Properties

Label 5077.2.a.c
Level 5077
Weight 2
Character orbit 5077.a
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

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Newspace parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(40.5400491062\)
Analytic rank: \(0\)
Dimension: \(216\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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 −2.74765 1.79689 5.54960 −1.53731 −4.93723 −2.66154 −9.75307 0.228810 4.22399
1.2 −2.71481 1.77107 5.37017 1.86347 −4.80810 4.83883 −9.14936 0.136673 −5.05896
1.3 −2.71273 −1.56061 5.35892 1.41855 4.23352 −1.24026 −9.11187 −0.564498 −3.84815
1.4 −2.68288 3.14006 5.19783 4.08506 −8.42439 −2.34598 −8.57939 6.85996 −10.9597
1.5 −2.66174 −1.61696 5.08487 2.63611 4.30394 0.680658 −8.21113 −0.385425 −7.01664
1.6 −2.65978 0.381674 5.07442 4.30968 −1.01517 0.973203 −8.17726 −2.85433 −11.4628
1.7 −2.65348 −0.258723 5.04097 −1.45018 0.686516 −0.380682 −8.06916 −2.93306 3.84804
1.8 −2.60586 −2.49081 4.79053 −1.82309 6.49071 1.00898 −7.27175 3.20413 4.75073
1.9 −2.60140 3.18807 4.76730 −0.824320 −8.29345 −1.42597 −7.19885 7.16377 2.14439
1.10 −2.52071 −0.980647 4.35400 −1.18681 2.47193 −1.94632 −5.93376 −2.03833 2.99161
1.11 −2.50572 0.313570 4.27863 0.450260 −0.785719 −2.26718 −5.70960 −2.90167 −1.12823
1.12 −2.49199 1.36067 4.21003 −1.81458 −3.39077 0.512290 −5.50738 −1.14858 4.52191
1.13 −2.48492 −1.01672 4.17484 0.988176 2.52648 3.63719 −5.40431 −1.96628 −2.45554
1.14 −2.46114 2.54758 4.05723 0.498025 −6.26997 −4.84312 −5.06313 3.49018 −1.22571
1.15 −2.46105 −2.68177 4.05676 2.96431 6.59997 0.509421 −5.06178 4.19189 −7.29531
1.16 −2.45990 1.58815 4.05112 −3.55113 −3.90668 −1.72696 −5.04554 −0.477790 8.73542
1.17 −2.43559 3.36410 3.93211 0.698081 −8.19357 2.30447 −4.70583 8.31717 −1.70024
1.18 −2.43502 2.39261 3.92934 2.97521 −5.82606 3.62580 −4.69798 2.72458 −7.24469
1.19 −2.42574 −1.56213 3.88424 2.05918 3.78933 −2.28895 −4.57068 −0.559747 −4.99504
1.20 −2.38830 −1.75089 3.70399 −3.96718 4.18166 −4.47052 −4.06966 0.0656264 9.47483
See next 80 embeddings (of 216 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.216
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(5077\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{216} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5077))\).