Properties

Label 8014.2.a.e
Level 8014
Weight 2
Character orbit 8014.a
Self dual Yes
Analytic conductor 63.992
Analytic rank 0
Dimension 91
CM No

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Newspace parameters

Level: \( N \) = \( 8014 = 2 \cdot 4007 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8014.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9921121799\)
Analytic rank: \(0\)
Dimension: \(91\)
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.

\(\operatorname{Tr}(f)(q) = \) \(91q \) \(\mathstrut -\mathstrut 91q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 91q^{4} \) \(\mathstrut +\mathstrut 22q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 14q^{7} \) \(\mathstrut -\mathstrut 91q^{8} \) \(\mathstrut +\mathstrut 123q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(91q \) \(\mathstrut -\mathstrut 91q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 91q^{4} \) \(\mathstrut +\mathstrut 22q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 14q^{7} \) \(\mathstrut -\mathstrut 91q^{8} \) \(\mathstrut +\mathstrut 123q^{9} \) \(\mathstrut -\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 59q^{11} \) \(\mathstrut -\mathstrut 2q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut +\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 23q^{15} \) \(\mathstrut +\mathstrut 91q^{16} \) \(\mathstrut +\mathstrut 25q^{17} \) \(\mathstrut -\mathstrut 123q^{18} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 22q^{20} \) \(\mathstrut +\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 59q^{22} \) \(\mathstrut +\mathstrut 36q^{23} \) \(\mathstrut +\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut 121q^{25} \) \(\mathstrut +\mathstrut 15q^{26} \) \(\mathstrut -\mathstrut 8q^{27} \) \(\mathstrut -\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 71q^{29} \) \(\mathstrut -\mathstrut 23q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 91q^{32} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 25q^{34} \) \(\mathstrut +\mathstrut 27q^{35} \) \(\mathstrut +\mathstrut 123q^{36} \) \(\mathstrut +\mathstrut 5q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut +\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut +\mathstrut 77q^{41} \) \(\mathstrut -\mathstrut 20q^{42} \) \(\mathstrut -\mathstrut 36q^{43} \) \(\mathstrut +\mathstrut 59q^{44} \) \(\mathstrut +\mathstrut 62q^{45} \) \(\mathstrut -\mathstrut 36q^{46} \) \(\mathstrut +\mathstrut 41q^{47} \) \(\mathstrut -\mathstrut 2q^{48} \) \(\mathstrut +\mathstrut 137q^{49} \) \(\mathstrut -\mathstrut 121q^{50} \) \(\mathstrut +\mathstrut 13q^{51} \) \(\mathstrut -\mathstrut 15q^{52} \) \(\mathstrut +\mathstrut 33q^{53} \) \(\mathstrut +\mathstrut 8q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 14q^{56} \) \(\mathstrut +\mathstrut 52q^{57} \) \(\mathstrut -\mathstrut 71q^{58} \) \(\mathstrut +\mathstrut 76q^{59} \) \(\mathstrut +\mathstrut 23q^{60} \) \(\mathstrut +\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 18q^{63} \) \(\mathstrut +\mathstrut 91q^{64} \) \(\mathstrut +\mathstrut 84q^{65} \) \(\mathstrut -\mathstrut 24q^{66} \) \(\mathstrut -\mathstrut 59q^{67} \) \(\mathstrut +\mathstrut 25q^{68} \) \(\mathstrut +\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 27q^{70} \) \(\mathstrut +\mathstrut 124q^{71} \) \(\mathstrut -\mathstrut 123q^{72} \) \(\mathstrut +\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 5q^{74} \) \(\mathstrut +\mathstrut 9q^{75} \) \(\mathstrut +\mathstrut 2q^{76} \) \(\mathstrut +\mathstrut 50q^{77} \) \(\mathstrut -\mathstrut 48q^{78} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 22q^{80} \) \(\mathstrut +\mathstrut 227q^{81} \) \(\mathstrut -\mathstrut 77q^{82} \) \(\mathstrut +\mathstrut 29q^{83} \) \(\mathstrut +\mathstrut 20q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 36q^{86} \) \(\mathstrut -\mathstrut 25q^{87} \) \(\mathstrut -\mathstrut 59q^{88} \) \(\mathstrut +\mathstrut 148q^{89} \) \(\mathstrut -\mathstrut 62q^{90} \) \(\mathstrut +\mathstrut 27q^{91} \) \(\mathstrut +\mathstrut 36q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut -\mathstrut 41q^{94} \) \(\mathstrut +\mathstrut 54q^{95} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut -\mathstrut 137q^{98} \) \(\mathstrut +\mathstrut 157q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.44800 1.00000 −2.43856 3.44800 4.30446 −1.00000 8.88870 2.43856
1.2 −1.00000 −3.41500 1.00000 2.43339 3.41500 −1.50978 −1.00000 8.66224 −2.43339
1.3 −1.00000 −3.27811 1.00000 4.00106 3.27811 −4.58549 −1.00000 7.74601 −4.00106
1.4 −1.00000 −3.27677 1.00000 −0.135024 3.27677 −2.05105 −1.00000 7.73722 0.135024
1.5 −1.00000 −3.21498 1.00000 −2.38557 3.21498 −0.918897 −1.00000 7.33611 2.38557
1.6 −1.00000 −3.13974 1.00000 3.30555 3.13974 0.656006 −1.00000 6.85799 −3.30555
1.7 −1.00000 −3.09151 1.00000 −2.61298 3.09151 −3.49285 −1.00000 6.55743 2.61298
1.8 −1.00000 −3.06251 1.00000 1.40510 3.06251 4.44564 −1.00000 6.37896 −1.40510
1.9 −1.00000 −2.93164 1.00000 −4.27136 2.93164 −1.93753 −1.00000 5.59453 4.27136
1.10 −1.00000 −2.86981 1.00000 −0.806947 2.86981 −4.79468 −1.00000 5.23582 0.806947
1.11 −1.00000 −2.86622 1.00000 0.269496 2.86622 2.82265 −1.00000 5.21519 −0.269496
1.12 −1.00000 −2.85455 1.00000 −2.30346 2.85455 3.17509 −1.00000 5.14844 2.30346
1.13 −1.00000 −2.66657 1.00000 3.59792 2.66657 3.19859 −1.00000 4.11059 −3.59792
1.14 −1.00000 −2.62836 1.00000 2.05043 2.62836 −5.05998 −1.00000 3.90825 −2.05043
1.15 −1.00000 −2.35351 1.00000 2.15005 2.35351 1.12674 −1.00000 2.53903 −2.15005
1.16 −1.00000 −2.32734 1.00000 3.86368 2.32734 −1.21196 −1.00000 2.41649 −3.86368
1.17 −1.00000 −2.31549 1.00000 0.682396 2.31549 −3.17347 −1.00000 2.36151 −0.682396
1.18 −1.00000 −2.25449 1.00000 0.777840 2.25449 1.47835 −1.00000 2.08272 −0.777840
1.19 −1.00000 −2.03768 1.00000 −1.30464 2.03768 −1.43874 −1.00000 1.15214 1.30464
1.20 −1.00000 −1.99318 1.00000 0.808905 1.99318 3.91873 −1.00000 0.972766 −0.808905
See all 91 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.91
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(4007\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3}^{91} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8014))\).