Properties

Label 8015.2.a.n
Level 8015
Weight 2
Character orbit 8015.a
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 68
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: \(68\)
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.

\(\operatorname{Tr}(f)(q) = \) \(68q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 83q^{4} \) \(\mathstrut -\mathstrut 68q^{5} \) \(\mathstrut +\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 68q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 86q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(68q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 83q^{4} \) \(\mathstrut -\mathstrut 68q^{5} \) \(\mathstrut +\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 68q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 86q^{9} \) \(\mathstrut -\mathstrut 9q^{10} \) \(\mathstrut +\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 9q^{12} \) \(\mathstrut +\mathstrut 15q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut +\mathstrut 109q^{16} \) \(\mathstrut +\mathstrut 7q^{17} \) \(\mathstrut +\mathstrut 39q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 83q^{20} \) \(\mathstrut +\mathstrut 56q^{22} \) \(\mathstrut +\mathstrut 36q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut 68q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 83q^{28} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut -\mathstrut 5q^{30} \) \(\mathstrut +\mathstrut 31q^{31} \) \(\mathstrut +\mathstrut 79q^{32} \) \(\mathstrut +\mathstrut 45q^{33} \) \(\mathstrut +\mathstrut 31q^{34} \) \(\mathstrut -\mathstrut 68q^{35} \) \(\mathstrut +\mathstrut 114q^{36} \) \(\mathstrut +\mathstrut 72q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 47q^{39} \) \(\mathstrut -\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 75q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut -\mathstrut 86q^{45} \) \(\mathstrut +\mathstrut 29q^{46} \) \(\mathstrut -\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 44q^{48} \) \(\mathstrut +\mathstrut 68q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 37q^{52} \) \(\mathstrut +\mathstrut 41q^{53} \) \(\mathstrut +\mathstrut 4q^{54} \) \(\mathstrut -\mathstrut 5q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 55q^{57} \) \(\mathstrut +\mathstrut 66q^{58} \) \(\mathstrut -\mathstrut 5q^{59} \) \(\mathstrut -\mathstrut 9q^{60} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 86q^{63} \) \(\mathstrut +\mathstrut 162q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut -\mathstrut 23q^{66} \) \(\mathstrut +\mathstrut 92q^{67} \) \(\mathstrut +\mathstrut 35q^{68} \) \(\mathstrut -\mathstrut 25q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 2q^{71} \) \(\mathstrut +\mathstrut 128q^{72} \) \(\mathstrut +\mathstrut 80q^{73} \) \(\mathstrut +\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 5q^{77} \) \(\mathstrut +\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 100q^{79} \) \(\mathstrut -\mathstrut 109q^{80} \) \(\mathstrut +\mathstrut 140q^{81} \) \(\mathstrut +\mathstrut 36q^{82} \) \(\mathstrut -\mathstrut 60q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut -\mathstrut 7q^{85} \) \(\mathstrut -\mathstrut 27q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 175q^{88} \) \(\mathstrut +\mathstrut 19q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut +\mathstrut 75q^{92} \) \(\mathstrut +\mathstrut 37q^{93} \) \(\mathstrut +\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 15q^{96} \) \(\mathstrut +\mathstrut 96q^{97} \) \(\mathstrut +\mathstrut 9q^{98} \) \(\mathstrut +\mathstrut 3q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.76919 2.35151 5.66840 −1.00000 −6.51177 1.00000 −10.1585 2.52960 2.76919
1.2 −2.73044 0.281096 5.45528 −1.00000 −0.767515 1.00000 −9.43443 −2.92099 2.73044
1.3 −2.66015 −2.46219 5.07642 −1.00000 6.54979 1.00000 −8.18374 3.06236 2.66015
1.4 −2.55606 −1.84104 4.53346 −1.00000 4.70581 1.00000 −6.47568 0.389420 2.55606
1.5 −2.40811 3.06409 3.79900 −1.00000 −7.37867 1.00000 −4.33220 6.38865 2.40811
1.6 −2.40730 0.0150324 3.79510 −1.00000 −0.0361876 1.00000 −4.32135 −2.99977 2.40730
1.7 −2.33888 −1.00822 3.47038 −1.00000 2.35811 1.00000 −3.43905 −1.98350 2.33888
1.8 −2.33656 2.32181 3.45950 −1.00000 −5.42504 1.00000 −3.41021 2.39080 2.33656
1.9 −2.27050 −2.16931 3.15517 −1.00000 4.92541 1.00000 −2.62281 1.70590 2.27050
1.10 −2.17774 0.311923 2.74253 −1.00000 −0.679286 1.00000 −1.61704 −2.90270 2.17774
1.11 −2.12688 0.933356 2.52363 −1.00000 −1.98514 1.00000 −1.11369 −2.12885 2.12688
1.12 −2.04947 −1.65528 2.20033 −1.00000 3.39245 1.00000 −0.410568 −0.260041 2.04947
1.13 −1.92788 −3.19402 1.71671 −1.00000 6.15768 1.00000 0.546142 7.20176 1.92788
1.14 −1.76060 2.09671 1.09972 −1.00000 −3.69147 1.00000 1.58503 1.39619 1.76060
1.15 −1.66934 1.36319 0.786696 −1.00000 −2.27563 1.00000 2.02542 −1.14171 1.66934
1.16 −1.64550 3.30855 0.707660 −1.00000 −5.44420 1.00000 2.12654 7.94648 1.64550
1.17 −1.48933 −2.36326 0.218100 −1.00000 3.51967 1.00000 2.65384 2.58500 1.48933
1.18 −1.39879 −1.98679 −0.0433739 −1.00000 2.77911 1.00000 2.85826 0.947327 1.39879
1.19 −1.37224 1.58108 −0.116968 −1.00000 −2.16961 1.00000 2.90498 −0.500189 1.37224
1.20 −1.36878 0.541505 −0.126449 −1.00000 −0.741199 1.00000 2.91064 −2.70677 1.36878
See all 68 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.68
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\):

\(T_{2}^{68} - \cdots\)
\(T_{3}^{68} - \cdots\)