Properties

Label 8014.2.a.d
Level 8014
Weight 2
Character orbit 8014.a
Self dual Yes
Analytic conductor 63.992
Analytic rank 0
Dimension 88
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: \(88\)
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.

\(\operatorname{Tr}(f)(q) = \) \(88q \) \(\mathstrut +\mathstrut 88q^{2} \) \(\mathstrut +\mathstrut 22q^{3} \) \(\mathstrut +\mathstrut 88q^{4} \) \(\mathstrut +\mathstrut 25q^{5} \) \(\mathstrut +\mathstrut 22q^{6} \) \(\mathstrut +\mathstrut 33q^{7} \) \(\mathstrut +\mathstrut 88q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(88q \) \(\mathstrut +\mathstrut 88q^{2} \) \(\mathstrut +\mathstrut 22q^{3} \) \(\mathstrut +\mathstrut 88q^{4} \) \(\mathstrut +\mathstrut 25q^{5} \) \(\mathstrut +\mathstrut 22q^{6} \) \(\mathstrut +\mathstrut 33q^{7} \) \(\mathstrut +\mathstrut 88q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut 25q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 22q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 33q^{14} \) \(\mathstrut +\mathstrut 47q^{15} \) \(\mathstrut +\mathstrut 88q^{16} \) \(\mathstrut +\mathstrut 19q^{17} \) \(\mathstrut +\mathstrut 108q^{18} \) \(\mathstrut +\mathstrut 33q^{19} \) \(\mathstrut +\mathstrut 25q^{20} \) \(\mathstrut +\mathstrut 48q^{21} \) \(\mathstrut +\mathstrut 70q^{22} \) \(\mathstrut +\mathstrut 77q^{23} \) \(\mathstrut +\mathstrut 22q^{24} \) \(\mathstrut +\mathstrut 109q^{25} \) \(\mathstrut +\mathstrut 31q^{26} \) \(\mathstrut +\mathstrut 88q^{27} \) \(\mathstrut +\mathstrut 33q^{28} \) \(\mathstrut +\mathstrut 83q^{29} \) \(\mathstrut +\mathstrut 47q^{30} \) \(\mathstrut +\mathstrut 51q^{31} \) \(\mathstrut +\mathstrut 88q^{32} \) \(\mathstrut +\mathstrut 30q^{33} \) \(\mathstrut +\mathstrut 19q^{34} \) \(\mathstrut +\mathstrut 40q^{35} \) \(\mathstrut +\mathstrut 108q^{36} \) \(\mathstrut +\mathstrut 45q^{37} \) \(\mathstrut +\mathstrut 33q^{38} \) \(\mathstrut +\mathstrut 82q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut +\mathstrut 35q^{41} \) \(\mathstrut +\mathstrut 48q^{42} \) \(\mathstrut +\mathstrut 78q^{43} \) \(\mathstrut +\mathstrut 70q^{44} \) \(\mathstrut +\mathstrut 37q^{45} \) \(\mathstrut +\mathstrut 77q^{46} \) \(\mathstrut +\mathstrut 59q^{47} \) \(\mathstrut +\mathstrut 22q^{48} \) \(\mathstrut +\mathstrut 103q^{49} \) \(\mathstrut +\mathstrut 109q^{50} \) \(\mathstrut +\mathstrut 21q^{51} \) \(\mathstrut +\mathstrut 31q^{52} \) \(\mathstrut +\mathstrut 58q^{53} \) \(\mathstrut +\mathstrut 88q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 33q^{56} \) \(\mathstrut -\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 83q^{58} \) \(\mathstrut +\mathstrut 54q^{59} \) \(\mathstrut +\mathstrut 47q^{60} \) \(\mathstrut +\mathstrut 18q^{61} \) \(\mathstrut +\mathstrut 51q^{62} \) \(\mathstrut +\mathstrut 47q^{63} \) \(\mathstrut +\mathstrut 88q^{64} \) \(\mathstrut +\mathstrut 34q^{65} \) \(\mathstrut +\mathstrut 30q^{66} \) \(\mathstrut +\mathstrut 88q^{67} \) \(\mathstrut +\mathstrut 