Properties

Label 8017.2.a.a
Level 8017
Weight 2
Character orbit 8017.a
Self dual Yes
Analytic conductor 64.016
Analytic rank 1
Dimension 327
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: \(1\)
Dimension: \(327\)
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.

\(\operatorname{Tr}(f)(q) = \) \(327q \) \(\mathstrut -\mathstrut 23q^{2} \) \(\mathstrut -\mathstrut 48q^{3} \) \(\mathstrut +\mathstrut 315q^{4} \) \(\mathstrut -\mathstrut 55q^{5} \) \(\mathstrut -\mathstrut 38q^{6} \) \(\mathstrut -\mathstrut 87q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 303q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(327q \) \(\mathstrut -\mathstrut 23q^{2} \) \(\mathstrut -\mathstrut 48q^{3} \) \(\mathstrut +\mathstrut 315q^{4} \) \(\mathstrut -\mathstrut 55q^{5} \) \(\mathstrut -\mathstrut 38q^{6} \) \(\mathstrut -\mathstrut 87q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 303q^{9} \) \(\mathstrut -\mathstrut 48q^{10} \) \(\mathstrut -\mathstrut 70q^{11} \) \(\mathstrut -\mathstrut 120q^{12} \) \(\mathstrut -\mathstrut 53q^{13} \) \(\mathstrut -\mathstrut 52q^{14} \) \(\mathstrut -\mathstrut 77q^{15} \) \(\mathstrut +\mathstrut 295q^{16} \) \(\mathstrut -\mathstrut 164q^{17} \) \(\mathstrut -\mathstrut 58q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 153q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 68q^{22} \) \(\mathstrut -\mathstrut 256q^{23} \) \(\mathstrut -\mathstrut 107q^{24} \) \(\mathstrut +\mathstrut 288q^{25} \) \(\mathstrut -\mathstrut 95q^{26} \) \(\mathstrut -\mathstrut 189q^{27} \) \(\mathstrut -\mathstrut 167q^{28} \) \(\mathstrut -\mathstrut 99q^{29} \) \(\mathstrut -\mathstrut 81q^{30} \) \(\mathstrut -\mathstrut 71q^{31} \) \(\mathstrut -\mathstrut 146q^{32} \) \(\mathstrut -\mathstrut 95q^{33} \) \(\mathstrut -\mathstrut 40q^{34} \) \(\mathstrut -\mathstrut 192q^{35} \) \(\mathstrut +\mathstrut 261q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 179q^{38} \) \(\mathstrut -\mathstrut 115q^{39} \) \(\mathstrut -\mathstrut 121q^{40} \) \(\mathstrut -\mathstrut 111q^{41} \) \(\mathstrut -\mathstrut 62q^{42} \) \(\mathstrut -\mathstrut 110q^{43} \) \(\mathstrut -\mathstrut 157q^{44} \) \(\mathstrut -\mathstrut 137q^{45} \) \(\mathstrut -\mathstrut 11q^{46} \) \(\mathstrut -\mathstrut 324q^{47} \) \(\mathstrut -\mathstrut 236q^{48} \) \(\mathstrut +\mathstrut 296q^{49} \) \(\mathstrut -\mathstrut 73q^{50} \) \(\mathstrut -\mathstrut 88q^{51} \) \(\mathstrut -\mathstrut 138q^{52} \) \(\mathstrut -\mathstrut 170q^{53} \) \(\mathstrut -\mathstrut 127q^{54} \) \(\mathstrut -\mathstrut 151q^{55} \) \(\mathstrut -\mathstrut 151q^{56} \) \(\mathstrut -\mathstrut 106q^{57} \) \(\mathstrut -\mathstrut 81q^{58} \) \(\mathstrut -\mathstrut 123q^{59} \) \(\mathstrut -\mathstrut 83q^{60} \) \(\mathstrut -\mathstrut 62q^{61} \) \(\mathstrut -\mathstrut 287q^{62} \) \(\mathstrut -\mathstrut 400q^{63} \) \(\mathstrut +\mathstrut 263q^{64} \) \(\mathstrut -\mathstrut 143q^{65} \) \(\mathstrut -\mathstrut 64q^{66} \) \(\mathstrut -\mathstrut 95q^{67} \) \(\mathstrut -\mathstrut 