Properties

Label 8043.2.a.p
Level 8043
Weight 2
Character orbit 8043.a
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 41
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(41\)
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.

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

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 −2.57226 1.00000 4.61651 −1.43347 −2.57226 −1.00000 −6.73035 1.00000 3.68726
1.2 −2.55869 1.00000 4.54691 3.93576 −2.55869 −1.00000 −6.51676 1.00000 −10.0704
1.3 −2.49955 1.00000 4.24777 0.613091 −2.49955 −1.00000 −5.61841 1.00000 −1.53245
1.4 −2.47532 1.00000 4.12722 0.0852785 −2.47532 −1.00000 −5.26555 1.00000 −0.211092
1.5 −2.19335 1.00000 2.81079 2.36378 −2.19335 −1.00000 −1.77834 1.00000 −5.18459
1.6 −2.12488 1.00000 2.51510 −3.15534 −2.12488 −1.00000 −1.09452 1.00000 6.70470
1.7 −1.94758 1.00000 1.79306 −3.71036 −1.94758 −1.00000 0.403025 1.00000 7.22621
1.8 −1.89059 1.00000 1.57433 4.31318 −1.89059 −1.00000 0.804769 1.00000 −8.15444
1.9 −1.69372 1.00000 0.868693 0.0642137 −1.69372 −1.00000 1.91612 1.00000 −0.108760
1.10 −1.63354 1.00000 0.668453 0.761062 −1.63354 −1.00000 2.17513 1.00000 −1.24323
1.11 −1.54858 1.00000 0.398108 −1.62644 −1.54858 −1.00000 2.48066 1.00000 2.51868
1.12 −1.37206 1.00000 −0.117446 2.69535 −1.37206 −1.00000 2.90527 1.00000 −3.69819
1.13 −1.27831 1.00000 −0.365914 2.18195 −1.27831 −1.00000 3.02438 1.00000 −2.78922
1.14 −1.15673 1.00000 −0.661981 0.288867 −1.15673 −1.00000 3.07919 1.00000 −0.334140
1.15 −0.551667 1.00000 −1.69566 −2.77566 −0.551667 −1.00000 2.03878 1.00000 1.53124
1.16 −0.546836 1.00000 −1.70097 −3.64117 −0.546836 −1.00000 2.02382 1.00000 1.99112
1.17 −0.306328 1.00000 −1.90616 −2.43700 −0.306328 −1.00000 1.19657 1.00000 0.746523
1.18 −0.216725 1.00000 −1.95303 3.49022 −0.216725 −1.00000 0.856722 1.00000 −0.756418
1.19 −0.0276074 1.00000 −1.99924 0.000693755 0 −0.0276074 −1.00000 0.110409 1.00000 −1.91528e−5 0
1.20 0.415908 1.00000 −1.82702 −0.732616 0.415908 −1.00000 −1.59169 1.00000 −0.304701
See all 41 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.41
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(7\) \(1\)
\(383\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8043))\):

\(T_{2}^{41} - \cdots\)
\(T_{5}^{41} - \cdots\)
\(T_{11}^{41} - \cdots\)