Properties

Label 8043.2.a.t
Level 8043
Weight 2
Character orbit 8043.a
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
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: \(52\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 52q + 3q^{2} - 52q^{3} + 61q^{4} - 7q^{5} - 3q^{6} + 52q^{7} + 24q^{8} + 52q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 52q + 3q^{2} - 52q^{3} + 61q^{4} - 7q^{5} - 3q^{6} + 52q^{7} + 24q^{8} + 52q^{9} - 2q^{10} + 9q^{11} - 61q^{12} + 44q^{13} + 3q^{14} + 7q^{15} + 95q^{16} - 6q^{17} + 3q^{18} + 7q^{19} - 21q^{20} - 52q^{21} + 19q^{22} - 4q^{23} - 24q^{24} + 83q^{25} - 5q^{26} - 52q^{27} + 61q^{28} + 31q^{29} + 2q^{30} + 11q^{31} + 71q^{32} - 9q^{33} + 17q^{34} - 7q^{35} + 61q^{36} + 71q^{37} - 8q^{38} - 44q^{39} + 20q^{40} - 25q^{41} - 3q^{42} + 75q^{43} + 14q^{44} - 7q^{45} + 36q^{46} - 20q^{47} - 95q^{48} + 52q^{49} + 26q^{50} + 6q^{51} + 88q^{52} + 70q^{53} - 3q^{54} + 12q^{55} + 24q^{56} - 7q^{57} + 48q^{58} - 27q^{59} + 21q^{60} + 59q^{61} - 23q^{62} + 52q^{63} + 138q^{64} + 44q^{65} - 19q^{66} + 65q^{67} - 8q^{68} + 4q^{69} - 2q^{70} - 11q^{71} + 24q^{72} + 34q^{73} + 38q^{74} - 83q^{75} + 31q^{76} + 9q^{77} + 5q^{78} + 74q^{79} - 5q^{80} + 52q^{81} + 51q^{82} - 30q^{83} - 61q^{84} + 70q^{85} + 29q^{86} - 31q^{87} + 90q^{88} - q^{89} - 2q^{90} + 44q^{91} + 34q^{92} - 11q^{93} + 27q^{94} + 9q^{95} - 71q^{96} + 73q^{97} + 3q^{98} + 9q^{99} + O(q^{100}) \)

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 −2.75477 −1.00000 5.58878 −0.0622071 2.75477 1.00000 −9.88627 1.00000 0.171367
1.2 −2.71076 −1.00000 5.34821 0.130231 2.71076 1.00000 −9.07620 1.00000 −0.353025
1.3 −2.56328 −1.00000 4.57042 −4.02293 2.56328 1.00000 −6.58873 1.00000 10.3119
1.4 −2.55848 −1.00000 4.54580 3.55238 2.55848 1.00000 −6.51338 1.00000 −9.08869
1.5 −2.45692 −1.00000 4.03647 −2.79922 2.45692 1.00000 −5.00345 1.00000 6.87748
1.6 −2.35415 −1.00000 3.54201 −1.85354 2.35415 1.00000 −3.63012 1.00000 4.36349
1.7 −2.28128 −1.00000 3.20426 2.19375 2.28128 1.00000 −2.74725 1.00000 −5.00457
1.8 −1.95494 −1.00000 1.82179 −1.46647 1.95494 1.00000 0.348396 1.00000 2.86686
1.9 −1.95089 −1.00000 1.80596 3.26605 1.95089 1.00000 0.378554 1.00000 −6.37169
1.10 −1.90192 −1.00000 1.61732 0.767188 1.90192 1.00000 0.727834 1.00000 −1.45913
1.11 −1.85290 −1.00000 1.43325 −3.21014 1.85290 1.00000 1.05014 1.00000 5.94808
1.12 −1.77779 −1.00000 1.16053 3.56820 1.77779 1.00000 1.49240 1.00000 −6.34350
1.13 −1.64173 −1.00000 0.695293 0.237832 1.64173 1.00000 2.14198 1.00000 −0.390457
1.14 −1.61741 −1.00000 0.616031 −3.81830 1.61741 1.00000 2.23845 1.00000 6.17577
1.15 −1.58348 −1.00000 0.507395 −2.03406 1.58348 1.00000 2.36350 1.00000 3.22089
1.16 −1.33568 −1.00000 −0.215968 1.69750 1.33568 1.00000 2.95982 1.00000 −2.26731
1.17 −1.10272 −1.00000 −0.784010 0.760743 1.10272 1.00000 3.06998 1.00000 −0.838886
1.18 −0.890431 −1.00000 −1.20713 −2.94587 0.890431 1.00000 2.85573 1.00000 2.62309
1.19 −0.869058 −1.00000 −1.24474 −3.05181 0.869058 1.00000 2.81987 1.00000 2.65220
1.20 −0.837626 −1.00000 −1.29838 2.34855 0.837626 1.00000 2.76281 1.00000 −1.96721
See all 52 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.52
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8043))\):

\(T_{2}^{52} - \cdots\)
\(T_{5}^{52} + \cdots\)
\(T_{11}^{52} - \cdots\)