Properties

Label 5.8.a.a
Level 5
Weight 8
Character orbit 5.a
Self dual Yes
Analytic conductor 1.562
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 5.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.56192512742\)
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

\(f(q)\) \(=\) \( q - 14q^{2} - 48q^{3} + 68q^{4} + 125q^{5} + 672q^{6} - 1644q^{7} + 840q^{8} + 117q^{9} + O(q^{10}) \) \( q - 14q^{2} - 48q^{3} + 68q^{4} + 125q^{5} + 672q^{6} - 1644q^{7} + 840q^{8} + 117q^{9} - 1750q^{10} + 172q^{11} - 3264q^{12} + 3862q^{13} + 23016q^{14} - 6000q^{15} - 20464q^{16} - 12254q^{17} - 1638q^{18} - 25940q^{19} + 8500q^{20} + 78912q^{21} - 2408q^{22} + 12972q^{23} - 40320q^{24} + 15625q^{25} - 54068q^{26} + 99360q^{27} - 111792q^{28} - 81610q^{29} + 84000q^{30} - 156888q^{31} + 178976q^{32} - 8256q^{33} + 171556q^{34} - 205500q^{35} + 7956q^{36} + 110126q^{37} + 363160q^{38} - 185376q^{39} + 105000q^{40} + 467882q^{41} - 1104768q^{42} - 499208q^{43} + 11696q^{44} + 14625q^{45} - 181608q^{46} - 396884q^{47} + 982272q^{48} + 1879193q^{49} - 218750q^{50} + 588192q^{51} + 262616q^{52} - 1280498q^{53} - 1391040q^{54} + 21500q^{55} - 1380960q^{56} + 1245120q^{57} + 1142540q^{58} - 1337420q^{59} - 408000q^{60} - 923978q^{61} + 2196432q^{62} - 192348q^{63} + 113728q^{64} + 482750q^{65} + 115584q^{66} - 797304q^{67} - 833272q^{68} - 622656q^{69} + 2877000q^{70} + 5103392q^{71} + 98280q^{72} - 4267478q^{73} - 1541764q^{74} - 750000q^{75} - 1763920q^{76} - 282768q^{77} + 2595264q^{78} - 960q^{79} - 2558000q^{80} - 5025159q^{81} - 6550348q^{82} + 6140832q^{83} + 5366016q^{84} - 1531750q^{85} + 6988912q^{86} + 3917280q^{87} + 144480q^{88} + 2010570q^{89} - 204750q^{90} - 6349128q^{91} + 882096q^{92} + 7530624q^{93} + 5556376q^{94} - 3242500q^{95} - 8590848q^{96} - 4881934q^{97} - 26308702q^{98} + 20124q^{99} + O(q^{100}) \)

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
−14.0000 −48.0000 68.0000 125.000 672.000 −1644.00 840.000 117.000 −1750.00
\(n\): 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
\(5\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} + 14 \) acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(5))\).