Properties

Label 8027.2.a.f
Level 8027
Weight 2
Character orbit 8027.a
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
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.

\(\operatorname{Tr}(f)(q) = \) \(176q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 22q^{3} \) \(\mathstrut +\mathstrut 203q^{4} \) \(\mathstrut +\mathstrut 28q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 30q^{7} \) \(\mathstrut +\mathstrut 51q^{8} \) \(\mathstrut +\mathstrut 204q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(176q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 22q^{3} \) \(\mathstrut +\mathstrut 203q^{4} \) \(\mathstrut +\mathstrut 28q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 30q^{7} \) \(\mathstrut +\mathstrut 51q^{8} \) \(\mathstrut +\mathstrut 204q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 46q^{12} \) \(\mathstrut +\mathstrut 87q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 257q^{16} \) \(\mathstrut +\mathstrut 14q^{17} \) \(\mathstrut +\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 45q^{20} \) \(\mathstrut +\mathstrut 23q^{21} \) \(\mathstrut +\mathstrut 62q^{22} \) \(\mathstrut +\mathstrut 176q^{23} \) \(\mathstrut +\mathstrut 33q^{24} \) \(\mathstrut +\mathstrut 272q^{25} \) \(\mathstrut +\mathstrut 31q^{26} \) \(\mathstrut +\mathstrut 82q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 75q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut +\mathstrut 73q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut +\mathstrut 30q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 44q^{35} \) \(\mathstrut +\mathstrut 264q^{36} \) \(\mathstrut +\mathstrut 236q^{37} \) \(\mathstrut -\mathstrut 21q^{38} \) \(\mathstrut +\mathstrut 17q^{39} \) \(\mathstrut +\mathstrut 43q^{40} \) \(\mathstrut +\mathstrut 51q^{41} \) \(\mathstrut +\mathstrut 38q^{42} \) \(\mathstrut +\mathstrut 51q^{43} \) \(\mathstrut +\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 127q^{45} \) \(\mathstrut +\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 61q^{48} \) \(\mathstrut +\mathstrut 268q^{49} \) \(\mathstrut +\mathstrut 55q^{50} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 166q^{52} \) \(\mathstrut +\mathstrut 63q^{53} \) \(\mathstrut -\mathstrut 32q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 72q^{57} \) \(\mathstrut +\mathstrut 98q^{58} \) \(\mathstrut +\mathstrut 95q^{59} \) \(\mathstrut -\mathstrut 7q^{60} \) \(\mathstrut +\mathstrut 73q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 365q^{64} \) \(\mathstrut +\mathstrut 19q^{65} \) \(\mathstrut -\mathstrut 28q^{66} \) \(\mathstrut +\mathstrut 138q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut +\mathstrut 100q^{70} \) \(\mathstrut +\mathstrut 85q^{71} \) \(\mathstrut +\mathstrut 129q^{72} \) \(\mathstrut +\mathstrut 118q^{73} \) \(\mathstrut -\mathstrut 21q^{74} \) \(\mathstrut -\mathstrut 12q^{75} \) \(\mathstrut +\mathstrut 52q^{76} \) \(\mathstrut +\mathstrut 75q^{77} \) \(\mathstrut +\mathstrut 97q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 280q^{81} \) \(\mathstrut +\mathstrut 67q^{82} \) \(\mathstrut +\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 51q^{84} \) \(\mathstrut +\mathstrut 169q^{85} \) \(\mathstrut -\mathstrut 39q^{86} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 159q^{88} \) \(\mathstrut +\mathstrut 38q^{89} \) \(\mathstrut +\mathstrut 22q^{90} \) \(\mathstrut +\mathstrut 90q^{91} \) \(\mathstrut +\mathstrut 203q^{92} \) \(\mathstrut +\mathstrut 230q^{93} \) \(\mathstrut +\mathstrut 63q^{94} \) \(\mathstrut +\mathstrut 30q^{95} \) \(\mathstrut +\mathstrut 107q^{96} \) \(\mathstrut +\mathstrut 161q^{97} \) \(\mathstrut +\mathstrut 58q^{98} \) \(\mathstrut +\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.81854 −0.267983 5.94415 −3.79404 0.755319 −0.324133 −11.1167 −2.92819 10.6936
1.2 −2.77938 1.07296 5.72495 0.733926 −2.98217 −2.15808 −10.3531 −1.84875 −2.03986
1.3 −2.77677 −3.10732 5.71046 −0.966106 8.62833 4.66578 −10.3031 6.65546 2.68266
1.4 −2.73914 3.04549 5.50288 3.66953 −8.34203 −3.05286 −9.59489 6.27504 −10.0514
1.5 −2.73308 2.04263 5.46974 2.78212 −5.58268 3.87331 −9.48308 1.17234 −7.60375
1.6 −2.66575 −2.58411 5.10620 3.82950 6.88858 −0.0815082 −8.28034 3.67762 −10.2085
1.7 −2.63657 1.64340 4.95152 −0.607936 −4.33295 −1.90677 −7.78191 −0.299236 1.60287
1.8 −2.63094 −2.05461 4.92184 −2.98457 5.40556 0.228878 −7.68717 1.22144 7.85221
1.9 −2.62656 1.97110 4.89882 −2.67061 −5.17721 3.82377 −7.61393 0.885230 7.01453
1.10 −2.59269 0.175910 4.72203 3.23280 −0.456079 2.53654 −7.05738 −2.96906 −8.38164
1.11 −2.57713 −1.48333 4.64158 −1.39440 3.82274 −5.10805 −6.80769 −0.799719 3.59355
1.12 −2.54982 −0.805163 4.50159 −2.33665 2.05302 2.59075 −6.37861 −2.35171 5.95805
1.13 −2.47345 −2.21693 4.11797 −0.996079 5.48348 1.88032 −5.23870 1.91479 2.46376
1.14 −2.45769 0.342548 4.04026 −0.529727 −0.841878 −2.69173 −5.01433 −2.88266 1.30191
1.15 −2.43642 −3.01973 3.93613 2.61235 7.35732 −1.67075 −4.71721 6.11876 −6.36478
1.16 −2.41247 2.73531 3.82000 −4.06212 −6.59885 3.23940 −4.39069 4.48192 9.79973
1.17 −2.38066 0.526357 3.66755 −2.52733 −1.25308 3.59846 −3.96986 −2.72295 6.01672
1.18 −2.32771 −1.02581 3.41824 4.27433 2.38779 1.70170 −3.30124 −1.94772 −9.94939
1.19 −2.32736 −1.68164 3.41663 2.73432 3.91378 2.98551 −3.29700 −0.172094 −6.36375
1.20 −2.30965 1.95797 3.33448 2.21374 −4.52222 4.98325 −3.08217 0.833638 −5.11297
See next 80 embeddings (of 176 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.176
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
\(23\) \(-1\)
\(349\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{176} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8027))\).