q^{29} \) \(\mathstrut +\mathstrut 48q^{30} \) \(\mathstrut +\mathstrut 236q^{31} \) \(\mathstrut +\mathstrut 32q^{32} \) \(\mathstrut -\mathstrut 96q^{33} \) \(\mathstrut -\mathstrut 228q^{34} \) \(\mathstrut -\mathstrut 84q^{35} \) \(\mathstrut -\mathstrut 92q^{36} \) \(\mathstrut +\mathstrut 146q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 112q^{39} \) \(\mathstrut -\mathstrut 96q^{40} \) \(\mathstrut +\mathstrut 126q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 376q^{43} \) \(\mathstrut +\mathstrut 192q^{44} \) \(\mathstrut +\mathstrut 276q^{45} \) \(\mathstrut -\mathstrut 240q^{46} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut -\mathstrut 32q^{48} \) \(\mathstrut +\mathstrut 49q^{49} \) \(\mathstrut +\mathstrut 38q^{50} \) \(\mathstrut +\mathstrut 228q^{51} \) \(\mathstrut +\mathstrut 224q^{52} \) \(\mathstrut +\mathstrut 174q^{53} \) \(\mathstrut +\mathstrut 200q^{54} \) \(\mathstrut -\mathstrut 576q^{55} \) \(\mathstrut +\mathstrut 56q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 108q^{58} \) \(\mathstrut +\mathstrut 138q^{59} \) \(\mathstrut +\mathstrut 96q^{60} \) \(\mathstrut +\mathstrut 380q^{61} \) \(\mathstrut +\mathstrut 472q^{62} \) \(\mathstrut -\mathstrut 161q^{63} \) \(\mathstrut +\mathstrut 64q^{64} \) \(\mathstrut -\mathstrut 672q^{65} \) \(\mathstrut -\mathstrut 192q^{66} \) \(\mathstrut -\mathstrut 484q^{67} \) \(\mathstrut -\mathstrut 456q^{68} \) \(\mathstrut +\mathstrut 240q^{69} \) \(\mathstrut -\mathstrut 168q^{70} \) \(\mathstrut +\mathstrut 576q^{71} \) \(\mathstrut -\mathstrut 184q^{72} \) \(\mathstrut -\mathstrut 1150q^{73} \) \(\mathstrut +\mathstrut 292q^{74} \) \(\mathstrut -\mathstrut 38q^{75} \) \(\mathstrut +\mathstrut 8q^{76} \) \(\mathstrut +\mathstrut 336q^{77} \) \(\mathstrut -\mathstrut 224q^{78} \) \(\mathstrut +\mathstrut 776q^{79} \) \(\mathstrut -\mathstrut 192q^{80} \) \(\mathstrut +\mathstrut 421q^{81} \) \(\mathstrut +\mathstrut 252q^{82} \) \(\mathstrut +\mathstrut 378q^{83} \) \(\mathstrut -\mathstrut 56q^{84} \) \(\mathstrut +\mathstrut 1368q^{85} \) \(\mathstrut -\mathstrut 752q^{86} \) \(\mathstrut +\mathstrut 108q^{87} \) \(\mathstrut +\mathstrut 384q^{88} \) \(\mathstrut -\mathstrut 390q^{89} \) \(\mathstrut +\mathstrut 552q^{90} \) \(\mathstrut +\mathstrut 392q^{91} \) \(\mathstrut -\mathstrut 480q^{92} \) \(\mathstrut -\mathstrut 472q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 24q^{95} \) \(\mathstrut -\mathstrut 64q^{96} \) \(\mathstrut -\mathstrut 1330q^{97} \) \(\mathstrut +\mathstrut 98q^{98} \) \(\mathstrut -\mathstrut 1104q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
2.00000 −2.00000 4.00000 −12.0000 −4.00000 7.00000 8.00000 −23.0000 −24.0000
\(n\): 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
\(2\) \(-1\)
\(7\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3} \) \(\mathstrut +\mathstrut 2 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(14))\).