Properties

Label 8007.2.a.i
Level 8007
Weight 2
Character orbit 8007.a
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 63
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(63\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 63q + 10q^{2} + 63q^{3} + 70q^{4} + 19q^{5} + 10q^{6} + 11q^{7} + 27q^{8} + 63q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 63q + 10q^{2} + 63q^{3} + 70q^{4} + 19q^{5} + 10q^{6} + 11q^{7} + 27q^{8} + 63q^{9} + 4q^{10} + 23q^{11} + 70q^{12} + 10q^{13} + 18q^{14} + 19q^{15} + 72q^{16} + 63q^{17} + 10q^{18} + 6q^{19} + 48q^{20} + 11q^{21} + 21q^{22} + 44q^{23} + 27q^{24} + 110q^{25} + 41q^{26} + 63q^{27} + 26q^{28} + 35q^{29} + 4q^{30} + q^{31} + 54q^{32} + 23q^{33} + 10q^{34} + 47q^{35} + 70q^{36} + 40q^{37} + 38q^{38} + 10q^{39} - 10q^{40} + 35q^{41} + 18q^{42} + 27q^{43} + 46q^{44} + 19q^{45} + 8q^{46} + 29q^{47} + 72q^{48} + 114q^{49} + 27q^{50} + 63q^{51} - q^{52} + 75q^{53} + 10q^{54} + 5q^{55} + 24q^{56} + 6q^{57} + 41q^{58} + 105q^{59} + 48q^{60} + 5q^{61} + 22q^{62} + 11q^{63} + 61q^{64} + 49q^{65} + 21q^{66} + 4q^{67} + 70q^{68} + 44q^{69} - 16q^{70} + 16q^{71} + 27q^{72} + 39q^{73} + 54q^{74} + 110q^{75} + 6q^{76} + 88q^{77} + 41q^{78} + 16q^{79} + 102q^{80} + 63q^{81} - 29q^{82} + 73q^{83} + 26q^{84} + 19q^{85} + 46q^{86} + 35q^{87} + 18q^{88} + 88q^{89} + 4q^{90} - 15q^{91} + 110q^{92} + q^{93} - 8q^{94} + 28q^{95} + 54q^{96} + 70q^{97} + 33q^{98} + 23q^{99} + O(q^{100}) \)

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 −2.76200 1.00000 5.62867 −0.159585 −2.76200 −3.17690 −10.0224 1.00000 0.440774
1.2 −2.70479 1.00000 5.31589 4.10743 −2.70479 3.26601 −8.96878 1.00000 −11.1097
1.3 −2.58914 1.00000 4.70363 −1.26310 −2.58914 −1.23370 −7.00007 1.00000 3.27035
1.4 −2.40365 1.00000 3.77751 −0.410000 −2.40365 −0.100135 −4.27252 1.00000 0.985496
1.5 −2.34343 1.00000 3.49167 2.63222 −2.34343 1.69426 −3.49562 1.00000 −6.16842
1.6 −2.27277 1.00000 3.16549 3.41153 −2.27277 4.87508 −2.64888 1.00000 −7.75362
1.7 −2.21840 1.00000 2.92128 −1.40773 −2.21840 0.0138217 −2.04376 1.00000 3.12290
1.8 −2.18826 1.00000 2.78847 −0.00677076 −2.18826 −4.11828 −1.72538 1.00000 0.0148162
1.9 −2.12676 1.00000 2.52310 −0.0337885 −2.12676 4.05166 −1.11251 1.00000 0.0718600
1.10 −2.11232 1.00000 2.46191 −3.85779 −2.11232 0.0837724 −0.975695 1.00000 8.14890
1.11 −2.02903 1.00000 2.11694 4.33739 −2.02903 −3.04221 −0.237280 1.00000 −8.80067
1.12 −1.99602 1.00000 1.98408 2.66347 −1.99602 −1.66715 0.0317759 1.00000 −5.31632
1.13 −1.80525 1.00000 1.25895 −4.24051 −1.80525 −2.73260 1.33779 1.00000 7.65520
1.14 −1.76021 1.00000 1.09834 1.37447 −1.76021 3.49395 1.58711 1.00000 −2.41936
1.15 −1.74167 1.00000 1.03340 −2.69066 −1.74167 0.494465 1.68349 1.00000 4.68623
1.16 −1.25126 1.00000 −0.434343 3.57483 −1.25126 −4.07525 3.04600 1.00000 −4.47305
1.17 −1.23503 1.00000 −0.474692 0.598945 −1.23503 −4.57610 3.05633 1.00000 −0.739717
1.18 −1.22360 1.00000 −0.502806 1.43997 −1.22360 −1.77841 3.06243 1.00000 −1.76195
1.19 −1.05868 1.00000 −0.879191 −2.81588 −1.05868 4.49493 3.04815 1.00000 2.98112
1.20 −1.04403 1.00000 −0.910007 3.07941 −1.04403 2.83741 3.03813 1.00000 −3.21499
See all 63 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.63
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
\(3\) \(-1\)
\(17\) \(-1\)
\(157\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{63} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8007))\).