Properties

Label 8035.2.a.b
Level 8035
Weight 2
Character orbit 8035.a
Self dual Yes
Analytic conductor 64.160
Analytic rank 1
Dimension 114
CM No

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Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(1\)
Dimension: \(114\)
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.

\(\operatorname{Tr}(f)(q) = \) \(114q \) \(\mathstrut -\mathstrut 17q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut +\mathstrut 114q^{5} \) \(\mathstrut -\mathstrut 24q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 66q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(114q \) \(\mathstrut -\mathstrut 17q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut +\mathstrut 114q^{5} \) \(\mathstrut -\mathstrut 24q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 66q^{9} \) \(\mathstrut -\mathstrut 17q^{10} \) \(\mathstrut -\mathstrut 44q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 26q^{13} \) \(\mathstrut -\mathstrut 43q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 59q^{16} \) \(\mathstrut -\mathstrut 57q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 69q^{19} \) \(\mathstrut +\mathstrut 93q^{20} \) \(\mathstrut -\mathstrut 107q^{21} \) \(\mathstrut -\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 45q^{24} \) \(\mathstrut +\mathstrut 114q^{25} \) \(\mathstrut -\mathstrut 54q^{26} \) \(\mathstrut -\mathstrut 34q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut -\mathstrut 166q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 67q^{31} \) \(\mathstrut -\mathstrut 98q^{32} \) \(\mathstrut -\mathstrut 38q^{33} \) \(\mathstrut -\mathstrut 41q^{34} \) \(\mathstrut -\mathstrut 11q^{35} \) \(\mathstrut -\mathstrut 3q^{36} \) \(\mathstrut -\mathstrut 44q^{37} \) \(\mathstrut -\mathstrut 19q^{38} \) \(\mathstrut -\mathstrut 66q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 141q^{41} \) \(\mathstrut +\mathstrut q^{42} \) \(\mathstrut -\mathstrut 30q^{43} \) \(\mathstrut -\mathstrut 125q^{44} \) \(\mathstrut +\mathstrut 66q^{45} \) \(\mathstrut -\mathstrut 59q^{46} \) \(\mathstrut -\mathstrut 17q^{47} \) \(\mathstrut -\mathstrut 35q^{48} \) \(\mathstrut -\mathstrut 15q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 67q^{51} \) \(\mathstrut -\mathstrut 26q^{52} \) \(\mathstrut -\mathstrut 154q^{53} \) \(\mathstrut -\mathstrut 45q^{54} \) \(\mathstrut -\mathstrut 44q^{55} \) \(\mathstrut -\mathstrut 118q^{56} \) \(\mathstrut -\mathstrut 70q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut -\mathstrut 25q^{60} \) \(\mathstrut -\mathstrut 144q^{61} \) \(\mathstrut -\mathstrut 35q^{62} \) \(\mathstrut -\mathstrut 25q^{63} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 26q^{65} \) \(\mathstrut -\mathstrut 68q^{66} \) \(\mathstrut -\mathstrut 2q^{67} \) \(\mathstrut -\mathstrut 99q^{68} \) \(\mathstrut -\mathstrut 118q^{69} \) \(\mathstrut -\mathstrut 43q^{70} \) \(\mathstrut -\mathstrut 104q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 107q^{74} \) \(\mathstrut -\mathstrut 10q^{75} \) \(\mathstrut -\mathstrut 172q^{76} \) \(\mathstrut -\mathstrut 100q^{77} \) \(\mathstrut -\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 91q^{79} \) \(\mathstrut +\mathstrut 59q^{80} \) \(\mathstrut -\mathstrut 54q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut -\mathstrut 156q^{84} \) \(\mathstrut -\mathstrut 57q^{85} \) \(\mathstrut -\mathstrut 50q^{86} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 150q^{89} \) \(\mathstrut -\mathstrut 33q^{90} \) \(\mathstrut -\mathstrut 54q^{91} \) \(\mathstrut -\mathstrut 77q^{92} \) \(\mathstrut -\mathstrut 50q^{93} \) \(\mathstrut -\mathstrut 105q^{94} \) \(\mathstrut -\mathstrut 69q^{95} \) \(\mathstrut -\mathstrut 78q^{96} \) \(\mathstrut -\mathstrut 31q^{97} \) \(\mathstrut -\mathstrut 64q^{98} \) \(\mathstrut -\mathstrut 101q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.80100 2.46905 5.84558 1.00000 −6.91579 0.471155 −10.7715 3.09620 −2.80100
1.2 −2.78782 −2.79744 5.77196 1.00000 7.79878 4.93098 −10.5155 4.82570 −2.78782
1.3 −2.71845 −0.706981 5.38997 1.00000 1.92189 −1.47518 −9.21545 −2.50018 −2.71845
1.4 −2.70261 −0.768131 5.30408 1.00000 2.07595 0.883099 −8.92963 −2.40998 −2.70261
1.5 −2.64032 0.589008 4.97127 1.00000 −1.55517 2.76981 −7.84509 −2.65307 −2.64032
1.6 −2.56613 −1.08918 4.58500 1.00000 2.79497 0.189836 −6.63344 −1.81369 −2.56613
1.7 −2.55456 3.12928 4.52579 1.00000 −7.99394 −0.305694 −6.45228 6.79240 −2.55456
1.8 −2.52790 2.08229 4.39026 1.00000 −5.26382 −1.56131 −6.04233 1.33594 −2.52790
1.9 −2.52703 0.421733 4.38589 1.00000 −1.06573 −3.93159 −6.02922 −2.82214 −2.52703
1.10 −2.49776 0.530865 4.23883 1.00000 −1.32598 3.05763 −5.59207 −2.71818 −2.49776
1.11 −2.43125 1.69464 3.91096 1.00000 −4.12009 3.32974 −4.64601 −0.128198 −2.43125
1.12 −2.42522 −2.38106 3.88170 1.00000 5.77461 1.76614 −4.56353 2.66946 −2.42522
1.13 −2.41255 0.682970 3.82038 1.00000 −1.64770 −2.72500 −4.39175 −2.53355 −2.41255
1.14 −2.39306 2.37672 3.72672 1.00000 −5.68762 −3.85134 −4.13213 2.64878 −2.39306
1.15 −2.24666 −1.32930 3.04747 1.00000 2.98648 −2.44152 −2.35330 −1.23296 −2.24666
1.16 −2.22296 −1.69364 2.94157 1.00000 3.76490 0.866301 −2.09307 −0.131588 −2.22296
1.17 −2.17370 0.0354109 2.72495 1.00000 −0.0769725 3.07468 −1.57583 −2.99875 −2.17370
1.18 −2.14559 −2.44526 2.60354 1.00000 5.24651 −2.98560 −1.29496 2.97929 −2.14559
1.19 −2.12278 −3.22748 2.50621 1.00000 6.85125 1.25827 −1.07458 7.41664 −2.12278
1.20 −2.11941 −2.29188 2.49192 1.00000 4.85744 5.02774 −1.04258 2.25270 −2.11941
See next 80 embeddings (of 114 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.114
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(1607\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{114} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8035))\).