442q^{68} \) \(\mathstrut -\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut 26q^{70} \) \(\mathstrut -\mathstrut 210q^{71} \) \(\mathstrut -\mathstrut 129q^{72} \) \(\mathstrut -\mathstrut 121q^{73} \) \(\mathstrut -\mathstrut 159q^{74} \) \(\mathstrut -\mathstrut 194q^{75} \) \(\mathstrut -\mathstrut 86q^{76} \) \(\mathstrut -\mathstrut 178q^{77} \) \(\mathstrut -\mathstrut 68q^{78} \) \(\mathstrut -\mathstrut 145q^{79} \) \(\mathstrut -\mathstrut 338q^{80} \) \(\mathstrut +\mathstrut 259q^{81} \) \(\mathstrut -\mathstrut 103q^{82} \) \(\mathstrut -\mathstrut 418q^{83} \) \(\mathstrut -\mathstrut 102q^{84} \) \(\mathstrut -\mathstrut 40q^{85} \) \(\mathstrut -\mathstrut 89q^{86} \) \(\mathstrut -\mathstrut 372q^{87} \) \(\mathstrut -\mathstrut 186q^{88} \) \(\mathstrut -\mathstrut 100q^{89} \) \(\mathstrut -\mathstrut 150q^{90} \) \(\mathstrut -\mathstrut 69q^{91} \) \(\mathstrut -\mathstrut 458q^{92} \) \(\mathstrut -\mathstrut 81q^{93} \) \(\mathstrut -\mathstrut 46q^{94} \) \(\mathstrut -\mathstrut 377q^{95} \) \(\mathstrut -\mathstrut 190q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut -\mathstrut 147q^{98} \) \(\mathstrut -\mathstrut 171q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.79695 −1.72914 5.82292 −0.405996 4.83631 −2.26625 −10.6925 −0.0100790 1.13555
1.2 −2.79413 −2.90420 5.80714 −2.69949 8.11470 −0.505392 −10.6376 5.43438 7.54271
1.3 −2.77418 0.313969 5.69607 4.29926 −0.871005 −0.431093 −10.2536 −2.90142 −11.9269
1.4 −2.76749 2.84439 5.65899 −0.717749 −7.87182 −1.28590 −10.1262 5.09057 1.98636
1.5 −2.76002 −0.752350 5.61769 −2.62302 2.07650 4.59409 −9.98488 −2.43397 7.23958
1.6 −2.74897 0.108150 5.55686 1.28185 −0.297303 2.70833 −9.77771 −2.98830 −3.52377
1.7 −2.74759 −3.21743 5.54926 2.43668 8.84019 −3.59070 −9.75191 7.35187 −6.69501
1.8 −2.73986 −0.187585 5.50685 −3.57442 0.513957 1.37739 −9.60828 −2.96481 9.79342
1.9 −2.73007 2.35314 5.45331 −1.11386 −6.42426 −0.749989 −9.42779 2.53728 3.04092
1.10 −2.72447 0.869183 5.42273 2.47434 −2.36806 −1.68212 −9.32512 −2.24452 −6.74127
1.11 −2.72133 1.64758 5.40564 −2.87444 −4.48362 −4.41970 −9.26787 −0.285473 7.82231
1.12 −2.70756 −2.54523 5.33088 0.896657 6.89137 3.68403 −9.01856 3.47821 −2.42775
1.13 −2.67797 1.71362 5.17153 −1.95790 −4.58901 3.43960 −8.49326 −0.0635223 5.24319
1.14 −2.67394 −1.93873 5.14997 −1.50753 5.18405 −1.18909 −8.42282 0.758668 4.03106
1.15 −2.65464 2.85639 5.04709 2.05834 −7.58268 0.740875 −8.08892 5.15896 −5.46413
1.16 −2.60838 2.59159 4.80367 −3.67050 −6.75986 1.01472 −7.31304 3.71634 9.57408
1.17 −2.59947 −1.49239 4.75723 4.02767 3.87942 −3.51002 −7.16732 −0.772773 −10.4698
1.18 −2.59616 −1.46619 4.74007 −0.558786 3.80647 −4.63820 −7.11368 −0.850285 1.45070
1.19 −2.58656 2.73680 4.69031 2.52723 −7.07890 −4.80679 −6.95866 4.49006 −6.53684
1.20 −2.58337 1.72136 4.67379 0.176863 −4.44690 3.62607 −6.90738 −0.0369272 −0.456901
See next 80 embeddings (of 327 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.327
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

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