Properties

Label 8021.2.a.a
Level 8021
Weight 2
Character orbit 8021.a
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

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Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
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.

\(\operatorname{Tr}(f)(q) = \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 53q^{12} \) \(\mathstrut +\mathstrut 134q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 87q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 52q^{22} \) \(\mathstrut -\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 117q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 21q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 86q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 54q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 57q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 148q^{55} \) \(\mathstrut -\mathstrut 47q^{56} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 64q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut -\mathstrut 58q^{63} \) \(\mathstrut -\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 110q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 150q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 228q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 77q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 62q^{92} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 87q^{94} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 193q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.76381 −0.591714 5.63866 2.62273 1.63539 1.07036 −10.0566 −2.64987 −7.24873
1.2 −2.68511 2.15795 5.20984 −0.637263 −5.79434 0.252834 −8.61877 1.65675 1.71112
1.3 −2.59685 −2.33995 4.74363 −3.06624 6.07651 0.887424 −7.12481 2.47538 7.96257
1.4 −2.56606 0.368471 4.58465 3.51803 −0.945517 1.16169 −6.63237 −2.86423 −9.02747
1.5 −2.56319 1.05402 4.56992 0.0841128 −2.70164 2.43328 −6.58720 −1.88905 −0.215597
1.6 −2.55271 −2.07589 4.51632 1.36107 5.29914 −3.73550 −6.42344 1.30931 −3.47441
1.7 −2.51883 −2.43350 4.34452 −0.221192 6.12959 −1.84924 −5.90546 2.92194 0.557145
1.8 −2.48492 −2.97194 4.17482 3.21951 7.38503 2.90175 −5.40425 5.83242 −8.00022
1.9 −2.48308 1.22996 4.16571 3.96003 −3.05409 −1.52214 −5.37763 −1.48721 −9.83308
1.10 −2.45973 −2.31536 4.05029 −2.20524 5.69516 −0.890619 −5.04316 2.36088 5.42429
1.11 −2.38388 0.0725376 3.68286 −3.05924 −0.172921 −4.27004 −4.01173 −2.99474 7.29285
1.12 −2.37815 2.24175 3.65561 2.50193 −5.33123 −3.50735 −3.93730 2.02545 −5.94998
1.13 −2.36088 0.842254 3.57377 −1.49212 −1.98846 −1.11078 −3.71549 −2.29061 3.52272
1.14 −2.34085 2.34194 3.47957 −2.42598 −5.48214 1.51832 −3.46345 2.48470 5.67886
1.15 −2.26323 2.87488 3.12222 0.727126 −6.50652 0.231070 −2.53984 5.26494 −1.64565
1.16 −2.25892 1.96923 3.10273 −2.33615 −4.44833 −1.78149 −2.49097 0.877859 5.27718
1.17 −2.22845 −2.09787 2.96601 −1.11575 4.67502 −1.94623 −2.15271 1.40108 2.48640
1.18 −2.20714 −0.230793 2.87148 −0.451913 0.509393 5.18852 −1.92347 −2.94673 0.997437
1.19 −2.13613 −0.639809 2.56307 0.116719 1.36672 −4.16794 −1.20279 −2.59064 −0.249327
1.20 −2.09018 −2.33308 2.36887 1.26900 4.87656 3.93400 −0.771000 2.44324 −2.65245
See next 80 embeddings (of 134 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.134
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(13\) \(-1\)
\(617\) \(-1\)