Properties

Label 8023.2.a.c
Level 8023
Weight 2
Character orbit 8023.a
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
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: \(158\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 158q - 24q^{2} - 23q^{3} + 158q^{4} - 31q^{5} - 17q^{6} - 2q^{7} - 69q^{8} + 135q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 158q - 24q^{2} - 23q^{3} + 158q^{4} - 31q^{5} - 17q^{6} - 2q^{7} - 69q^{8} + 135q^{9} - 10q^{10} - 10q^{11} - 46q^{12} - 28q^{13} - 27q^{14} - 41q^{15} + 150q^{16} - 137q^{17} - 67q^{18} - 42q^{19} - 66q^{20} - 46q^{21} - 8q^{22} - 26q^{23} - 48q^{24} + 129q^{25} - 67q^{26} - 89q^{27} - 21q^{28} - 79q^{29} - 11q^{30} + 7q^{31} - 147q^{32} - 112q^{33} - 28q^{34} - 53q^{35} + 141q^{36} - 60q^{37} - 53q^{38} - 3q^{39} - 48q^{40} - 128q^{41} + 32q^{42} - 63q^{43} - 88q^{45} - 2q^{46} - 92q^{47} - 131q^{48} + 122q^{49} - 116q^{50} - 12q^{51} - 89q^{52} - 94q^{53} - 71q^{54} - 12q^{55} - 104q^{56} - 93q^{57} - 65q^{58} - 54q^{59} - 12q^{60} + 17q^{61} - 97q^{62} - 28q^{63} + 163q^{64} - 163q^{65} - 65q^{66} - 35q^{67} - 217q^{68} - 46q^{69} - 79q^{70} - 158q^{71} - 99q^{72} - 165q^{73} - 94q^{75} - 93q^{76} - 140q^{77} + 25q^{78} - 61q^{79} - 134q^{80} + 114q^{81} + 10q^{82} - 158q^{83} - 160q^{84} + 23q^{85} - 122q^{86} - 71q^{87} - 14q^{88} - 251q^{89} - 6q^{90} - 57q^{91} - 58q^{92} - 52q^{93} - 64q^{94} - 84q^{95} - 98q^{96} - 48q^{97} - 84q^{98} + 85q^{99} + O(q^{100}) \)

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 −2.79904 −0.951830 5.83462 2.72456 2.66421 1.55879 −10.7333 −2.09402 −7.62616
1.2 −2.78025 −2.83508 5.72982 −1.35792 7.88223 4.56765 −10.3698 5.03765 3.77538
1.3 −2.75717 −0.782411 5.60200 −3.11881 2.15724 0.297168 −9.93135 −2.38783 8.59909
1.4 −2.74732 2.10960 5.54775 3.39073 −5.79574 −0.0705501 −9.74679 1.45041 −9.31541
1.5 −2.74512 2.49890 5.53568 0.133996 −6.85979 0.778013 −9.70588 3.24451 −0.367836
1.6 −2.73131 −2.15430 5.46003 −2.36711 5.88407 −3.03890 −9.45041 1.64103 6.46530
1.7 −2.70862 0.748763 5.33660 −3.98594 −2.02811 0.912141 −9.03756 −2.43935 10.7964
1.8 −2.70672 −0.0191468 5.32634 0.870977 0.0518250 −3.03945 −9.00349 −2.99963 −2.35749
1.9 −2.67852 0.688962 5.17445 −3.33373 −1.84540 3.78681 −8.50280 −2.52533 8.92945
1.10 −2.65311 3.18762 5.03901 1.63340 −8.45712 −4.20358 −8.06283 7.16092 −4.33359
1.11 −2.60210 −3.36394 4.77094 3.49358 8.75331 4.61670 −7.21028 8.31606 −9.09066
1.12 −2.54938 0.0117245 4.49933 3.26987 −0.0298901 −0.929031 −6.37175 −2.99986 −8.33615
1.13 −2.54054 2.90668 4.45432 −2.39844 −7.38453 0.864832 −6.23529 5.44881 6.09333
1.14 −2.51950 −2.51323 4.34790 1.49157 6.33210 −1.81281 −5.91556 3.31634 −3.75802
1.15 −2.49733 −3.32636 4.23663 −4.15753 8.30700 −2.74619 −5.58560 8.06465 10.3827
1.16 −2.47274 −2.32483 4.11444 −0.448444 5.74869 4.71625 −5.22846 2.40481 1.10889
1.17 −2.44908 −0.864554 3.99799 2.08542 2.11736 −1.35512 −4.89325 −2.25255 −5.10735
1.18 −2.43745 −0.327529 3.94116 −2.07610 0.798335 −0.184041 −4.73147 −2.89272 5.06038
1.19 −2.36796 1.87225 3.60725 0.382969 −4.43341 2.54225 −3.80591 0.505313 −0.906856
1.20 −2.36619 −2.12839 3.59886 0.442767 5.03618 −4.08071 −3.78320 1.53005 −1.04767
See next 80 embeddings (of 158 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.158
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 \(T_{2}^{158} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8023))\).