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.

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

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 −2.77376 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:
Format:

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\):

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