Properties

Label 8041.2.a.i
Level 8041
Weight 2
Character orbit 8041.a
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(78\)
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.

\(\operatorname{Tr}(f)(q) = \) \(78q \) \(\mathstrut +\mathstrut 7q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 91q^{4} \) \(\mathstrut +\mathstrut 17q^{5} \) \(\mathstrut +\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 102q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(78q \) \(\mathstrut +\mathstrut 7q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 91q^{4} \) \(\mathstrut +\mathstrut 17q^{5} \) \(\mathstrut +\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 102q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut +\mathstrut 78q^{11} \) \(\mathstrut +\mathstrut 31q^{12} \) \(\mathstrut -\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 31q^{14} \) \(\mathstrut +\mathstrut 38q^{15} \) \(\mathstrut +\mathstrut 121q^{16} \) \(\mathstrut -\mathstrut 78q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 51q^{20} \) \(\mathstrut +\mathstrut 6q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 48q^{23} \) \(\mathstrut +\mathstrut 11q^{24} \) \(\mathstrut +\mathstrut 101q^{25} \) \(\mathstrut +\mathstrut 18q^{26} \) \(\mathstrut +\mathstrut 46q^{27} \) \(\mathstrut +\mathstrut 27q^{28} \) \(\mathstrut +\mathstrut 22q^{29} \) \(\mathstrut +\mathstrut 14q^{30} \) \(\mathstrut +\mathstrut 56q^{31} \) \(\mathstrut +\mathstrut 83q^{32} \) \(\mathstrut +\mathstrut 10q^{33} \) \(\mathstrut -\mathstrut 7q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 139q^{36} \) \(\mathstrut +\mathstrut 53q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut +\mathstrut 79q^{39} \) \(\mathstrut -\mathstrut q^{40} \) \(\mathstrut +\mathstrut 23q^{41} \) \(\mathstrut +\mathstrut 17q^{42} \) \(\mathstrut -\mathstrut 78q^{43} \) \(\mathstrut +\mathstrut 91q^{44} \) \(\mathstrut +\mathstrut 76q^{45} \) \(\mathstrut +\mathstrut 21q^{46} \) \(\mathstrut +\mathstrut 57q^{47} \) \(\mathstrut +\mathstrut 78q^{48} \) \(\mathstrut +\mathstrut 115q^{49} \) \(\mathstrut +\mathstrut 58q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 63q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut +\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 111q^{56} \) \(\mathstrut -\mathstrut 11q^{57} \) \(\mathstrut +\mathstrut 36q^{58} \) \(\mathstrut +\mathstrut 71q^{59} \) \(\mathstrut +\mathstrut 36q^{60} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 5q^{62} \) \(\mathstrut +\mathstrut 71q^{63} \) \(\mathstrut +\mathstrut 183q^{64} \) \(\mathstrut +\mathstrut 47q^{65} \) \(\mathstrut +\mathstrut 12q^{66} \) \(\mathstrut +\mathstrut 11q^{67} \) \(\mathstrut -\mathstrut 91q^{68} \) \(\mathstrut +\mathstrut 31q^{69} \) \(\mathstrut +\mathstrut 33q^{70} \) \(\mathstrut +\mathstrut 159q^{71} \) \(\mathstrut +\mathstrut 59q^{72} \) \(\mathstrut +\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut 4q^{74} \) \(\mathstrut +\mathstrut 83q^{75} \) \(\mathstrut -\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 11q^{77} \) \(\mathstrut +\mathstrut 101q^{78} \) \(\mathstrut +\mathstrut 35q^{79} \) \(\mathstrut +\mathstrut 85q^{80} \) \(\mathstrut +\mathstrut 170q^{81} \) \(\mathstrut +\mathstrut 98q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 44q^{84} \) \(\mathstrut -\mathstrut 17q^{85} \) \(\mathstrut -\mathstrut 7q^{86} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 33q^{88} \) \(\mathstrut +\mathstrut 50q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut +\mathstrut 86q^{91} \) \(\mathstrut +\mathstrut 106q^{92} \) \(\mathstrut +\mathstrut 68q^{93} \) \(\mathstrut -\mathstrut q^{94} \) \(\mathstrut +\mathstrut 109q^{95} \) \(\mathstrut -\mathstrut 50q^{96} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut 106q^{98} \) \(\mathstrut +\mathstrut 102q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.81193 3.07426 5.90697 1.69870 −8.64463 0.0326130 −10.9861 6.45110 −4.77662
1.2 −2.68205 1.14586 5.19341 0.981432 −3.07326 −5.03314 −8.56488 −1.68700 −2.63225
1.3 −2.66059 −0.870455 5.07876 −2.53728 2.31593 1.57807 −8.19134 −2.24231 6.75067
1.4 −2.59406 −1.64341 4.72913 −1.77081 4.26309 −2.35395 −7.07951 −0.299219 4.59358
1.5 −2.55392 1.24868 4.52253 4.26646 −3.18904 −0.595052 −6.44234 −1.44079 −10.8962
1.6 −2.53120 −2.76336 4.40698 3.58460 6.99462 −0.727911 −6.09254 4.63616 −9.07334
1.7 −2.36526 −1.70691 3.59444 −0.509718 4.03728 0.312769 −3.77127 −0.0864584 1.20561
1.8 −2.35944 3.36081 3.56697 −2.07702 −7.92965 −0.337523 −3.69718 8.29507 4.90061
1.9 −2.30463 −0.694087 3.31131 3.08057 1.59961 3.70671 −3.02207 −2.51824 −7.09957
1.10 −2.28473 −0.648502 3.22000 −1.19117 1.48165 3.55276 −2.78738 −2.57944 2.72151
1.11 −2.24742 2.50303 3.05092 1.29850 −5.62537 3.89591 −2.36186 3.26514 −2.91829
1.12 −2.05622 −3.10600 2.22804 −2.37865 6.38662 −3.40012 −0.468901 6.64724 4.89103
1.13 −1.93837 −3.28485 1.75726 −1.73342 6.36724 2.63625 0.470510 7.79024 3.36000
1.14 −1.93129 −1.02169 1.72989 3.42042 1.97319 −3.76946 0.521655 −1.95614 −6.60584
1.15 −1.90003 1.99775 1.61013 −3.13238 −3.79579 −0.279659 0.740768 0.990997 5.95163
1.16 −1.80887 0.743622 1.27201 1.40249 −1.34511 −0.305829 1.31684 −2.44703 −2.53691
1.17 −1.73352 2.13034 1.00511 −4.15912 −3.69300 −1.81917 1.72467 1.53836 7.20994
1.18 −1.70714 3.00412 0.914329 2.58179 −5.12845 −2.99512 1.85339 6.02473 −4.40747
1.19 −1.53655 0.0485562 0.360996 −0.584069 −0.0746091 −1.23435 2.51842 −2.99764 0.897453
1.20 −1.52440 −2.61179 0.323806 2.08851 3.98143 2.52784 2.55520 3.82147 −3.18374
See all 78 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.78
Significant digits:
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Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(11\) \(-1\)
\(17\) \(1\)
\(43\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{78} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8041))\).