Properties

Label 8042.2.a.c
Level 8042
Weight 2
Character orbit 8042.a
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 86q - 86q^{2} + 12q^{3} + 86q^{4} - 4q^{5} - 12q^{6} + 35q^{7} - 86q^{8} + 72q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 86q - 86q^{2} + 12q^{3} + 86q^{4} - 4q^{5} - 12q^{6} + 35q^{7} - 86q^{8} + 72q^{9} + 4q^{10} + 13q^{11} + 12q^{12} + 45q^{13} - 35q^{14} + 17q^{15} + 86q^{16} + 5q^{17} - 72q^{18} + 47q^{19} - 4q^{20} + 15q^{21} - 13q^{22} + 6q^{23} - 12q^{24} + 112q^{25} - 45q^{26} + 51q^{27} + 35q^{28} - 14q^{29} - 17q^{30} + 24q^{31} - 86q^{32} + 43q^{33} - 5q^{34} + 42q^{35} + 72q^{36} + 61q^{37} - 47q^{38} + 20q^{39} + 4q^{40} - 16q^{41} - 15q^{42} + 72q^{43} + 13q^{44} + 6q^{45} - 6q^{46} + 11q^{47} + 12q^{48} + 89q^{49} - 112q^{50} + 56q^{51} + 45q^{52} - 7q^{53} - 51q^{54} + 48q^{55} - 35q^{56} + 65q^{57} + 14q^{58} + 24q^{59} + 17q^{60} + 31q^{61} - 24q^{62} + 98q^{63} + 86q^{64} - 9q^{65} - 43q^{66} + 157q^{67} + 5q^{68} + q^{69} - 42q^{70} - 11q^{71} - 72q^{72} + 74q^{73} - 61q^{74} + 76q^{75} + 47q^{76} - 13q^{77} - 20q^{78} + 57q^{79} - 4q^{80} + 34q^{81} + 16q^{82} + 65q^{83} + 15q^{84} + 102q^{85} - 72q^{86} + 49q^{87} - 13q^{88} - 34q^{89} - 6q^{90} + 91q^{91} + 6q^{92} + 57q^{93} - 11q^{94} - 13q^{95} - 12q^{96} + 64q^{97} - 89q^{98} + 56q^{99} + O(q^{100}) \)

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 −1.00000 −3.40447 1.00000 −1.12046 3.40447 3.83806 −1.00000 8.59041 1.12046
1.2 −1.00000 −3.12962 1.00000 1.55366 3.12962 0.219811 −1.00000 6.79451 −1.55366
1.3 −1.00000 −3.00414 1.00000 −0.143261 3.00414 −0.146700 −1.00000 6.02484 0.143261
1.4 −1.00000 −2.84562 1.00000 0.429228 2.84562 3.51713 −1.00000 5.09754 −0.429228
1.5 −1.00000 −2.78277 1.00000 −4.36753 2.78277 −3.26500 −1.00000 4.74379 4.36753
1.6 −1.00000 −2.75315 1.00000 3.02853 2.75315 4.50146 −1.00000 4.57981 −3.02853
1.7 −1.00000 −2.59394 1.00000 −0.859547 2.59394 −3.29568 −1.00000 3.72855 0.859547
1.8 −1.00000 −2.58298 1.00000 0.255702 2.58298 −2.29966 −1.00000 3.67181 −0.255702
1.9 −1.00000 −2.54862 1.00000 −1.05969 2.54862 −0.366146 −1.00000 3.49545 1.05969
1.10 −1.00000 −2.53308 1.00000 −2.12930 2.53308 −1.20392 −1.00000 3.41648 2.12930
1.11 −1.00000 −2.49912 1.00000 −3.77840 2.49912 −0.508744 −1.00000 3.24558 3.77840
1.12 −1.00000 −2.38541 1.00000 2.54225 2.38541 3.05592 −1.00000 2.69019 −2.54225
1.13 −1.00000 −2.19026 1.00000 −2.77068 2.19026 3.06919 −1.00000 1.79726 2.77068
1.14 −1.00000 −2.17249 1.00000 −0.488966 2.17249 −0.203617 −1.00000 1.71971 0.488966
1.15 −1.00000 −2.17138 1.00000 3.37288 2.17138 0.0526160 −1.00000 1.71488 −3.37288
1.16 −1.00000 −2.10336 1.00000 −2.86600 2.10336 3.42965 −1.00000 1.42413 2.86600
1.17 −1.00000 −2.02152 1.00000 3.49725 2.02152 −2.15386 −1.00000 1.08655 −3.49725
1.18 −1.00000 −2.00326 1.00000 3.10974 2.00326 0.986750 −1.00000 1.01305 −3.10974
1.19 −1.00000 −1.95612 1.00000 0.359780 1.95612 −1.34656 −1.00000 0.826410 −0.359780
1.20 −1.00000 −1.75423 1.00000 −3.88795 1.75423 3.77690 −1.00000 0.0773276 3.88795
See all 86 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.86
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(4021\) \(-1\)