Properties

Label 8023.2.a.e
Level 8023
Weight 2
Character orbit 8023.a
Self dual Yes
Analytic conductor 64.064
Analytic rank 0
Dimension 172
CM No

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Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(0\)
Dimension: \(172\)
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.

\(\operatorname{Tr}(f)(q) = \) \(172q \) \(\mathstrut +\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 18q^{3} \) \(\mathstrut +\mathstrut 180q^{4} \) \(\mathstrut +\mathstrut 28q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 72q^{8} \) \(\mathstrut +\mathstrut 198q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(172q \) \(\mathstrut +\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 18q^{3} \) \(\mathstrut +\mathstrut 180q^{4} \) \(\mathstrut +\mathstrut 28q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 72q^{8} \) \(\mathstrut +\mathstrut 198q^{9} \) \(\mathstrut +\mathstrut 14q^{10} \) \(\mathstrut +\mathstrut 20q^{11} \) \(\mathstrut +\mathstrut 54q^{12} \) \(\mathstrut +\mathstrut 36q^{13} \) \(\mathstrut +\mathstrut 26q^{14} \) \(\mathstrut +\mathstrut 32q^{15} \) \(\mathstrut +\mathstrut 196q^{16} \) \(\mathstrut +\mathstrut 123q^{17} \) \(\mathstrut +\mathstrut 74q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut +\mathstrut 70q^{20} \) \(\mathstrut +\mathstrut 37q^{21} \) \(\mathstrut +\mathstrut 11q^{22} \) \(\mathstrut +\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 62q^{24} \) \(\mathstrut +\mathstrut 210q^{25} \) \(\mathstrut +\mathstrut 50q^{26} \) \(\mathstrut +\mathstrut 69q^{27} \) \(\mathstrut +\mathstrut 42q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 36q^{30} \) \(\mathstrut +\mathstrut 10q^{31} \) \(\mathstrut +\mathstrut 168q^{32} \) \(\mathstrut +\mathstrut 124q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 59q^{35} \) \(\mathstrut +\mathstrut 192q^{36} \) \(\mathstrut +\mathstrut 40q^{37} \) \(\mathstrut +\mathstrut 58q^{38} \) \(\mathstrut +\mathstrut 15q^{39} \) \(\mathstrut +\mathstrut 7q^{40} \) \(\mathstrut +\mathstrut 155q^{41} \) \(\mathstrut -\mathstrut 6q^{42} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 22q^{44} \) \(\mathstrut +\mathstrut 76q^{45} \) \(\mathstrut +\mathstrut q^{46} \) \(\mathstrut +\mathstrut 71q^{47} \) \(\mathstrut +\mathstrut 144q^{48} \) \(\mathstrut +\mathstrut 206q^{49} \) \(\mathstrut +\mathstrut 126q^{50} \) \(\mathstrut +\mathstrut 33q^{51} \) \(\mathstrut +\mathstrut 71q^{52} \) \(\mathstrut +\mathstrut 101q^{53} \) \(\mathstrut +\mathstrut 92q^{54} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut +\mathstrut 57q^{56} \) \(\mathstrut +\mathstrut 114q^{57} \) \(\mathstrut +\mathstrut 4q^{58} \) \(\mathstrut +\mathstrut 71q^{59} \) \(\mathstrut +\mathstrut 38q^{60} \) \(\mathstrut +\mathstrut 50q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 14q^{63} \) \(\mathstrut +\mathstrut 240q^{64} \) \(\mathstrut +\mathstrut 143q^{65} \) \(\mathstrut +\mathstrut 21q^{66} \) \(\mathstrut +\mathstrut 8q^{67} \) \(\mathstrut +\mathstrut 192q^{68} \) \(\mathstrut +\mathstrut 41q^{69} \) \(\mathstrut -\mathstrut 12q^{70} \) \(\mathstrut -\mathstrut 172q^{71} \) \(\mathstrut +\mathstrut 156q^{72} \) \(\mathstrut +\mathstrut 128q^{73} \) \(\mathstrut +\mathstrut 30q^{74} \) \(\mathstrut +\mathstrut 72q^{75} \) \(\mathstrut +\mathstrut 74q^{76} \) \(\mathstrut +\mathstrut 127q^{77} \) \(\mathstrut +\mathstrut 107q^{78} \) \(\mathstrut +\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut 50q^{80} \) \(\mathstrut +\mathstrut 236q^{81} \) \(\mathstrut +\mathstrut 42q^{82} \) \(\mathstrut +\mathstrut 140q^{83} \) \(\mathstrut +\mathstrut 71q^{84} \) \(\mathstrut +\mathstrut 55q^{85} \) \(\mathstrut +\mathstrut 46q^{86} \) \(\mathstrut +\mathstrut 100q^{87} \) \(\mathstrut -\mathstrut 31q^{88} \) \(\mathstrut +\mathstrut 215q^{89} \) \(\mathstrut -\mathstrut 7q^{90} \) \(\mathstrut +\mathstrut 22q^{91} \) \(\mathstrut -\mathstrut 15q^{92} \) \(\mathstrut +\mathstrut 60q^{93} \) \(\mathstrut +\mathstrut 5q^{94} \) \(\mathstrut +\mathstrut 74q^{95} \) \(\mathstrut +\mathstrut 182q^{96} \) \(\mathstrut +\mathstrut 120q^{97} \) \(\mathstrut +\mathstrut 164q^{98} \) \(\mathstrut +\mathstrut 60q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.71525 −0.0977350 5.37257 1.14210 0.265375 −3.48491 −9.15737 −2.99045 −3.10108
1.2 −2.68727 1.51064 5.22143 0.313283 −4.05950 −2.80560 −8.65687 −0.717969 −0.841876
1.3 −2.68206 0.545640 5.19345 −2.53261 −1.46344 −1.66793 −8.56503 −2.70228 6.79262
1.4 −2.63836 2.01648 4.96097 1.04348 −5.32021 3.03248 −7.81211 1.06619 −2.75309
1.5 −2.61555 2.99326 4.84110 −2.84869 −7.82902 0.984788 −7.43104 5.95960 7.45089
1.6 −2.60904 −1.86481 4.80711 2.29669 4.86538 1.81523 −7.32387 0.477530 −5.99216
1.7 −2.59149 −2.64740 4.71583 −3.26554 6.86073 0.687432 −7.03805 4.00875 8.46262
1.8 −2.58451 1.24090 4.67970 4.06279 −3.20713 2.63982 −6.92572 −1.46016 −10.5003
1.9 −2.55716 −1.44904 4.53909 −0.0718207 3.70544 2.77634 −6.49287 −0.900274 0.183657
1.10 −2.47898 −2.90151 4.14536 3.57893 7.19280 −1.12807 −5.31832 5.41877 −8.87212
1.11 −2.46646 2.78762 4.08340 2.84947 −6.87554 −3.94161 −5.13862 4.77082 −7.02810
1.12 −2.44664 −2.78774 3.98604 −0.315327 6.82060 −4.26739 −4.85913 4.77151 0.771492
1.13 −2.39224 −1.88283 3.72279 −1.64189 4.50418 −4.12017 −4.12133 0.545055 3.92779
1.14 −2.39089 1.71669 3.71638 −1.13551 −4.10443 −3.27571 −4.10367 −0.0529740 2.71487
1.15 −2.38785 2.31804 3.70185 2.20960 −5.53514 3.66496 −4.06377 2.37331 −5.27621
1.16 −2.37665 −1.52236 3.64846 1.09798 3.61812 2.78247 −3.91780 −0.682408 −2.60952
1.17 −2.34076 −0.698142 3.47917 4.27326 1.63419 −0.686172 −3.46239 −2.51260 −10.0027
1.18 −2.32376 2.08372 3.39986 −3.01109 −4.84207 −1.67398 −3.25293 1.34190 6.99706
1.19 −2.31555 −0.113923 3.36176 1.48156 0.263794 4.57358 −3.15322 −2.98702 −3.43063
1.20 −2.30435 −0.933250 3.31004 −0.282102 2.15054 1.67948 −3.01880 −2.12904 0.650063
See next 80 embeddings (of 172 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.172
Significant digits:
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Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(71\) \(1\)
\(113\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{172} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8023))\).