Properties

Label 7.4.a.a
Level 7
Weight 4
Character orbit 7.a
Self dual Yes
Analytic conductor 0.413
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(0.41301337004\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut -\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut -\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 32q^{15} \) \(\mathstrut +\mathstrut 41q^{16} \) \(\mathstrut +\mathstrut 54q^{17} \) \(\mathstrut +\mathstrut 23q^{18} \) \(\mathstrut -\mathstrut 110q^{19} \) \(\mathstrut -\mathstrut 112q^{20} \) \(\mathstrut +\mathstrut 14q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 48q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 131q^{25} \) \(\mathstrut -\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 49q^{28} \) \(\mathstrut -\mathstrut 110q^{29} \) \(\mathstrut +\mathstrut 32q^{30} \) \(\mathstrut +\mathstrut 12q^{31} \) \(\mathstrut -\mathstrut 161q^{32} \) \(\mathstrut +\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 54q^{34} \) \(\mathstrut -\mathstrut 112q^{35} \) \(\mathstrut +\mathstrut 161q^{36} \) \(\mathstrut -\mathstrut 246q^{37} \) \(\mathstrut +\mathstrut 110q^{38} \) \(\mathstrut -\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 240q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut -\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 128q^{43} \) \(\mathstrut +\mathstrut 56q^{44} \) \(\mathstrut -\mathstrut 368q^{45} \) \(\mathstrut -\mathstrut 48q^{46} \) \(\mathstrut +\mathstrut 324q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 49q^{49} \) \(\mathstrut -\mathstrut 131q^{50} \) \(\mathstrut -\mathstrut 108q^{51} \) \(\mathstrut -\mathstrut 196q^{52} \) \(\mathstrut -\mathstrut 162q^{53} \) \(\mathstrut -\mathstrut 100q^{54} \) \(\mathstrut -\mathstrut 128q^{55} \) \(\mathstrut -\mathstrut 105q^{56} \) \(\mathstrut +\mathstrut 220q^{57} \) \(\mathstrut +\mathstrut 110q^{58} \) \(\mathstrut +\mathstrut 810q^{59} \) \(\mathstrut +\mathstrut 224q^{60} \) \(\mathstrut -\mathstrut 488q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 161q^{63} \) \(\mathstrut -\mathstrut 167q^{64} \) \(\mathstrut +\mathstrut 448q^{65} \) \(\mathstrut -\mathstrut 16q^{66} \) \(\mathstrut +\mathstrut 244q^{67} \) \(\mathstrut -\mathstrut 378q^{68} \) \(\mathstrut -\mathstrut 96q^{69} \) \(\mathstrut +\mathstrut 112q^{70} \) \(\mathstrut -\mathstrut 768q^{71} \) \(\mathstrut -\mathstrut 345q^{72} \) \(\mathstrut -\mathstrut 702q^{73} \) \(\mathstrut +\mathstrut 246q^{74} \) \(\mathstrut -\mathstrut 262q^{75} \) \(\mathstrut +\mathstrut 770q^{76} \) \(\mathstrut +\mathstrut 56q^{77} \) \(\mathstrut +\mathstrut 56q^{78} \) \(\mathstrut +\mathstrut 440q^{79} \) \(\mathstrut +\mathstrut 656q^{80} \) \(\mathstrut +\mathstrut 421q^{81} \) \(\mathstrut -\mathstrut 182q^{82} \) \(\mathstrut -\mathstrut 1302q^{83} \) \(\mathstrut -\mathstrut 98q^{84} \) \(\mathstrut +\mathstrut 864q^{85} \) \(\mathstrut -\mathstrut 128q^{86} \) \(\mathstrut +\mathstrut 220q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut +\mathstrut 730q^{89} \) \(\mathstrut +\mathstrut 368q^{90} \) \(\mathstrut -\mathstrut 196q^{91} \) \(\mathstrut -\mathstrut 336q^{92} \) \(\mathstrut -\mathstrut 24q^{93} \) \(\mathstrut -\mathstrut 324q^{94} \) \(\mathstrut -\mathstrut 1760q^{95} \) \(\mathstrut +\mathstrut 322q^{96} \) \(\mathstrut +\mathstrut 294q^{97} \) \(\mathstrut -\mathstrut 49q^{98} \) \(\mathstrut +\mathstrut 184q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
−1.00000 −2.00000 −7.00000 16.0000 2.00000 −7.00000 15.0000 −23.0000 −16.0000
\(n\): 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
\(7\) \(1\)

Hecke kernels

There are no other newforms in \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\).