Properties

Label 8023.2.a.d
Level 8023
Weight 2
Character orbit 8023.a
Self dual Yes
Analytic conductor 64.064
Analytic rank 0
Dimension 165
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: \(165\)
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.

\(\operatorname{Tr}(f)(q) = \) \(165q \) \(\mathstrut +\mathstrut 22q^{2} \) \(\mathstrut +\mathstrut 18q^{3} \) \(\mathstrut +\mathstrut 166q^{4} \) \(\mathstrut +\mathstrut 28q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 24q^{7} \) \(\mathstrut +\mathstrut 66q^{8} \) \(\mathstrut +\mathstrut 177q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(165q \) \(\mathstrut +\mathstrut 22q^{2} \) \(\mathstrut +\mathstrut 18q^{3} \) \(\mathstrut +\mathstrut 166q^{4} \) \(\mathstrut +\mathstrut 28q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 24q^{7} \) \(\mathstrut +\mathstrut 66q^{8} \) \(\mathstrut +\mathstrut 177q^{9} \) \(\mathstrut +\mathstrut 14q^{10} \) \(\mathstrut +\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 54q^{12} \) \(\mathstrut +\mathstrut 44q^{13} \) \(\mathstrut +\mathstrut 26q^{14} \) \(\mathstrut +\mathstrut 24q^{15} \) \(\mathstrut +\mathstrut 168q^{16} \) \(\mathstrut +\mathstrut 143q^{17} \) \(\mathstrut +\mathstrut 57q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut +\mathstrut 49q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 52q^{23} \) \(\mathstrut +\mathstrut 27q^{24} \) \(\mathstrut +\mathstrut 175q^{25} \) \(\mathstrut +\mathstrut 48q^{26} \) \(\mathstrut +\mathstrut 69q^{27} \) \(\mathstrut +\mathstrut 28q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 28q^{31} \) \(\mathstrut +\mathstrut 114q^{32} \) \(\mathstrut +\mathstrut 110q^{33} \) \(\mathstrut +\mathstrut 55q^{34} \) \(\mathstrut +\mathstrut 67q^{35} \) \(\mathstrut +\mathstrut 202q^{36} \) \(\mathstrut +\mathstrut 44q^{37} \) \(\mathstrut +\mathstrut 35q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 53q^{40} \) \(\mathstrut +\mathstrut 141q^{41} \) \(\mathstrut +\mathstrut 40q^{42} \) \(\mathstrut +\mathstrut 29q^{43} \) \(\mathstrut +\mathstrut 52q^{44} \) \(\mathstrut +\mathstrut 54q^{45} \) \(\mathstrut +\mathstrut 29q^{46} \) \(\mathstrut +\mathstrut 87q^{47} \) \(\mathstrut +\mathstrut 53q^{48} \) \(\mathstrut +\mathstrut 143q^{49} \) \(\mathstrut +\mathstrut 16q^{50} \) \(\mathstrut +\mathstrut 37q^{51} \) \(\mathstrut +\mathstrut 105q^{52} \) \(\mathstrut +\mathstrut 101q^{53} \) \(\mathstrut -\mathstrut 36q^{54} \) \(\mathstrut +\mathstrut 72q^{55} \) \(\mathstrut +\mathstrut 57q^{56} \) \(\mathstrut +\mathstrut 82q^{57} \) \(\mathstrut +\mathstrut 4q^{58} \) \(\mathstrut +\mathstrut 103q^{59} \) \(\mathstrut +\mathstrut 53q^{60} \) \(\mathstrut +\mathstrut 16q^{61} \) \(\mathstrut +\mathstrut 54q^{62} \) \(\mathstrut +\mathstrut 126q^{63} \) \(\mathstrut +\mathstrut 136q^{64} \) \(\mathstrut +\mathstrut 159q^{65} \) \(\mathstrut +\mathstrut 53q^{66} \) \(\mathstrut +\mathstrut 60q^{67} \) \(\mathstrut +\mathstrut 220q^{68} \) \(\mathstrut +\mathstrut 81q^{69} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 165q^{71} \) \(\mathstrut +\mathstrut 176q^{72} \) \(\mathstrut +\mathstrut 124q^{73} \) \(\mathstrut +\mathstrut 29q^{74} \) \(\mathstrut +\mathstrut 44q^{75} \) \(\mathstrut +\mathstrut 18q^{76} \) \(\mathstrut +\mathstrut 127q^{77} \) \(\mathstrut -\mathstrut 91q^{78} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut +\mathstrut 158q^{80} \) \(\mathstrut +\mathstrut 213q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut +\mathstrut 116q^{83} \) \(\mathstrut +\mathstrut 67q^{84} \) \(\mathstrut +\mathstrut 59q^{85} \) \(\mathstrut +\mathstrut 30q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut +\mathstrut 79q^{88} \) \(\mathstrut +\mathstrut 195q^{89} \) \(\mathstrut +\mathstrut 16q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 173q^{92} \) \(\mathstrut +\mathstrut 116q^{93} \) \(\mathstrut +\mathstrut 53q^{94} \) \(\mathstrut +\mathstrut 26q^{95} \) \(\mathstrut -\mathstrut 36q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 150q^{98} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.77651 2.27500 5.70902 0.808124 −6.31657 0.0647974 −10.2981 2.17564 −2.24377
1.2 −2.72160 −0.981025 5.40712 −1.25328 2.66996 −1.09644 −9.27282 −2.03759 3.41092
1.3 −2.70370 −2.31695 5.31001 3.41961 6.26435 0.731020 −8.94928 2.36827 −9.24561
1.4 −2.64042 3.27801 4.97182 3.57654 −8.65532 2.80854 −7.84685 7.74534 −9.44356
1.5 −2.62951 0.0659678 4.91432 1.30562 −0.173463 −3.45826 −7.66322 −2.99565 −3.43314
1.6 −2.60713 −0.132138 4.79710 −1.04101 0.344501 4.69646 −7.29239 −2.98254 2.71405
1.7 −2.57888 −1.57055 4.65062 −2.72522 4.05026 −1.77487 −6.83564 −0.533376 7.02803
1.8 −2.52899 1.55552 4.39577 −1.46602 −3.93388 0.126533 −6.05887 −0.580366 3.70754
1.9 −2.51204 1.13882 4.31034 2.43582 −2.86077 −2.08264 −5.80366 −1.70308 −6.11887
1.10 −2.49309 −1.90773 4.21552 0.893200 4.75615 0.632761 −5.52349 0.639435 −2.22683
1.11 −2.44821 2.59661 3.99372 −2.59026 −6.35704 −1.59374 −4.88104 3.74237 6.34149
1.12 −2.38214 3.08941 3.67457 1.88389 −7.35940 1.49844 −3.98905 6.54446 −4.48768
1.13 −2.35257 −0.106381 3.53459 1.14622 0.250270 −0.376719 −3.61023 −2.98868 −2.69657
1.14 −2.33295 −2.77061 3.44267 −1.81617 6.46371 3.36128 −3.36567 4.67630 4.23705
1.15 −2.29416 −0.794120 3.26316 4.14537 1.82184 3.97505 −2.89789 −2.36937 −9.51013
1.16 −2.29110 0.370553 3.24912 −0.295381 −0.848972 0.894029 −2.86186 −2.86269 0.676746
1.17 −2.25574 0.317472 3.08836 −3.70971 −0.716135 −3.94071 −2.45506 −2.89921 8.36814
1.18 −2.20645 2.85395 2.86841 −2.79248 −6.29710 1.10201 −1.91611 5.14504 6.16145
1.19 −2.16974 −2.66568 2.70776 −3.38518 5.78382 −1.43929 −1.53565 4.10584 7.34496
1.20 −2.14746 −2.07357 2.61157 2.08017 4.45290 −3.04722 −1.31333 1.29970 −4.46708
See next 80 embeddings (of 165 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.165
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 \(T_{2}^{165} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8023))\).