19q^{68} \) \(\mathstrut +\mathstrut 62q^{69} \) \(\mathstrut +\mathstrut 40q^{70} \) \(\mathstrut +\mathstrut 139q^{71} \) \(\mathstrut +\mathstrut 108q^{72} \) \(\mathstrut -\mathstrut 6q^{73} \) \(\mathstrut +\mathstrut 45q^{74} \) \(\mathstrut +\mathstrut 45q^{75} \) \(\mathstrut +\mathstrut 33q^{76} \) \(\mathstrut +\mathstrut 37q^{77} \) \(\mathstrut +\mathstrut 82q^{78} \) \(\mathstrut +\mathstrut 94q^{79} \) \(\mathstrut +\mathstrut 25q^{80} \) \(\mathstrut +\mathstrut 112q^{81} \) \(\mathstrut +\mathstrut 35q^{82} \) \(\mathstrut +\mathstrut 58q^{83} \) \(\mathstrut +\mathstrut 48q^{84} \) \(\mathstrut +\mathstrut 83q^{85} \) \(\mathstrut +\mathstrut 78q^{86} \) \(\mathstrut +\mathstrut 21q^{87} \) \(\mathstrut +\mathstrut 70q^{88} \) \(\mathstrut +\mathstrut 99q^{89} \) \(\mathstrut +\mathstrut 37q^{90} \) \(\mathstrut +\mathstrut 53q^{91} \) \(\mathstrut +\mathstrut 77q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut +\mathstrut 59q^{94} \) \(\mathstrut +\mathstrut 92q^{95} \) \(\mathstrut +\mathstrut 22q^{96} \) \(\mathstrut +\mathstrut 16q^{97} \) \(\mathstrut +\mathstrut 103q^{98} \) \(\mathstrut +\mathstrut 150q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.16888 1.00000 −3.03965 −3.16888 −1.28246 1.00000 7.04180 −3.03965
1.2 1.00000 −3.12886 1.00000 −3.66535 −3.12886 −1.84514 1.00000 6.78979 −3.66535
1.3 1.00000 −3.10448 1.00000 0.173688 −3.10448 1.24358 1.00000 6.63780 0.173688
1.4 1.00000 −3.04316 1.00000 −0.962647 −3.04316 −3.42904 1.00000 6.26085 −0.962647
1.5 1.00000 −2.99129 1.00000 3.54646 −2.99129 3.26038 1.00000 5.94783 3.54646
1.6 1.00000 −2.86657 1.00000 1.56518 −2.86657 1.43265 1.00000 5.21723 1.56518
1.7 1.00000 −2.85388 1.00000 2.67388 −2.85388 −3.36481 1.00000 5.14465 2.67388
1.8 1.00000 −2.73672 1.00000 0.860575 −2.73672 1.51345 1.00000 4.48964 0.860575
1.9 1.00000 −2.70222 1.00000 −2.93383 −2.70222 0.0783633 1.00000 4.30198 −2.93383
1.10 1.00000 −2.54334 1.00000 −2.99370 −2.54334 4.07188 1.00000 3.46859 −2.99370
1.11 1.00000 −2.45668 1.00000 −0.657543 −2.45668 4.85111 1.00000 3.03526 −0.657543
1.12 1.00000 −2.35449 1.00000 0.804852 −2.35449 −4.41664 1.00000 2.54362 0.804852
1.13 1.00000 −2.31166 1.00000 3.57384 −2.31166 5.01483 1.00000 2.34377 3.57384
1.14 1.00000 −2.26140 1.00000 −1.73870 −2.26140 −2.77914 1.00000 2.11392 −1.73870
1.15 1.00000 −2.06866 1.00000 −2.92371 −2.06866 1.17237 1.00000 1.27934 −2.92371
1.16 1.00000 −1.99037 1.00000 3.42776 −1.99037 −3.66396 1.00000 0.961556 3.42776
1.17 1.00000 −1.96788 1.00000 −0.993306 −1.96788 −1.68889 1.00000 0.872539 −0.993306
1.18 1.00000 −1.89544 1.00000 2.04321 −1.89544 2.48866 1.00000 0.592677 2.04321
1.19 1.00000 −1.85163 1.00000 2.24102 −1.85163 −0.974679 1.00000 0.428551 2.24102
1.20 1.00000 −1.79579 1.00000 2.85204 −1.79579 0.325395 1.00000 0.224869 2.85204
See all 88 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.88
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 \(T_{3}^{88} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8014))\).