Properties

Label 8015.2.a.o
Level 8015
Weight 2
Character orbit 8015.a
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 73
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(73\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 73q + 7q^{2} + 14q^{3} + 95q^{4} + 73q^{5} - q^{6} + 73q^{7} + 18q^{8} + 111q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 73q + 7q^{2} + 14q^{3} + 95q^{4} + 73q^{5} - q^{6} + 73q^{7} + 18q^{8} + 111q^{9} + 7q^{10} + 27q^{11} + 21q^{12} + 21q^{13} + 7q^{14} + 14q^{15} + 135q^{16} + 23q^{17} + 41q^{18} + 26q^{19} + 95q^{20} + 14q^{21} + 48q^{22} + 16q^{23} - q^{24} + 73q^{25} + 7q^{26} + 44q^{27} + 95q^{28} + 66q^{29} - q^{30} + 23q^{31} + 3q^{32} + 77q^{33} + 29q^{34} + 73q^{35} + 142q^{36} + 66q^{37} - 12q^{38} + 53q^{39} + 18q^{40} + 50q^{41} - q^{42} + 43q^{43} + 37q^{44} + 111q^{45} + 65q^{46} + 28q^{47} - 20q^{48} + 73q^{49} + 7q^{50} + 71q^{51} + 29q^{52} - 7q^{53} - 16q^{54} + 27q^{55} + 18q^{56} + 33q^{57} + 48q^{58} + 16q^{59} + 21q^{60} + 42q^{61} - 3q^{62} + 111q^{63} + 216q^{64} + 21q^{65} - 53q^{66} + 48q^{67} + 13q^{68} + 73q^{69} + 7q^{70} + 68q^{71} + 18q^{72} + 65q^{73} + 4q^{74} + 14q^{75} + 37q^{76} + 27q^{77} + 60q^{78} + 116q^{79} + 135q^{80} + 177q^{81} + 20q^{82} + 40q^{83} + 21q^{84} + 23q^{85} + 35q^{86} - 14q^{87} + 47q^{88} + 59q^{89} + 41q^{90} + 21q^{91} + 3q^{92} + 37q^{93} - 11q^{94} + 26q^{95} - 23q^{96} + 70q^{97} + 7q^{98} + 49q^{99} + O(q^{100}) \)

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 −2.77376 0.883907 5.69373 1.00000 −2.45174 1.00000 −10.2455 −2.21871 −2.77376
1.2 −2.76326 3.03127 5.63562 1.00000 −8.37621 1.00000 −10.0462 6.18862 −2.76326
1.3 −2.72942 −2.22505 5.44974 1.00000 6.07311 1.00000 −9.41580 1.95086 −2.72942
1.4 −2.69749 −3.25136 5.27643 1.00000 8.77051 1.00000 −8.83812 7.57137 −2.69749
1.5 −2.68177 −0.319561 5.19187 1.00000 0.856987 1.00000 −8.55985 −2.89788 −2.68177
1.6 −2.45360 1.56371 4.02015 1.00000 −3.83672 1.00000 −4.95665 −0.554809 −2.45360
1.7 −2.45327 3.30020 4.01854 1.00000 −8.09629 1.00000 −4.95203 7.89132 −2.45327
1.8 −2.45229 −0.606235 4.01370 1.00000 1.48666 1.00000 −4.93818 −2.63248 −2.45229
1.9 −2.41178 −1.36759 3.81666 1.00000 3.29833 1.00000 −4.38139 −1.12969 −2.41178
1.10 −2.29631 0.975796 3.27305 1.00000 −2.24073 1.00000 −2.92333 −2.04782 −2.29631
1.11 −2.19612 2.45439 2.82293 1.00000 −5.39013 1.00000 −1.80725 3.02403 −2.19612
1.12 −2.19191 −0.935723 2.80448 1.00000 2.05102 1.00000 −1.76336 −2.12442 −2.19191
1.13 −2.08852 −0.140980 2.36194 1.00000 0.294440 1.00000 −0.755913 −2.98012 −2.08852
1.14 −2.01224 2.54989 2.04911 1.00000 −5.13098 1.00000 −0.0988175 3.50192 −2.01224
1.15 −1.86693 −0.178602 1.48541 1.00000 0.333437 1.00000 0.960700 −2.96810 −1.86693
1.16 −1.84781 −2.80168 1.41441 1.00000 5.17697 1.00000 1.08207 4.84939 −1.84781
1.17 −1.63497 2.59836 0.673111 1.00000 −4.24822 1.00000 2.16942 3.75146 −1.63497
1.18 −1.53607 −1.95086 0.359523 1.00000 2.99667 1.00000 2.51989 0.805862 −1.53607
1.19 −1.50054 2.96680 0.251626 1.00000 −4.45181 1.00000 2.62351 5.80192 −1.50054
1.20 −1.40112 2.16021 −0.0368596 1.00000 −3.02672 1.00000 2.85389 1.66651 −1.40112
See all 73 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.73
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
\(5\) \(-1\)
\(7\) \(-1\)
\(229\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\):

\(T_{2}^{73} - \cdots\)
\(T_{3}^{73} - \cdots\)