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

Related objects

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.

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

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 −2.78224 −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: Complex embeddings Normalized embeddings Satake parameters Satake angles

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

 $$T_{2}^{45} + \cdots$$ $$T_{3}^{45} - \cdots$$