# 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

# 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: $$0$$ 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.

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

## 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 −2.76919 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: 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 $$S_{2}^{\mathrm{new}}(\Gamma_0(8015))$$:

 $$T_{2}^{68} - \cdots$$ $$T_{3}^{68} - \cdots$$