Properties

Label 8043.2.a.o
Level 8043
Weight 2
Character orbit 8043.a
Self dual Yes
Analytic conductor 64.224
Analytic rank 1
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: \(1\)
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.

\(\operatorname{Tr}(f)(q) = \) \(41q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 41q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 41q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 41q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(41q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 41q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 41q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 41q^{9} \) \(\mathstrut -\mathstrut 18q^{10} \) \(\mathstrut -\mathstrut 17q^{11} \) \(\mathstrut -\mathstrut 34q^{12} \) \(\mathstrut -\mathstrut 38q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 4q^{18} \) \(\mathstrut -\mathstrut 15q^{19} \) \(\mathstrut +\mathstrut 23q^{20} \) \(\mathstrut -\mathstrut 41q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 16q^{25} \) \(\mathstrut +\mathstrut 15q^{26} \) \(\mathstrut -\mathstrut 41q^{27} \) \(\mathstrut +\mathstrut 34q^{28} \) \(\mathstrut -\mathstrut 27q^{29} \) \(\mathstrut +\mathstrut 18q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut +\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 9q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 34q^{36} \) \(\mathstrut -\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 38q^{39} \) \(\mathstrut -\mathstrut 52q^{40} \) \(\mathstrut +\mathstrut 29q^{41} \) \(\mathstrut +\mathstrut 4q^{42} \) \(\mathstrut -\mathstrut 47q^{43} \) \(\mathstrut -\mathstrut 20q^{44} \) \(\mathstrut +\mathstrut 5q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut +\mathstrut 26q^{47} \) \(\mathstrut -\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 41q^{49} \) \(\mathstrut -\mathstrut 23q^{50} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 64q^{52} \) \(\mathstrut -\mathstrut 66q^{53} \) \(\mathstrut +\mathstrut 4q^{54} \) \(\mathstrut -\mathstrut 14q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 15q^{57} \) \(\mathstrut -\mathstrut 50q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut -\mathstrut 23q^{60} \) \(\mathstrut -\mathstrut 47q^{61} \) \(\mathstrut +\mathstrut 5q^{62} \) \(\mathstrut +\mathstrut 41q^{63} \) \(\mathstrut -\mathstrut 37q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 31q^{66} \) \(\mathstrut -\mathstrut 73q^{67} \) \(\mathstrut +\mathstrut 10q^{68} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 18q^{70} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut -\mathstrut 15q^{72} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut +\mathstrut 18q^{74} \) \(\mathstrut -\mathstrut 16q^{75} \) \(\mathstrut -\mathstrut 37q^{76} \) \(\mathstrut -\mathstrut 17q^{77} \) \(\mathstrut -\mathstrut 15q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut +\mathstrut 63q^{80} \) \(\mathstrut +\mathstrut 41q^{81} \) \(\mathstrut -\mathstrut 31q^{82} \) \(\mathstrut +\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 34q^{84} \) \(\mathstrut -\mathstrut 82q^{85} \) \(\mathstrut -\mathstrut 39q^{86} \) \(\mathstrut +\mathstrut 27q^{87} \) \(\mathstrut -\mathstrut 132q^{88} \) \(\mathstrut +\mathstrut 17q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 38q^{91} \) \(\mathstrut -\mathstrut 26q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 9q^{94} \) \(\mathstrut -\mathstrut q^{95} \) \(\mathstrut +\mathstrut 24q^{96} \) \(\mathstrut -\mathstrut 73q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 17q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.77034 −1.00000 5.67480 3.96125 2.77034 1.00000 −10.1805 1.00000 −10.9740
1.2 −2.55146 −1.00000 4.50996 0.568399 2.55146 1.00000 −6.40408 1.00000 −1.45025
1.3 −2.48498 −1.00000 4.17514 −2.72732 2.48498 1.00000 −5.40520 1.00000 6.77735
1.4 −2.47042 −1.00000 4.10295 −0.537322 2.47042 1.00000 −5.19517 1.00000 1.32741
1.5 −2.38443 −1.00000 3.68550 2.70331 2.38443 1.00000 −4.01897 1.00000 −6.44585
1.6 −2.34884 −1.00000 3.51704 1.78966 2.34884 1.00000 −3.56329 1.00000 −4.20363
1.7 −2.07017 −1.00000 2.28561 2.60848 2.07017 1.00000 −0.591253 1.00000 −5.40001
1.8 −1.93313 −1.00000 1.73699 −1.84501 1.93313 1.00000 0.508439 1.00000 3.56663
1.9 −1.86200 −1.00000 1.46705 0.268615 1.86200 1.00000 0.992360 1.00000 −0.500162
1.10 −1.81957 −1.00000 1.31084 0.0545380 1.81957 1.00000 1.25397 1.00000 −0.0992358
1.11 −1.72607 −1.00000 0.979322 −3.72360 1.72607 1.00000 1.76176 1.00000 6.42720
1.12 −1.36181 −1.00000 −0.145472 2.48570 1.36181 1.00000 2.92173 1.00000 −3.38505
1.13 −1.34769 −1.00000 −0.183736 1.68166 1.34769 1.00000 2.94300 1.00000 −2.26635
1.14 −1.32430 −1.00000 −0.246218 −1.21552 1.32430 1.00000 2.97468 1.00000 1.60972
1.15 −0.980315 −1.00000 −1.03898 −1.72725 0.980315 1.00000 2.97916 1.00000 1.69325
1.16 −0.973977 −1.00000 −1.05137 4.11702 0.973977 1.00000 2.97196 1.00000 −4.00988
1.17 −0.605577 −1.00000 −1.63328 2.30178 0.605577 1.00000 2.20023 1.00000 −1.39391
1.18 −0.555636 −1.00000 −1.69127 −1.46250 0.555636 1.00000 2.05100 1.00000 0.812618
1.19 −0.426737 −1.00000 −1.81790 −3.28382 0.426737 1.00000 1.62924 1.00000 1.40133
1.20 −0.386440 −1.00000 −1.85066 −2.37424 0.386440 1.00000 1.48805 1.00000 0.917500
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8043))\):

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