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

Related objects

Downloads

Learn more about

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

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

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
−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 \( T_{2} + 10 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(7))\).