Properties

Label 8043.2.a.u
Level 8043
Weight 2
Character orbit 8043.a
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 53
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: \(53\)
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.

\(\operatorname{Tr}(f)(q) = \) \(53q \) \(\mathstrut +\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut 53q^{3} \) \(\mathstrut +\mathstrut 63q^{4} \) \(\mathstrut +\mathstrut 24q^{5} \) \(\mathstrut +\mathstrut 11q^{6} \) \(\mathstrut +\mathstrut 53q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 53q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(53q \) \(\mathstrut +\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut 53q^{3} \) \(\mathstrut +\mathstrut 63q^{4} \) \(\mathstrut +\mathstrut 24q^{5} \) \(\mathstrut +\mathstrut 11q^{6} \) \(\mathstrut +\mathstrut 53q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 53q^{9} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 46q^{11} \) \(\mathstrut +\mathstrut 63q^{12} \) \(\mathstrut +\mathstrut 32q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 24q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut +\mathstrut 46q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut 53q^{20} \) \(\mathstrut +\mathstrut 53q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 68q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 53q^{27} \) \(\mathstrut +\mathstrut 63q^{28} \) \(\mathstrut +\mathstrut 55q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut +\mathstrut 51q^{32} \) \(\mathstrut +\mathstrut 46q^{33} \) \(\mathstrut -\mathstrut 7q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 63q^{36} \) \(\mathstrut +\mathstrut 53q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut +\mathstrut 32q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut +\mathstrut 38q^{41} \) \(\mathstrut +\mathstrut 11q^{42} \) \(\mathstrut +\mathstrut 36q^{43} \) \(\mathstrut +\mathstrut 70q^{44} \) \(\mathstrut +\mathstrut 24q^{45} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 51q^{47} \) \(\mathstrut +\mathstrut 67q^{48} \) \(\mathstrut +\mathstrut 53q^{49} \) \(\mathstrut +\mathstrut 32q^{50} \) \(\mathstrut +\mathstrut 46q^{51} \) \(\mathstrut +\mathstrut 10q^{52} \) \(\mathstrut +\mathstrut 104q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut +\mathstrut 4q^{58} \) \(\mathstrut +\mathstrut 36q^{59} \) \(\mathstrut +\mathstrut 53q^{60} \) \(\mathstrut +\mathstrut 3q^{61} \) \(\mathstrut +\mathstrut 25q^{62} \) \(\mathstrut +\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 82q^{64} \) \(\mathstrut +\mathstrut 46q^{65} \) \(\mathstrut +\mathstrut 13q^{66} \) \(\mathstrut +\mathstrut 54q^{67} \) \(\mathstrut +\mathstrut 88q^{68} \) \(\mathstrut +\mathstrut 68q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut +\mathstrut 101q^{71} \) \(\mathstrut +\mathstrut 30q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut +\mathstrut 32q^{74} \) \(\mathstrut +\mathstrut 71q^{75} \) \(\mathstrut -\mathstrut 35q^{76} \) \(\mathstrut +\mathstrut 46q^{77} \) \(\mathstrut +\mathstrut 11q^{78} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut +\mathstrut 39q^{80} \) \(\mathstrut +\mathstrut 53q^{81} \) \(\mathstrut -\mathstrut 29q^{82} \) \(\mathstrut +\mathstrut 38q^{83} \) \(\mathstrut +\mathstrut 63q^{84} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 23q^{86} \) \(\mathstrut +\mathstrut 55q^{87} \) \(\mathstrut -\mathstrut 8q^{88} \) \(\mathstrut +\mathstrut 52q^{89} \) \(\mathstrut +\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 76q^{92} \) \(\mathstrut -\mathstrut 2q^{93} \) \(\mathstrut -\mathstrut 53q^{94} \) \(\mathstrut +\mathstrut 46q^{95} \) \(\mathstrut +\mathstrut 51q^{96} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 11q^{98} \) \(\mathstrut +\mathstrut 46q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.66147 1.00000 5.08344 2.81521 −2.66147 1.00000 −8.20648 1.00000 −7.49261
1.2 −2.65959 1.00000 5.07341 1.50911 −2.65959 1.00000 −8.17400 1.00000 −4.01361
1.3 −2.63741 1.00000 4.95592 0.460886 −2.63741 1.00000 −7.79596 1.00000 −1.21554
1.4 −2.39422 1.00000 3.73230 −2.33465 −2.39422 1.00000 −4.14751 1.00000 5.58967
1.5 −2.29113 1.00000 3.24926 −2.33697 −2.29113 1.00000 −2.86221 1.00000 5.35430
1.6 −2.26724 1.00000 3.14038 4.07533 −2.26724 1.00000 −2.58552 1.00000 −9.23976
1.7 −2.15559 1.00000 2.64657 3.65015 −2.15559 1.00000 −1.39373 1.00000 −7.86823
1.8 −2.10439 1.00000 2.42847 1.35273 −2.10439 1.00000 −0.901667 1.00000 −2.84668
1.9 −2.03619 1.00000 2.14608 −0.995010 −2.03619 1.00000 −0.297449 1.00000 2.02603
1.10 −1.92293 1.00000 1.69768 1.88319 −1.92293 1.00000 0.581347 1.00000 −3.62124
1.11 −1.78404 1.00000 1.18281 −2.51827 −1.78404 1.00000 1.45789 1.00000 4.49270
1.12 −1.46877 1.00000 0.157298 −1.01808 −1.46877 1.00000 2.70651 1.00000 1.49533
1.13 −1.45637 1.00000 0.121016 −1.02950 −1.45637 1.00000 2.73650 1.00000 1.49933
1.14 −1.32463 1.00000 −0.245346 4.05110 −1.32463 1.00000 2.97426 1.00000 −5.36623
1.15 −1.31380 1.00000 −0.273938 −2.47121 −1.31380 1.00000 2.98749 1.00000 3.24666
1.16 −1.27919 1.00000 −0.363673 3.49939 −1.27919 1.00000 3.02359 1.00000 −4.47639
1.17 −0.969084 1.00000 −1.06088 −0.461084 −0.969084 1.00000 2.96625 1.00000 0.446829
1.18 −0.817713 1.00000 −1.33134 0.352247 −0.817713 1.00000 2.72409 1.00000 −0.288037
1.19 −0.805347 1.00000 −1.35142 3.29338 −0.805347 1.00000 2.69905 1.00000 −2.65231
1.20 −0.701767 1.00000 −1.50752 −0.804883 −0.701767 1.00000 2.46146 1.00000 0.564840
See all 53 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.53
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8043))\):

\(T_{2}^{53} - \cdots\)
\(T_{5}^{53} - \cdots\)
\(T_{11}^{53} - \cdots\)