Properties

Label 8031.2.a.d
Level 8031
Weight 2
Character orbit 8031.a
Self dual Yes
Analytic conductor 64.128
Analytic rank 0
Dimension 132
CM No

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Newspace parameters

Level: \( N \) = \( 8031 = 3 \cdot 2677 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1278578633\)
Analytic rank: \(0\)
Dimension: \(132\)
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.

\(\operatorname{Tr}(f)(q) = \) \(132q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 132q^{3} \) \(\mathstrut +\mathstrut 156q^{4} \) \(\mathstrut +\mathstrut 20q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 44q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 132q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(132q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 132q^{3} \) \(\mathstrut +\mathstrut 156q^{4} \) \(\mathstrut +\mathstrut 20q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 44q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 132q^{9} \) \(\mathstrut +\mathstrut 40q^{10} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 156q^{12} \) \(\mathstrut +\mathstrut 62q^{13} \) \(\mathstrut +\mathstrut 25q^{14} \) \(\mathstrut +\mathstrut 20q^{15} \) \(\mathstrut +\mathstrut 192q^{16} \) \(\mathstrut +\mathstrut 77q^{17} \) \(\mathstrut +\mathstrut 4q^{18} \) \(\mathstrut +\mathstrut 86q^{19} \) \(\mathstrut +\mathstrut 26q^{20} \) \(\mathstrut +\mathstrut 44q^{21} \) \(\mathstrut +\mathstrut 52q^{22} \) \(\mathstrut +\mathstrut 17q^{23} \) \(\mathstrut +\mathstrut 9q^{24} \) \(\mathstrut +\mathstrut 212q^{25} \) \(\mathstrut +\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 132q^{27} \) \(\mathstrut +\mathstrut 95q^{28} \) \(\mathstrut +\mathstrut 52q^{29} \) \(\mathstrut +\mathstrut 40q^{30} \) \(\mathstrut +\mathstrut 59q^{31} \) \(\mathstrut -\mathstrut 8q^{32} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut +\mathstrut 41q^{34} \) \(\mathstrut +\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 156q^{36} \) \(\mathstrut +\mathstrut 76q^{37} \) \(\mathstrut +\mathstrut 2q^{38} \) \(\mathstrut +\mathstrut 62q^{39} \) \(\mathstrut +\mathstrut 91q^{40} \) \(\mathstrut +\mathstrut 114q^{41} \) \(\mathstrut +\mathstrut 25q^{42} \) \(\mathstrut +\mathstrut 173q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut +\mathstrut 48q^{46} \) \(\mathstrut +\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 192q^{48} \) \(\mathstrut +\mathstrut 262q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 77q^{51} \) \(\mathstrut +\mathstrut 144q^{52} \) \(\mathstrut +\mathstrut 15q^{53} \) \(\mathstrut +\mathstrut 4q^{54} \) \(\mathstrut +\mathstrut 111q^{55} \) \(\mathstrut +\mathstrut 66q^{56} \) \(\mathstrut +\mathstrut 86q^{57} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 20q^{59} \) \(\mathstrut +\mathstrut 26q^{60} \) \(\mathstrut +\mathstrut 182q^{61} \) \(\mathstrut +\mathstrut 16q^{62} \) \(\mathstrut +\mathstrut 44q^{63} \) \(\mathstrut +\mathstrut 255q^{64} \) \(\mathstrut +\mathstrut 70q^{65} \) \(\mathstrut +\mathstrut 52q^{66} \) \(\mathstrut +\mathstrut 169q^{67} \) \(\mathstrut +\mathstrut 128q^{68} \) \(\mathstrut +\mathstrut 17q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut +\mathstrut 23q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 148q^{73} \) \(\mathstrut +\mathstrut 57q^{74} \) \(\mathstrut +\mathstrut 212q^{75} \) \(\mathstrut +\mathstrut 143q^{76} \) \(\mathstrut +\mathstrut 31q^{77} \) \(\mathstrut +\mathstrut 13q^{78} \) \(\mathstrut +\mathstrut 152q^{79} \) \(\mathstrut +\mathstrut 27q^{80} \) \(\mathstrut +\mathstrut 132q^{81} \) \(\mathstrut +\mathstrut 67q^{82} \) \(\mathstrut +\mathstrut 28q^{83} \) \(\mathstrut +\mathstrut 95q^{84} \) \(\mathstrut +\mathstrut 88q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut +\mathstrut 52q^{87} \) \(\mathstrut +\mathstrut 130q^{88} \) \(\mathstrut +\mathstrut 136q^{89} \) \(\mathstrut +\mathstrut 40q^{90} \) \(\mathstrut +\mathstrut 125q^{91} \) \(\mathstrut +\mathstrut 59q^{93} \) \(\mathstrut +\mathstrut 95q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 8q^{96} \) \(\mathstrut +\mathstrut 147q^{97} \) \(\mathstrut -\mathstrut 18q^{98} \) \(\mathstrut +\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.80398 1.00000 5.86231 1.87605 −2.80398 3.15563 −10.8299 1.00000 −5.26041
1.2 −2.77294 1.00000 5.68922 −1.74396 −2.77294 0.0730159 −10.2300 1.00000 4.83589
1.3 −2.75661 1.00000 5.59891 −4.00125 −2.75661 −2.17438 −9.92081 1.00000 11.0299
1.4 −2.72616 1.00000 5.43195 −1.18317 −2.72616 −4.48555 −9.35605 1.00000 3.22552
1.5 −2.69638 1.00000 5.27048 2.40729 −2.69638 −4.24108 −8.81846 1.00000 −6.49098
1.6 −2.68578 1.00000 5.21342 1.21683 −2.68578 2.10686 −8.63055 1.00000 −3.26813
1.7 −2.67095 1.00000 5.13397 −2.93949 −2.67095 4.35242 −8.37068 1.00000 7.85124
1.8 −2.59180 1.00000 4.71742 2.79387 −2.59180 −2.04048 −7.04300 1.00000 −7.24116
1.9 −2.57206 1.00000 4.61548 3.83645 −2.57206 −2.68797 −6.72717 1.00000 −9.86756
1.10 −2.56954 1.00000 4.60252 −1.45340 −2.56954 2.82926 −6.68726 1.00000 3.73456
1.11 −2.55916 1.00000 4.54932 −0.940256 −2.55916 2.24269 −6.52413 1.00000 2.40627
1.12 −2.50203 1.00000 4.26014 −3.95750 −2.50203 1.89022 −5.65494 1.00000 9.90177
1.13 −2.48023 1.00000 4.15155 4.11076 −2.48023 4.68191 −5.33633 1.00000 −10.1956
1.14 −2.46874 1.00000 4.09466 −2.24657 −2.46874 4.89936 −5.17116 1.00000 5.54618
1.15 −2.45456 1.00000 4.02485 −4.17412 −2.45456 −1.11531 −4.97011 1.00000 10.2456
1.16 −2.29731 1.00000 3.27764 −1.75176 −2.29731 −2.80141 −2.93514 1.00000 4.02433
1.17 −2.23840 1.00000 3.01043 3.52664 −2.23840 3.86222 −2.26174 1.00000 −7.89403
1.18 −2.20104 1.00000 2.84456 0.313894 −2.20104 1.59317 −1.85890 1.00000 −0.690891
1.19 −2.19060 1.00000 2.79873 1.38696 −2.19060 −0.332475 −1.74969 1.00000 −3.03827
1.20 −2.17916 1.00000 2.74876 2.82413 −2.17916 4.47038 −1.63167 1.00000 −6.15424
See next 80 embeddings (of 132 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.132
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(2677\) \(1\)