Properties

Label 8043.2.a.q
Level 8043
Weight 2
Character orbit 8043.a
Self dual Yes
Analytic conductor 64.224
Analytic rank 1
Dimension 44
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: \(44\)
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.

\(\operatorname{Tr}(f)(q) = \) \(44q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 44q^{3} \) \(\mathstrut +\mathstrut 44q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 44q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 44q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(44q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 44q^{3} \) \(\mathstrut +\mathstrut 44q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 44q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 44q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 44q^{12} \) \(\mathstrut -\mathstrut 34q^{13} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 4q^{18} \) \(\mathstrut -\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 44q^{21} \) \(\mathstrut -\mathstrut 23q^{22} \) \(\mathstrut -\mathstrut 56q^{23} \) \(\mathstrut -\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 32q^{25} \) \(\mathstrut -\mathstrut 17q^{26} \) \(\mathstrut +\mathstrut 44q^{27} \) \(\mathstrut -\mathstrut 44q^{28} \) \(\mathstrut -\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 16q^{30} \) \(\mathstrut -\mathstrut 32q^{31} \) \(\mathstrut -\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 2q^{33} \) \(\mathstrut -\mathstrut 25q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 44q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 50q^{40} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 4q^{42} \) \(\mathstrut -\mathstrut 12q^{43} \) \(\mathstrut -\mathstrut 22q^{44} \) \(\mathstrut -\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 27q^{47} \) \(\mathstrut +\mathstrut 24q^{48} \) \(\mathstrut +\mathstrut 44q^{49} \) \(\mathstrut -\mathstrut 21q^{50} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 82q^{52} \) \(\mathstrut -\mathstrut 114q^{53} \) \(\mathstrut -\mathstrut 4q^{54} \) \(\mathstrut -\mathstrut 29q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut 26q^{58} \) \(\mathstrut -\mathstrut 40q^{59} \) \(\mathstrut -\mathstrut 39q^{60} \) \(\mathstrut -\mathstrut 47q^{61} \) \(\mathstrut -\mathstrut 37q^{62} \) \(\mathstrut -\mathstrut 44q^{63} \) \(\mathstrut -\mathstrut 5q^{64} \) \(\mathstrut -\mathstrut 20q^{65} \) \(\mathstrut -\mathstrut 23q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut -\mathstrut 72q^{68} \) \(\mathstrut -\mathstrut 56q^{69} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 65q^{71} \) \(\mathstrut -\mathstrut 15q^{72} \) \(\mathstrut -\mathstrut 21q^{73} \) \(\mathstrut -\mathstrut 26q^{74} \) \(\mathstrut +\mathstrut 32q^{75} \) \(\mathstrut -\mathstrut 15q^{76} \) \(\mathstrut +\mathstrut 2q^{77} \) \(\mathstrut -\mathstrut 17q^{78} \) \(\mathstrut +\mathstrut 6q^{79} \) \(\mathstrut -\mathstrut 77q^{80} \) \(\mathstrut +\mathstrut 44q^{81} \) \(\mathstrut -\mathstrut 51q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 44q^{84} \) \(\mathstrut -\mathstrut 26q^{85} \) \(\mathstrut -\mathstrut 65q^{86} \) \(\mathstrut -\mathstrut 33q^{87} \) \(\mathstrut -\mathstrut 84q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 16q^{90} \) \(\mathstrut +\mathstrut 34q^{91} \) \(\mathstrut -\mathstrut 140q^{92} \) \(\mathstrut -\mathstrut 32q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 50q^{95} \) \(\mathstrut -\mathstrut 34q^{96} \) \(\mathstrut -\mathstrut 83q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.76678 1.00000 5.65509 −0.763136 −2.76678 −1.00000 −10.1129 1.00000 2.11143
1.2 −2.62597 1.00000 4.89573 −3.97585 −2.62597 −1.00000 −7.60410 1.00000 10.4405
1.3 −2.55412 1.00000 4.52354 −2.76084 −2.55412 −1.00000 −6.44543 1.00000 7.05153
1.4 −2.54621 1.00000 4.48317 3.86614 −2.54621 −1.00000 −6.32268 1.00000 −9.84400
1.5 −2.45063 1.00000 4.00561 2.55159 −2.45063 −1.00000 −4.91502 1.00000 −6.25302
1.6 −2.33621 1.00000 3.45788 0.0158996 −2.33621 −1.00000 −3.40590 1.00000 −0.0371448
1.7 −2.16996 1.00000 2.70871 −0.0283937 −2.16996 −1.00000 −1.53788 1.00000 0.0616131
1.8 −2.14351 1.00000 2.59465 0.772092 −2.14351 −1.00000 −1.27463 1.00000 −1.65499
1.9 −2.03170 1.00000 2.12780 −1.52866 −2.03170 −1.00000 −0.259645 1.00000 3.10578
1.10 −2.01632 1.00000 2.06555 2.51738 −2.01632 −1.00000 −0.132166 1.00000 −5.07585
1.11 −1.73189 1.00000 0.999432 2.64661 −1.73189 −1.00000 1.73287 1.00000 −4.58362
1.12 −1.53916 1.00000 0.369005 0.549666 −1.53916 −1.00000 2.51036 1.00000 −0.846023
1.13 −1.50421 1.00000 0.262658 −3.49239 −1.50421 −1.00000 2.61333 1.00000 5.25330
1.14 −1.28577 1.00000 −0.346791 −1.72364 −1.28577 −1.00000 3.01744 1.00000 2.21621
1.15 −1.26807 1.00000 −0.392010 −2.94433 −1.26807 −1.00000 3.03323 1.00000 3.73361
1.16 −1.20214 1.00000 −0.554856 −0.710682 −1.20214 −1.00000 3.07130 1.00000 0.854341
1.17 −1.07517 1.00000 −0.844015 −3.93529 −1.07517 −1.00000 3.05779 1.00000 4.23110
1.18 −0.810573 1.00000 −1.34297 0.143356 −0.810573 −1.00000 2.70972 1.00000 −0.116200
1.19 −0.630759 1.00000 −1.60214 2.80904 −0.630759 −1.00000 2.27208 1.00000 −1.77183
1.20 −0.518887 1.00000 −1.73076 −2.15979 −0.518887 −1.00000 1.93584 1.00000 1.12069
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.44
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8043))\):

\(T_{2}^{44} + \cdots\)
\(T_{5}^{44} + \cdots\)
\(T_{11}^{44} + \cdots\)