Properties

Label 7.6.a.a
Level 7
Weight 6
Character orbit 7.a
Self dual Yes
Analytic conductor 1.123
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 7.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.12268673869\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 10q^{2} \) \(\mathstrut -\mathstrut 14q^{3} \) \(\mathstrut +\mathstrut 68q^{4} \) \(\mathstrut -\mathstrut 56q^{5} \) \(\mathstrut +\mathstrut 140q^{6} \) \(\mathstrut -\mathstrut 49q^{7} \) \(\mathstrut -\mathstrut 360q^{8} \) \(\mathstrut -\mathstrut 47q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 10q^{2} \) \(\mathstrut -\mathstrut 14q^{3} \) \(\mathstrut +\mathstrut 68q^{4} \) \(\mathstrut -\mathstrut 56q^{5} \) \(\mathstrut +\mathstrut 140q^{6} \) \(\mathstrut -\mathstrut 49q^{7} \) \(\mathstrut -\mathstrut 360q^{8} \) \(\mathstrut -\mathstrut 47q^{9} \) \(\mathstrut +\mathstrut 560q^{10} \) \(\mathstrut +\mathstrut 232q^{11} \) \(\mathstrut -\mathstrut 952q^{12} \) \(\mathstrut -\mathstrut 140q^{13} \) \(\mathstrut +\mathstrut 490q^{14} \) \(\mathstrut +\mathstrut 784q^{15} \) \(\mathstrut +\mathstrut 1424q^{16} \) \(\mathstrut -\mathstrut 1722q^{17} \) \(\mathstrut +\mathstrut 470q^{18} \) \(\mathstrut -\mathstrut 98q^{19} \) \(\mathstrut -\mathstrut 3808q^{20} \) \(\mathstrut +\mathstrut 686q^{21} \) \(\mathstrut -\mathstrut 2320q^{22} \) \(\mathstrut +\mathstrut 1824q^{23} \) \(\mathstrut +\mathstrut 5040q^{24} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut +\mathstrut 1400q^{26} \) \(\mathstrut +\mathstrut 4060q^{27} \) \(\mathstrut -\mathstrut 3332q^{28} \) \(\mathstrut +\mathstrut 3418q^{29} \) \(\mathstrut -\mathstrut 7840q^{30} \) \(\mathstrut -\mathstrut 7644q^{31} \) \(\mathstrut -\mathstrut 2720q^{32} \) \(\mathstrut -\mathstrut 3248q^{33} \) \(\mathstrut +\mathstrut 17220q^{34} \) \(\mathstrut +\mathstrut 2744q^{35} \) \(\mathstrut -\mathstrut 3196q^{36} \) \(\mathstrut -\mathstrut 10398q^{37} \) \(\mathstrut +\mathstrut 980q^{38} \) \(\mathstrut +\mathstrut 1960q^{39} \) \(\mathstrut +\mathstrut 20160q^{40} \) \(\mathstrut -\mathstrut 17962q^{41} \) \(\mathstrut -\mathstrut 6860q^{42} \) \(\mathstrut +\mathstrut 10880q^{43} \) \(\mathstrut +\mathstrut 15776q^{44} \) \(\mathstrut +\mathstrut 2632q^{45} \) \(\mathstrut -\mathstrut 18240q^{46} \) \(\mathstrut +\mathstrut 9324q^{47} \) \(\mathstrut -\mathstrut 19936q^{48} \) \(\mathstrut +\mathstrut 2401q^{49} \) \(\mathstrut -\mathstrut 110q^{50} \) \(\mathstrut +\mathstrut 24108q^{51} \) \(\mathstrut -\mathstrut 9520q^{52} \) \(\mathstrut +\mathstrut 2262q^{53} \) \(\mathstrut -\mathstrut 40600q^{54} \) \(\mathstrut -\mathstrut 12992q^{55} \) \(\mathstrut +\mathstrut 17640q^{56} \) \(\mathstrut +\mathstrut 1372q^{57} \) \(\mathstrut -\mathstrut 34180q^{58} \) \(\mathstrut -\mathstrut 2730q^{59} \) \(\mathstrut +\mathstrut 53312q^{60} \) \(\mathstrut +\mathstrut 25648q^{61} \) \(\mathstrut +\mathstrut 76440q^{62} \) \(\mathstrut +\mathstrut 2303q^{63} \) \(\mathstrut -\mathstrut 18368q^{64} \) \(\mathstrut +\mathstrut 7840q^{65} \) \(\mathstrut +\mathstrut 32480q^{66} \) \(\mathstrut -\mathstrut 48404q^{67} \) \(\mathstrut -\mathstrut 117096q^{68} \) \(\mathstrut -\mathstrut 25536q^{69} \) \(\mathstrut -\mathstrut 27440q^{70} \) \(\mathstrut -\mathstrut 58560q^{71} \) \(\mathstrut +\mathstrut 16920q^{72} \) \(\mathstrut +\mathstrut 68082q^{73} \) \(\mathstrut +\mathstrut 103980q^{74} \) \(\mathstrut -\mathstrut 154q^{75} \) \(\mathstrut -\mathstrut 6664q^{76} \) \(\mathstrut -\mathstrut 11368q^{77} \) \(\mathstrut -\mathstrut 19600q^{78} \) \(\mathstrut +\mathstrut 31784q^{79} \) \(\mathstrut -\mathstrut 79744q^{80} \) \(\mathstrut -\mathstrut 45419q^{81} \) \(\mathstrut +\mathstrut 179620q^{82} \) \(\mathstrut -\mathstrut 20538q^{83} \) \(\mathstrut +\mathstrut 46648q^{84} \) \(\mathstrut +\mathstrut 96432q^{85} \) \(\mathstrut -\mathstrut 108800q^{86} \) \(\mathstrut -\mathstrut 47852q^{87} \) \(\mathstrut -\mathstrut 83520q^{88} \) \(\mathstrut -\mathstrut 50582q^{89} \) \(\mathstrut -\mathstrut 26320q^{90} \) \(\mathstrut +\mathstrut 6860q^{91} \) \(\mathstrut +\mathstrut 124032q^{92} \) \(\mathstrut +\mathstrut 107016q^{93} \) \(\mathstrut -\mathstrut 93240q^{94} \) \(\mathstrut +\mathstrut 5488q^{95} \) \(\mathstrut +\mathstrut 38080q^{96} \) \(\mathstrut -\mathstrut 58506q^{97} \) \(\mathstrut -\mathstrut 24010q^{98} \) \(\mathstrut -\mathstrut 10904q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
−10.0000 −14.0000 68.0000 −56.0000 140.000 −49.0000 −360.000 −47.0000 560.000
\(n\): 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

This newform can be constructed as the kernel of the linear operator \(T_{2} \) \(\mathstrut +\mathstrut 10 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(7))\).