Properties

Label 5.10.a.a
Level 5
Weight 10
Character orbit 5.a
Self dual Yes
Analytic conductor 2.575
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 5.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(2.57517918082\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 114q^{3} \) \(\mathstrut -\mathstrut 448q^{4} \) \(\mathstrut -\mathstrut 625q^{5} \) \(\mathstrut +\mathstrut 912q^{6} \) \(\mathstrut +\mathstrut 4242q^{7} \) \(\mathstrut +\mathstrut 7680q^{8} \) \(\mathstrut -\mathstrut 6687q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 114q^{3} \) \(\mathstrut -\mathstrut 448q^{4} \) \(\mathstrut -\mathstrut 625q^{5} \) \(\mathstrut +\mathstrut 912q^{6} \) \(\mathstrut +\mathstrut 4242q^{7} \) \(\mathstrut +\mathstrut 7680q^{8} \) \(\mathstrut -\mathstrut 6687q^{9} \) \(\mathstrut +\mathstrut 5000q^{10} \) \(\mathstrut -\mathstrut 46208q^{11} \) \(\mathstrut +\mathstrut 51072q^{12} \) \(\mathstrut -\mathstrut 115934q^{13} \) \(\mathstrut -\mathstrut 33936q^{14} \) \(\mathstrut +\mathstrut 71250q^{15} \) \(\mathstrut +\mathstrut 167936q^{16} \) \(\mathstrut +\mathstrut 494842q^{17} \) \(\mathstrut +\mathstrut 53496q^{18} \) \(\mathstrut -\mathstrut 1008740q^{19} \) \(\mathstrut +\mathstrut 280000q^{20} \) \(\mathstrut -\mathstrut 483588q^{21} \) \(\mathstrut +\mathstrut 369664q^{22} \) \(\mathstrut -\mathstrut 532554q^{23} \) \(\mathstrut -\mathstrut 875520q^{24} \) \(\mathstrut +\mathstrut 390625q^{25} \) \(\mathstrut +\mathstrut 927472q^{26} \) \(\mathstrut +\mathstrut 3006180q^{27} \) \(\mathstrut -\mathstrut 1900416q^{28} \) \(\mathstrut +\mathstrut 4196390q^{29} \) \(\mathstrut -\mathstrut 570000q^{30} \) \(\mathstrut -\mathstrut 3365028q^{31} \) \(\mathstrut -\mathstrut 5275648q^{32} \) \(\mathstrut +\mathstrut 5267712q^{33} \) \(\mathstrut -\mathstrut 3958736q^{34} \) \(\mathstrut -\mathstrut 2651250q^{35} \) \(\mathstrut +\mathstrut 2995776q^{36} \) \(\mathstrut -\mathstrut 14931358q^{37} \) \(\mathstrut +\mathstrut 8069920q^{38} \) \(\mathstrut +\mathstrut 13216476q^{39} \) \(\mathstrut -\mathstrut 4800000q^{40} \) \(\mathstrut +\mathstrut 11056262q^{41} \) \(\mathstrut +\mathstrut 3868704q^{42} \) \(\mathstrut -\mathstrut 6396794q^{43} \) \(\mathstrut +\mathstrut 20701184q^{44} \) \(\mathstrut +\mathstrut 4179375q^{45} \) \(\mathstrut +\mathstrut 4260432q^{46} \) \(\mathstrut -\mathstrut 35559158q^{47} \) \(\mathstrut -\mathstrut 19144704q^{48} \) \(\mathstrut -\mathstrut 22359043q^{49} \) \(\mathstrut -\mathstrut 3125000q^{50} \) \(\mathstrut -\mathstrut 56411988q^{51} \) \(\mathstrut +\mathstrut 51938432q^{52} \) \(\mathstrut +\mathstrut 39738586q^{53} \) \(\mathstrut -\mathstrut 24049440q^{54} \) \(\mathstrut +\mathstrut 28880000q^{55} \) \(\mathstrut +\mathstrut 32578560q^{56} \) \(\mathstrut +\mathstrut 114996360q^{57} \) \(\mathstrut -\mathstrut 33571120q^{58} \) \(\mathstrut -\mathstrut 85185620q^{59} \) \(\mathstrut -\mathstrut 31920000q^{60} \) \(\mathstrut +\mathstrut 45748642q^{61} \) \(\mathstrut +\mathstrut 26920224q^{62} \) \(\mathstrut -\mathstrut 28366254q^{63} \) \(\mathstrut -\mathstrut 43778048q^{64} \) \(\mathstrut +\mathstrut 72458750q^{65} \) \(\mathstrut -\mathstrut 42141696q^{66} \) \(\mathstrut -\mathstrut 45286158q^{67} \) \(\mathstrut -\mathstrut 221689216q^{68} \) \(\mathstrut +\mathstrut 60711156q^{69} \) \(\mathstrut +\mathstrut 21210000q^{70} \) \(\mathstrut -\mathstrut 189967468q^{71} \) \(\mathstrut -\mathstrut 51356160q^{72} \) \(\mathstrut +\mathstrut 412170946q^{73} \) \(\mathstrut +\mathstrut 119450864q^{74} \) \(\mathstrut -\mathstrut 44531250q^{75} \) \(\mathstrut +\mathstrut 451915520q^{76} \) \(\mathstrut -\mathstrut 196014336q^{77} \) \(\mathstrut -\mathstrut 105731808q^{78} \) \(\mathstrut +\mathstrut 95040840q^{79} \) \(\mathstrut -\mathstrut 104960000q^{80} \) \(\mathstrut -\mathstrut 211084299q^{81} \) \(\mathstrut -\mathstrut 88450096q^{82} \) \(\mathstrut +\mathstrut 261706326q^{83} \) \(\mathstrut +\mathstrut 216647424q^{84} \) \(\mathstrut -\mathstrut 309276250q^{85} \) \(\mathstrut +\mathstrut 51174352q^{86} \) \(\mathstrut -\mathstrut 478388460q^{87} \) \(\mathstrut -\mathstrut 354877440q^{88} \) \(\mathstrut -\mathstrut 19938630q^{89} \) \(\mathstrut -\mathstrut 33435000q^{90} \) \(\mathstrut -\mathstrut 491792028q^{91} \) \(\mathstrut +\mathstrut 238584192q^{92} \) \(\mathstrut +\mathstrut 383613192q^{93} \) \(\mathstrut +\mathstrut 284473264q^{94} \) \(\mathstrut +\mathstrut 630462500q^{95} \) \(\mathstrut +\mathstrut 601423872q^{96} \) \(\mathstrut -\mathstrut 19503358q^{97} \) \(\mathstrut +\mathstrut 178872344q^{98} \) \(\mathstrut +\mathstrut 308992896q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
−8.00000 −114.000 −448.000 −625.000 912.000 4242.00 7680.00 −6687.00 5000.00
\(n\): 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 \(T_{2} \) \(\mathstrut +\mathstrut 8 \) acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(5))\).