Properties

Label 8006.2.a.c
Level 8006
Weight 2
Character orbit 8006.a
Self dual Yes
Analytic conductor 63.928
Analytic rank 0
Dimension 92
CM No

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Newspace parameters

Level: \( N \) = \( 8006 = 2 \cdot 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8006.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9282318582\)
Analytic rank: \(0\)
Dimension: \(92\)
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.

\(\operatorname{Tr}(f)(q) = \) \(92q \) \(\mathstrut -\mathstrut 92q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 92q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 92q^{8} \) \(\mathstrut +\mathstrut 104q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(92q \) \(\mathstrut -\mathstrut 92q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 92q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 92q^{8} \) \(\mathstrut +\mathstrut 104q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 40q^{13} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 15q^{15} \) \(\mathstrut +\mathstrut 92q^{16} \) \(\mathstrut -\mathstrut 14q^{17} \) \(\mathstrut -\mathstrut 104q^{18} \) \(\mathstrut +\mathstrut 64q^{19} \) \(\mathstrut +\mathstrut 10q^{20} \) \(\mathstrut +\mathstrut 54q^{21} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 49q^{23} \) \(\mathstrut +\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut 116q^{25} \) \(\mathstrut -\mathstrut 40q^{26} \) \(\mathstrut -\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 39q^{29} \) \(\mathstrut -\mathstrut 15q^{30} \) \(\mathstrut +\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 92q^{32} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 104q^{36} \) \(\mathstrut +\mathstrut 58q^{37} \) \(\mathstrut -\mathstrut 64q^{38} \) \(\mathstrut +\mathstrut 58q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut +\mathstrut 27q^{41} \) \(\mathstrut -\mathstrut 54q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 43q^{45} \) \(\mathstrut +\mathstrut 49q^{46} \) \(\mathstrut -\mathstrut 28q^{47} \) \(\mathstrut -\mathstrut 2q^{48} \) \(\mathstrut +\mathstrut 148q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut +\mathstrut 48q^{51} \) \(\mathstrut +\mathstrut 40q^{52} \) \(\mathstrut +\mathstrut 32q^{53} \) \(\mathstrut +\mathstrut 8q^{54} \) \(\mathstrut +\mathstrut 36q^{55} \) \(\mathstrut -\mathstrut 8q^{56} \) \(\mathstrut +\mathstrut 48q^{57} \) \(\mathstrut -\mathstrut 39q^{58} \) \(\mathstrut +\mathstrut 8q^{59} \) \(\mathstrut +\mathstrut 15q^{60} \) \(\mathstrut +\mathstrut 99q^{61} \) \(\mathstrut -\mathstrut 53q^{62} \) \(\mathstrut +\mathstrut 92q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut q^{66} \) \(\mathstrut +\mathstrut 48q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 63q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut -\mathstrut 104q^{72} \) \(\mathstrut +\mathstrut 49q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut +\mathstrut 16q^{75} \) \(\mathstrut +\mathstrut 64q^{76} \) \(\mathstrut +\mathstrut 41q^{77} \) \(\mathstrut -\mathstrut 58q^{78} \) \(\mathstrut +\mathstrut 143q^{79} \) \(\mathstrut +\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 124q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut -\mathstrut 24q^{83} \) \(\mathstrut +\mathstrut 54q^{84} \) \(\mathstrut +\mathstrut 121q^{85} \) \(\mathstrut -\mathstrut 40q^{86} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 43q^{90} \) \(\mathstrut +\mathstrut 67q^{91} \) \(\mathstrut -\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 43q^{93} \) \(\mathstrut +\mathstrut 28q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 74q^{97} \) \(\mathstrut -\mathstrut 148q^{98} \) \(\mathstrut +\mathstrut 86q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.33817 1.00000 2.91459 3.33817 −3.36056 −1.00000 8.14336 −2.91459
1.2 −1.00000 −3.29526 1.00000 0.810886 3.29526 0.489532 −1.00000 7.85871 −0.810886
1.3 −1.00000 −3.23769 1.00000 1.27122 3.23769 2.87873 −1.00000 7.48264 −1.27122
1.4 −1.00000 −3.23730 1.00000 −3.23542 3.23730 2.52954 −1.00000 7.48009 3.23542
1.5 −1.00000 −3.23032 1.00000 0.193126 3.23032 0.0724171 −1.00000 7.43498 −0.193126
1.6 −1.00000 −3.11194 1.00000 0.282330 3.11194 −3.77246 −1.00000 6.68416 −0.282330
1.7 −1.00000 −3.10076 1.00000 −2.40718 3.10076 −4.08337 −1.00000 6.61471 2.40718
1.8 −1.00000 −2.93049 1.00000 4.31127 2.93049 −2.38009 −1.00000 5.58776 −4.31127
1.9 −1.00000 −2.92008 1.00000 −3.64076 2.92008 −4.95153 −1.00000 5.52686 3.64076
1.10 −1.00000 −2.77089 1.00000 −0.296987 2.77089 3.25147 −1.00000 4.67784 0.296987
1.11 −1.00000 −2.73647 1.00000 2.71633 2.73647 −4.85274 −1.00000 4.48825 −2.71633
1.12 −1.00000 −2.54869 1.00000 0.707045 2.54869 4.56576 −1.00000 3.49580 −0.707045
1.13 −1.00000 −2.53187 1.00000 4.10502 2.53187 0.894818 −1.00000 3.41035 −4.10502
1.14 −1.00000 −2.53029 1.00000 −2.88347 2.53029 1.41548 −1.00000 3.40236 2.88347
1.15 −1.00000 −2.48256 1.00000 −0.944639 2.48256 −2.01033 −1.00000 3.16310 0.944639
1.16 −1.00000 −2.37750 1.00000 −3.81814 2.37750 −1.26090 −1.00000 2.65251 3.81814
1.17 −1.00000 −2.30799 1.00000 −1.49118 2.30799 3.38849 −1.00000 2.32682 1.49118
1.18 −1.00000 −2.07631 1.00000 0.619812 2.07631 2.12229 −1.00000 1.31108 −0.619812
1.19 −1.00000 −2.03971 1.00000 2.70555 2.03971 1.13459 −1.00000 1.16043 −2.70555
1.20 −1.00000 −1.98237 1.00000 −4.41598 1.98237 −1.54286 −1.00000 0.929796 4.41598
See all 92 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.92
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(4003\) \(-1\)