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.

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

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
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
\(2\) \(1\)
\(4021\) \(-1\)