Properties

Label 8017.2.a.b
Level 8017
Weight 2
Character orbit 8017.a
Self dual Yes
Analytic conductor 64.016
Analytic rank 0
Dimension 340
CM No

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Newspace parameters

Level: \( N \) = \( 8017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0160673005\)
Analytic rank: \(0\)
Dimension: \(340\)
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.

\(\operatorname{Tr}(f)(q) = \) \(340q \) \(\mathstrut +\mathstrut 20q^{2} \) \(\mathstrut +\mathstrut 44q^{3} \) \(\mathstrut +\mathstrut 350q^{4} \) \(\mathstrut +\mathstrut 53q^{5} \) \(\mathstrut +\mathstrut 34q^{6} \) \(\mathstrut +\mathstrut 81q^{7} \) \(\mathstrut +\mathstrut 54q^{8} \) \(\mathstrut +\mathstrut 360q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(340q \) \(\mathstrut +\mathstrut 20q^{2} \) \(\mathstrut +\mathstrut 44q^{3} \) \(\mathstrut +\mathstrut 350q^{4} \) \(\mathstrut +\mathstrut 53q^{5} \) \(\mathstrut +\mathstrut 34q^{6} \) \(\mathstrut +\mathstrut 81q^{7} \) \(\mathstrut +\mathstrut 54q^{8} \) \(\mathstrut +\mathstrut 360q^{9} \) \(\mathstrut +\mathstrut 36q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 92q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut +\mathstrut 44q^{14} \) \(\mathstrut +\mathstrut 71q^{15} \) \(\mathstrut +\mathstrut 362q^{16} \) \(\mathstrut +\mathstrut 162q^{17} \) \(\mathstrut +\mathstrut 41q^{18} \) \(\mathstrut +\mathstrut 49q^{19} \) \(\mathstrut +\mathstrut 147q^{20} \) \(\mathstrut +\mathstrut 41q^{21} \) \(\mathstrut +\mathstrut 32q^{22} \) \(\mathstrut +\mathstrut 244q^{23} \) \(\mathstrut +\mathstrut 85q^{24} \) \(\mathstrut +\mathstrut 355q^{25} \) \(\mathstrut +\mathstrut 83q^{26} \) \(\mathstrut +\mathstrut 155q^{27} \) \(\mathstrut +\mathstrut 129q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 51q^{30} \) \(\mathstrut +\mathstrut 65q^{31} \) \(\mathstrut +\mathstrut 113q^{32} \) \(\mathstrut +\mathstrut 73q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 200q^{35} \) \(\mathstrut +\mathstrut 380q^{36} \) \(\mathstrut +\mathstrut 28q^{37} \) \(\mathstrut +\mathstrut 171q^{38} \) \(\mathstrut +\mathstrut 117q^{39} \) \(\mathstrut +\mathstrut 95q^{40} \) \(\mathstrut +\mathstrut 115q^{41} \) \(\mathstrut +\mathstrut 42q^{42} \) \(\mathstrut +\mathstrut 98q^{43} \) \(\mathstrut +\mathstrut 139q^{44} \) \(\mathstrut +\mathstrut 127q^{45} \) \(\mathstrut +\mathstrut 29q^{46} \) \(\mathstrut +\mathstrut 312q^{47} \) \(\mathstrut +\mathstrut 168q^{48} \) \(\mathstrut +\mathstrut 365q^{49} \) \(\mathstrut +\mathstrut 64q^{50} \) \(\mathstrut +\mathstrut 72q^{51} \) \(\mathstrut +\mathstrut 100q^{52} \) \(\mathstrut +\mathstrut 154q^{53} \) \(\mathstrut +\mathstrut 89q^{54} \) \(\mathstrut +\mathstrut 161q^{55} \) \(\mathstrut +\mathstrut 89q^{56} \) \(\mathstrut +\mathstrut 82q^{57} \) \(\mathstrut +\mathstrut 29q^{58} \) \(\mathstrut +\mathstrut 149q^{59} \) \(\mathstrut +\mathstrut 93q^{60} \) \(\mathstrut +\mathstrut 70q^{61} \) \(\mathstrut +\mathstrut 257q^{62} \) \(\mathstrut +\mathstrut 376q^{63} \) \(\mathstrut +\mathstrut 346q^{64} \) \(\mathstrut +\mathstrut 125q^{65} \) \(\mathstrut +\mathstrut 48q^{66} \) \(\mathstrut +\mathstrut 65q^{67} \) \(\mathstrut +\mathstrut 464q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut -\mathstrut 54q^{70} \) \(\mathstrut +\mathstrut 216q^{71} \) \(\mathstrut +\mathstrut 90q^{72} \) \(\mathstrut +\mathstrut 93q^{73} \) \(\mathstrut +\mathstrut 147q^{74} \) \(\mathstrut +\mathstrut 162q^{75} \) \(\mathstrut +\mathstrut 64q^{76} \) \(\mathstrut +\mathstrut 190q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 139q^{79} \) \(\mathstrut +\mathstrut 274q^{80} \) \(\mathstrut +\mathstrut 376q^{81} \) \(\mathstrut +\mathstrut 59q^{82} \) \(\mathstrut +\mathstrut 402q^{83} \) \(\mathstrut +\mathstrut 10q^{84} \) \(\mathstrut +\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 53q^{86} \) \(\mathstrut +\mathstrut 364q^{87} \) \(\mathstrut +\mathstrut 42q^{88} \) \(\mathstrut +\mathstrut 114q^{89} \) \(\mathstrut +\mathstrut 126q^{90} \) \(\mathstrut +\mathstrut 43q^{91} \) \(\mathstrut +\mathstrut 422q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 347q^{95} \) \(\mathstrut +\mathstrut 146q^{96} \) \(\mathstrut +\mathstrut 47q^{97} \) \(\mathstrut +\mathstrut 96q^{98} \) \(\mathstrut +\mathstrut 129q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.82489 2.49518 5.98003 3.36028 −7.04861 4.80660 −11.2432 3.22590 −9.49245
1.2 −2.81482 0.685798 5.92319 0.844371 −1.93040 −4.31326 −11.0431 −2.52968 −2.37675
1.3 −2.75702 −3.03076 5.60115 −1.17209 8.35587 3.32948 −9.92845 6.18552 3.23147
1.4 −2.75627 0.354012 5.59704 −0.448330 −0.975755 −0.00120082 −9.91443 −2.87468 1.23572
1.5 −2.72150 1.69330 5.40656 −4.24685 −4.60831 −1.07458 −9.27094 −0.132735 11.5578
1.6 −2.70245 −0.906232 5.30323 2.51115 2.44905 2.28815 −8.92682 −2.17874 −6.78625
1.7 −2.68673 2.91370 5.21852 −0.199710 −7.82834 −2.77102 −8.64730 5.48967 0.536568
1.8 −2.67670 −1.97751 5.16470 −3.95415 5.29320 −4.51333 −8.47093 0.910563 10.5841
1.9 −2.67123 −2.04696 5.13545 2.79534 5.46788 −0.784684 −8.37550 1.19003 −7.46698
1.10 −2.65743 −2.52364 5.06196 4.19446 6.70640 4.50856 −8.13696 3.36874 −11.1465
1.11 −2.64379 0.908830 4.98964 −0.356677 −2.40276 −1.07237 −7.90399 −2.17403 0.942979
1.12 −2.62968 −1.21671 4.91523 1.08723 3.19957 0.844404 −7.66614 −1.51960 −2.85908
1.13 −2.61837 −0.666893 4.85585 −0.00270488 1.74617 0.156538 −7.47768 −2.55525 0.00708236
1.14 −2.61686 2.24685 4.84797 1.56834 −5.87971 3.28305 −7.45273 2.04835 −4.10414
1.15 −2.60921 3.19659 4.80800 −1.37562 −8.34060 −1.63991 −7.32666 7.21821 3.58928
1.16 −2.60414 2.31571 4.78154 3.50289 −6.03042 −2.38601 −7.24351 2.36250 −9.12202
1.17 −2.59088 −0.557344 4.71265 −1.39623 1.44401 −3.59677 −7.02815 −2.68937 3.61746
1.18 −2.56223 −1.92311 4.56505 0.295481 4.92747 2.92407 −6.57225 0.698367 −0.757092
1.19 −2.52841 −2.54349 4.39287 2.51878 6.43098 −1.43237 −6.05015 3.46932 −6.36851
1.20 −2.50135 −2.46945 4.25678 1.14683 6.17696 −1.51997 −5.64500 3.09817 −2.86862
See next 80 embeddings (of 340 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.340
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(8017\) \(-1\)