Properties

Label 8023.2.a.b
Level 8023
Weight 2
Character orbit 8023.a
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 155
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: \(1\)
Dimension: \(155\)
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.

\(\operatorname{Tr}(f)(q) = \) \(155q \) \(\mathstrut -\mathstrut 21q^{2} \) \(\mathstrut -\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut -\mathstrut 26q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(155q \) \(\mathstrut -\mathstrut 21q^{2} \) \(\mathstrut -\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut -\mathstrut 26q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 24q^{11} \) \(\mathstrut -\mathstrut 32q^{12} \) \(\mathstrut -\mathstrut 62q^{13} \) \(\mathstrut -\mathstrut 18q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 155q^{16} \) \(\mathstrut -\mathstrut 129q^{17} \) \(\mathstrut -\mathstrut 42q^{18} \) \(\mathstrut -\mathstrut 18q^{19} \) \(\mathstrut -\mathstrut 59q^{20} \) \(\mathstrut -\mathstrut 45q^{21} \) \(\mathstrut -\mathstrut 17q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 27q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 44q^{26} \) \(\mathstrut -\mathstrut 43q^{27} \) \(\mathstrut -\mathstrut 100q^{28} \) \(\mathstrut -\mathstrut 52q^{29} \) \(\mathstrut -\mathstrut 39q^{30} \) \(\mathstrut -\mathstrut 56q^{31} \) \(\mathstrut -\mathstrut 145q^{32} \) \(\mathstrut -\mathstrut 126q^{33} \) \(\mathstrut -\mathstrut q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 131q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 91q^{38} \) \(\mathstrut -\mathstrut 29q^{39} \) \(\mathstrut -\mathstrut 5q^{40} \) \(\mathstrut -\mathstrut 163q^{41} \) \(\mathstrut -\mathstrut 80q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 118q^{44} \) \(\mathstrut -\mathstrut 66q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 111q^{47} \) \(\mathstrut -\mathstrut 89q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 121q^{50} \) \(\mathstrut +\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 111q^{52} \) \(\mathstrut -\mathstrut 93q^{53} \) \(\mathstrut -\mathstrut 68q^{54} \) \(\mathstrut -\mathstrut 60q^{55} \) \(\mathstrut -\mathstrut 27q^{56} \) \(\mathstrut -\mathstrut 106q^{57} \) \(\mathstrut +\mathstrut 16q^{58} \) \(\mathstrut -\mathstrut 79q^{59} \) \(\mathstrut -\mathstrut 103q^{60} \) \(\mathstrut -\mathstrut 74q^{61} \) \(\mathstrut -\mathstrut 102q^{62} \) \(\mathstrut -\mathstrut 118q^{63} \) \(\mathstrut +\mathstrut 175q^{64} \) \(\mathstrut -\mathstrut 109q^{65} \) \(\mathstrut +\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 18q^{67} \) \(\mathstrut -\mathstrut 346q^{68} \) \(\mathstrut -\mathstrut 39q^{69} \) \(\mathstrut +\mathstrut 32q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut -\mathstrut 203q^{72} \) \(\mathstrut -\mathstrut 108q^{73} \) \(\mathstrut -\mathstrut 87q^{74} \) \(\mathstrut -\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 121q^{77} \) \(\mathstrut -\mathstrut 75q^{78} \) \(\mathstrut -\mathstrut 6q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut +\mathstrut 107q^{81} \) \(\mathstrut -\mathstrut 30q^{82} \) \(\mathstrut -\mathstrut 116q^{83} \) \(\mathstrut -\mathstrut 5q^{84} \) \(\mathstrut -\mathstrut 53q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut -\mathstrut 100q^{87} \) \(\mathstrut -\mathstrut 43q^{88} \) \(\mathstrut -\mathstrut 189q^{89} \) \(\mathstrut -\mathstrut 76q^{90} \) \(\mathstrut +\mathstrut 14q^{91} \) \(\mathstrut -\mathstrut 99q^{92} \) \(\mathstrut -\mathstrut 72q^{93} \) \(\mathstrut +\mathstrut 17q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 50q^{96} \) \(\mathstrut -\mathstrut 184q^{97} \) \(\mathstrut -\mathstrut 249q^{98} \) \(\mathstrut -\mathstrut 114q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.80015 0.646146 5.84081 1.34449 −1.80930 3.74304 −10.7548 −2.58250 −3.76478
1.2 −2.79202 −1.96792 5.79536 4.22861 5.49445 −4.72825 −10.5967 0.872693 −11.8064
1.3 −2.78061 −3.43962 5.73182 −0.171450 9.56425 −3.12589 −10.3767 8.83098 0.476736
1.4 −2.76736 2.97864 5.65827 −2.08289 −8.24297 −3.08270 −10.1238 5.87230 5.76411
1.5 −2.76547 1.71486 5.64781 −3.60382 −4.74239 −5.22895 −10.0879 −0.0592525 9.96624
1.6 −2.74054 −1.55820 5.51058 −1.15483 4.27031 −0.0750165 −9.62090 −0.572020 3.16485
1.7 −2.73747 2.98404 5.49374 −2.59125 −8.16872 4.93159 −9.56402 5.90448 7.09348
1.8 −2.68312 −1.89873 5.19916 −4.03080 5.09454 2.89742 −8.58374 0.605189 10.8151
1.9 −2.67037 −1.29029 5.13085 2.33945 3.44554 3.27756 −8.36052 −1.33516 −6.24718
1.10 −2.57631 −2.78784 4.63739 0.760791 7.18234 −2.92762 −6.79473 4.77204 −1.96004
1.11 −2.57492 1.14041 4.63023 3.61279 −2.93647 −3.17107 −6.77264 −1.69947 −9.30267
1.12 −2.57220 −0.502356 4.61621 −1.32474 1.29216 1.13423 −6.72941 −2.74764 3.40751
1.13 −2.52683 1.49048 4.38485 −0.343930 −3.76619 0.360206 −6.02610 −0.778467 0.869051
1.14 −2.48799 −3.03020 4.19010 −2.87287 7.53911 1.28027 −5.44894 6.18210 7.14768
1.15 −2.47623 2.90051 4.13171 3.57414 −7.18232 −0.249825 −5.27860 5.41293 −8.85040
1.16 −2.46916 1.70167 4.09677 −3.39881 −4.20171 3.51551 −5.17727 −0.104305 8.39223
1.17 −2.45088 1.23773 4.00682 3.46965 −3.03354 −0.238635 −4.91847 −1.46802 −8.50371
1.18 −2.44945 −0.158730 3.99982 −2.39064 0.388803 −3.35946 −4.89848 −2.97480 5.85577
1.19 −2.44920 −0.457827 3.99860 −3.52685 1.12131 −3.81804 −4.89498 −2.79039 8.63798
1.20 −2.32032 0.985491 3.38390 2.02170 −2.28666 0.848897 −3.21110 −2.02881 −4.69101
See next 80 embeddings (of 155 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.155
Significant digits:
Format:

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 \(T_{2}^{155} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8023))\).