Properties

Label 8015.2.a.j
Level 8015
Weight 2
Character orbit 8015.a
Self dual Yes
Analytic conductor 64.000
Analytic rank 1
Dimension 45
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: \(1\)
Dimension: \(45\)
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.

\(\operatorname{Tr}(f)(q) = \) \(45q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut -\mathstrut 45q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 45q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 29q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(45q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut -\mathstrut 45q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 45q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 29q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut q^{11} \) \(\mathstrut -\mathstrut 3q^{12} \) \(\mathstrut -\mathstrut 21q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 7q^{17} \) \(\mathstrut -\mathstrut 36q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 34q^{22} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut +\mathstrut 45q^{25} \) \(\mathstrut -\mathstrut q^{26} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 34q^{28} \) \(\mathstrut +\mathstrut 10q^{29} \) \(\mathstrut -\mathstrut q^{30} \) \(\mathstrut -\mathstrut 27q^{31} \) \(\mathstrut -\mathstrut 26q^{32} \) \(\mathstrut -\mathstrut 39q^{33} \) \(\mathstrut -\mathstrut 13q^{34} \) \(\mathstrut -\mathstrut 45q^{35} \) \(\mathstrut -\mathstrut 3q^{36} \) \(\mathstrut -\mathstrut 72q^{37} \) \(\mathstrut +\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 37q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut q^{42} \) \(\mathstrut -\mathstrut 49q^{43} \) \(\mathstrut +\mathstrut 5q^{44} \) \(\mathstrut -\mathstrut 29q^{45} \) \(\mathstrut -\mathstrut 67q^{46} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 8q^{48} \) \(\mathstrut +\mathstrut 45q^{49} \) \(\mathstrut -\mathstrut 6q^{50} \) \(\mathstrut -\mathstrut 49q^{51} \) \(\mathstrut -\mathstrut 47q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 12q^{54} \) \(\mathstrut +\mathstrut q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 77q^{57} \) \(\mathstrut -\mathstrut 50q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 3q^{60} \) \(\mathstrut -\mathstrut 36q^{61} \) \(\mathstrut +\mathstrut 17q^{62} \) \(\mathstrut +\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 5q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut -\mathstrut 8q^{66} \) \(\mathstrut -\mathstrut 80q^{67} \) \(\mathstrut +\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 12q^{71} \) \(\mathstrut -\mathstrut 97q^{72} \) \(\mathstrut -\mathstrut 55q^{73} \) \(\mathstrut +\mathstrut 32q^{74} \) \(\mathstrut -\mathstrut 37q^{76} \) \(\mathstrut -\mathstrut q^{77} \) \(\mathstrut +\mathstrut 20q^{78} \) \(\mathstrut -\mathstrut 94q^{79} \) \(\mathstrut -\mathstrut 8q^{80} \) \(\mathstrut -\mathstrut 19q^{81} \) \(\mathstrut -\mathstrut 36q^{82} \) \(\mathstrut +\mathstrut 24q^{83} \) \(\mathstrut -\mathstrut 3q^{84} \) \(\mathstrut +\mathstrut 7q^{85} \) \(\mathstrut -\mathstrut 3q^{86} \) \(\mathstrut -\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut +\mathstrut 36q^{90} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 65q^{92} \) \(\mathstrut -\mathstrut 71q^{93} \) \(\mathstrut -\mathstrut 53q^{94} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 13q^{96} \) \(\mathstrut -\mathstrut 110q^{97} \) \(\mathstrut -\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.78224 −1.94372 5.74083 −1.00000 5.40788 1.00000 −10.4079 0.778035 2.78224
1.2 −2.58820 1.46821 4.69879 −1.00000 −3.80002 1.00000 −6.98503 −0.844367 2.58820
1.3 −2.51360 3.19000 4.31820 −1.00000 −8.01840 1.00000 −5.82702 7.17611 2.51360
1.4 −2.46499 0.580032 4.07617 −1.00000 −1.42977 1.00000 −5.11774 −2.66356 2.46499
1.5 −2.28900 0.276088 3.23954 −1.00000 −0.631967 1.00000 −2.83731 −2.92378 2.28900
1.6 −2.26339 2.16114 3.12292 −1.00000 −4.89149 1.00000 −2.54160 1.67051 2.26339
1.7 −2.24619 −2.43741 3.04539 −1.00000 5.47490 1.00000 −2.34814 2.94098 2.24619
1.8 −2.21589 −3.14559 2.91017 −1.00000 6.97028 1.00000 −2.01683 6.89472 2.21589
1.9 −1.81008 −0.874461 1.27639 −1.00000 1.58284 1.00000 1.30979 −2.23532 1.81008
1.10 −1.69745 0.851741 0.881321 −1.00000 −1.44578 1.00000 1.89890 −2.27454 1.69745
1.11 −1.67660 −1.48567 0.810994 −1.00000 2.49087 1.00000 1.99349 −0.792790 1.67660
1.12 −1.65958 −1.94100 0.754194 −1.00000 3.22125 1.00000 2.06751 0.767498 1.65958
1.13 −1.60365 2.74735 0.571694 −1.00000 −4.40579 1.00000 2.29050 4.54792 1.60365
1.14 −1.48089 −0.908664 0.193023 −1.00000 1.34563 1.00000 2.67593 −2.17433 1.48089
1.15 −1.27565 −2.40768 −0.372716 −1.00000 3.07136 1.00000 3.02676 2.79693 1.27565
1.16 −1.13794 1.06234 −0.705083 −1.00000 −1.20889 1.00000 3.07823 −1.87143 1.13794
1.17 −0.903684 3.04554 −1.18335 −1.00000 −2.75220 1.00000 2.87675 6.27529 0.903684
1.18 −0.883459 2.68305 −1.21950 −1.00000 −2.37036 1.00000 2.84430 4.19874 0.883459
1.19 −0.647127 −0.415940 −1.58123 −1.00000 0.269166 1.00000 2.31751 −2.82699 0.647127
1.20 −0.556743 −0.855264 −1.69004 −1.00000 0.476163 1.00000 2.05440 −2.26852 0.556743
See all 45 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.45
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\):

\(T_{2}^{45} + \cdots\)
\(T_{3}^{45} - \cdots\)