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

Related objects

Downloads

Learn more about

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.

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

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 −2.81193 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:
Format:

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8041))\).