Properties

Label 8015.2.a.l
Level 8015
Weight 2
Character orbit 8015.a
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.78055 0.298033 5.73146 −1.00000 −0.828697 −1.00000 −10.3755 −2.91118 2.78055
1.2 −2.65622 −1.51381 5.05553 −1.00000 4.02102 −1.00000 −8.11618 −0.708384 2.65622
1.3 −2.61699 0.399813 4.84863 −1.00000 −1.04630 −1.00000 −7.45482 −2.84015 2.61699
1.4 −2.48664 3.28438 4.18340 −1.00000 −8.16709 −1.00000 −5.42933 7.78717 2.48664
1.5 −2.41590 1.84179 3.83658 −1.00000 −4.44959 −1.00000 −4.43701 0.392199 2.41590
1.6 −2.35302 1.42181 3.53669 −1.00000 −3.34553 −1.00000 −3.61585 −0.978466 2.35302
1.7 −2.28892 −1.23476 3.23914 −1.00000 2.82625 −1.00000 −2.83628 −1.47538 2.28892
1.8 −2.23328 1.54114 2.98754 −1.00000 −3.44181 −1.00000 −2.20546 −0.624877 2.23328
1.9 −2.20228 −3.01220 2.85005 −1.00000 6.63371 −1.00000 −1.87206 6.07333 2.20228
1.10 −2.17211 3.11306 2.71804 −1.00000 −6.76191 −1.00000 −1.55967 6.69117 2.17211
1.11 −2.12264 −2.04208 2.50559 −1.00000 4.33460 −1.00000 −1.07319 1.17010 2.12264
1.12 −1.90469 −0.920285 1.62783 −1.00000 1.75286 −1.00000 0.708859 −2.15308 1.90469
1.13 −1.87703 −2.63781 1.52324 −1.00000 4.95125 −1.00000 0.894900 3.95806 1.87703
1.14 −1.76681 2.93332 1.12163 −1.00000 −5.18264 −1.00000 1.55191 5.60439 1.76681
1.15 −1.54368 0.772565 0.382940 −1.00000 −1.19259 −1.00000 2.49622 −2.40314 1.54368
1.16 −1.46418 −1.88953 0.143813 −1.00000 2.76661 −1.00000 2.71779 0.570340 1.46418
1.17 −1.44897 −0.334420 0.0995284 −1.00000 0.484566 −1.00000 2.75374 −2.88816 1.44897
1.18 −1.34348 −2.34976 −0.195065 −1.00000 3.15685 −1.00000 2.94902 2.52136 1.34348
1.19 −1.28523 −0.829686 −0.348175 −1.00000 1.06634 −1.00000 3.01795 −2.31162 1.28523
1.20 −1.21148 1.67937 −0.532324 −1.00000 −2.03452 −1.00000 3.06785 −0.179714 1.21148
See all 62 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.62
Significant digits:
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Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(7\) \(1\)
\(229\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\):

\(T_{2}^{62} - \cdots\)
\(T_{3}^{62} - \cdots\)