Properties

Label 8015.2.a.m
Level 8015
Weight 2
Character orbit 8015.a
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 67
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: \(67\)
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.

\(\operatorname{Tr}(f)(q) = \) \(67q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 73q^{4} \) \(\mathstrut +\mathstrut 67q^{5} \) \(\mathstrut +\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 67q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(67q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 73q^{4} \) \(\mathstrut +\mathstrut 67q^{5} \) \(\mathstrut +\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 67q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut +\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 9q^{12} \) \(\mathstrut +\mathstrut 19q^{13} \) \(\mathstrut -\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 93q^{16} \) \(\mathstrut +\mathstrut 7q^{17} \) \(\mathstrut +\mathstrut 9q^{18} \) \(\mathstrut +\mathstrut 36q^{19} \) \(\mathstrut +\mathstrut 73q^{20} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 37q^{24} \) \(\mathstrut +\mathstrut 67q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 6q^{27} \) \(\mathstrut -\mathstrut 73q^{28} \) \(\mathstrut +\mathstrut 56q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 63q^{31} \) \(\mathstrut +\mathstrut 27q^{32} \) \(\mathstrut +\mathstrut 51q^{33} \) \(\mathstrut +\mathstrut 55q^{34} \) \(\mathstrut -\mathstrut 67q^{35} \) \(\mathstrut +\mathstrut 148q^{36} \) \(\mathstrut +\mathstrut 28q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 84q^{41} \) \(\mathstrut -\mathstrut 17q^{42} \) \(\mathstrut -\mathstrut 11q^{43} \) \(\mathstrut +\mathstrut 41q^{44} \) \(\mathstrut +\mathstrut 97q^{45} \) \(\mathstrut +\mathstrut 17q^{46} \) \(\mathstrut -\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut +\mathstrut 3q^{50} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut +\mathstrut 49q^{52} \) \(\mathstrut +\mathstrut 3q^{53} \) \(\mathstrut +\mathstrut 20q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut -\mathstrut 12q^{56} \) \(\mathstrut +\mathstrut 45q^{57} \) \(\mathstrut +\mathstrut 22q^{58} \) \(\mathstrut +\mathstrut 80q^{59} \) \(\mathstrut +\mathstrut 9q^{60} \) \(\mathstrut +\mathstrut 64q^{61} \) \(\mathstrut -\mathstrut 37q^{62} \) \(\mathstrut -\mathstrut 97q^{63} \) \(\mathstrut +\mathstrut 110q^{64} \) \(\mathstrut +\mathstrut 19q^{65} \) \(\mathstrut +\mathstrut 75q^{66} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 7q^{68} \) \(\mathstrut +\mathstrut 107q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut +\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 83q^{73} \) \(\mathstrut +\mathstrut 52q^{74} \) \(\mathstrut +\mathstrut 115q^{76} \) \(\mathstrut -\mathstrut 11q^{77} \) \(\mathstrut -\mathstrut 70q^{78} \) \(\mathstrut -\mathstrut 32q^{79} \) \(\mathstrut +\mathstrut 93q^{80} \) \(\mathstrut +\mathstrut 183q^{81} \) \(\mathstrut +\mathstrut 56q^{82} \) \(\mathstrut -\mathstrut 58q^{83} \) \(\mathstrut -\mathstrut 9q^{84} \) \(\mathstrut +\mathstrut 7q^{85} \) \(\mathstrut +\mathstrut 51q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 5q^{88} \) \(\mathstrut +\mathstrut 129q^{89} \) \(\mathstrut +\mathstrut 9q^{90} \) \(\mathstrut -\mathstrut 19q^{91} \) \(\mathstrut -\mathstrut 37q^{92} \) \(\mathstrut +\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 89q^{94} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut +\mathstrut 129q^{96} \) \(\mathstrut +\mathstrut 126q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.79998 −2.08197 5.83989 1.00000 5.82947 −1.00000 −10.7516 1.33460 −2.79998
1.2 −2.72902 1.60790 5.44753 1.00000 −4.38799 −1.00000 −9.40835 −0.414653 −2.72902
1.3 −2.66598 2.60914 5.10744 1.00000 −6.95591 −1.00000 −8.28438 3.80761 −2.66598
1.4 −2.55168 −1.07267 4.51109 1.00000 2.73711 −1.00000 −6.40752 −1.84938 −2.55168
1.5 −2.54658 −2.85949 4.48508 1.00000 7.28192 −1.00000 −6.32845 5.17667 −2.54658
1.6 −2.53656 −2.78475 4.43415 1.00000 7.06368 −1.00000 −6.17438 4.75481 −2.53656
1.7 −2.40339 −1.71467 3.77630 1.00000 4.12102 −1.00000 −4.26915 −0.0599106 −2.40339
1.8 −2.30662 1.34001 3.32049 1.00000 −3.09089 −1.00000 −3.04587 −1.20437 −2.30662
1.9 −2.25277 3.29965 3.07495 1.00000 −7.43334 −1.00000 −2.42162 7.88769 −2.25277
1.10 −2.05677 1.58909 2.23031 1.00000 −3.26839 −1.00000 −0.473688 −0.474802 −2.05677
1.11 −1.94503 2.18285 1.78313 1.00000 −4.24571 −1.00000 0.421811 1.76484 −1.94503
1.12 −1.89706 −1.32001 1.59885 1.00000 2.50414 −1.00000 0.761013 −1.25758 −1.89706
1.13 −1.83785 1.36680 1.37770 1.00000 −2.51199 −1.00000 1.14369 −1.13184 −1.83785
1.14 −1.82956 −1.24341 1.34731 1.00000 2.27489 −1.00000 1.19414 −1.45394 −1.82956
1.15 −1.80341 0.567965 1.25230 1.00000 −1.02428 −1.00000 1.34841 −2.67742 −1.80341
1.16 −1.76232 −3.28691 1.10578 1.00000 5.79259 −1.00000 1.57590 7.80377 −1.76232
1.17 −1.76209 −0.304110 1.10496 1.00000 0.535869 −1.00000 1.57714 −2.90752 −1.76209
1.18 −1.50021 0.266806 0.250644 1.00000 −0.400267 −1.00000 2.62441 −2.92881 −1.50021
1.19 −1.44039 2.88342 0.0747197 1.00000 −4.15325 −1.00000 2.77315 5.31413 −1.44039
1.20 −1.42994 −3.33526 0.0447232 1.00000 4.76921 −1.00000 2.79592 8.12394 −1.42994
See all 67 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.67
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\):

\(T_{2}^{67} - \cdots\)
\(T_{3}^{67} - \cdots\)