Properties

Label 6015.2.a.i
Level 6015
Weight 2
Character orbit 6015.a
Self dual Yes
Analytic conductor 48.030
Analytic rank 0
Dimension 43
CM No

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Newspace parameters

Level: \( N \) = \( 6015 = 3 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0300168158\)
Analytic rank: \(0\)
Dimension: \(43\)
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.

\(\operatorname{Tr}(f)(q) = \) \(43q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 43q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 14q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 43q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(43q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 43q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 14q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 43q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut +\mathstrut 19q^{11} \) \(\mathstrut +\mathstrut 61q^{12} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 43q^{15} \) \(\mathstrut +\mathstrut 85q^{16} \) \(\mathstrut +\mathstrut 40q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 43q^{19} \) \(\mathstrut +\mathstrut 61q^{20} \) \(\mathstrut +\mathstrut 14q^{21} \) \(\mathstrut +\mathstrut 19q^{22} \) \(\mathstrut +\mathstrut 12q^{23} \) \(\mathstrut +\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 43q^{25} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 36q^{28} \) \(\mathstrut +\mathstrut 41q^{29} \) \(\mathstrut +\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 33q^{31} \) \(\mathstrut +\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 19q^{33} \) \(\mathstrut +\mathstrut 20q^{34} \) \(\mathstrut +\mathstrut 14q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 18q^{40} \) \(\mathstrut +\mathstrut 47q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut +\mathstrut 73q^{43} \) \(\mathstrut +\mathstrut 5q^{44} \) \(\mathstrut +\mathstrut 43q^{45} \) \(\mathstrut +\mathstrut 21q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut +\mathstrut 85q^{48} \) \(\mathstrut +\mathstrut 87q^{49} \) \(\mathstrut +\mathstrut 3q^{50} \) \(\mathstrut +\mathstrut 40q^{51} \) \(\mathstrut +\mathstrut 18q^{52} \) \(\mathstrut +\mathstrut 17q^{53} \) \(\mathstrut +\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 19q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 43q^{57} \) \(\mathstrut -\mathstrut 16q^{58} \) \(\mathstrut +\mathstrut 21q^{59} \) \(\mathstrut +\mathstrut 61q^{60} \) \(\mathstrut +\mathstrut 77q^{61} \) \(\mathstrut +\mathstrut 15q^{62} \) \(\mathstrut +\mathstrut 14q^{63} \) \(\mathstrut +\mathstrut 112q^{64} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 26q^{67} \) \(\mathstrut +\mathstrut 50q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut +\mathstrut 2q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 49q^{73} \) \(\mathstrut -\mathstrut 34q^{74} \) \(\mathstrut +\mathstrut 43q^{75} \) \(\mathstrut +\mathstrut 50q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 59q^{79} \) \(\mathstrut +\mathstrut 85q^{80} \) \(\mathstrut +\mathstrut 43q^{81} \) \(\mathstrut -\mathstrut 45q^{82} \) \(\mathstrut -\mathstrut 3q^{83} \) \(\mathstrut +\mathstrut 36q^{84} \) \(\mathstrut +\mathstrut 40q^{85} \) \(\mathstrut -\mathstrut 35q^{86} \) \(\mathstrut +\mathstrut 41q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 57q^{89} \) \(\mathstrut +\mathstrut 3q^{90} \) \(\mathstrut +\mathstrut 11q^{91} \) \(\mathstrut -\mathstrut 9q^{92} \) \(\mathstrut +\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 52q^{94} \) \(\mathstrut +\mathstrut 43q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 7q^{97} \) \(\mathstrut -\mathstrut 32q^{98} \) \(\mathstrut +\mathstrut 19q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.80316 1.00000 5.85773 1.00000 −2.80316 1.72166 −10.8139 1.00000 −2.80316
1.2 −2.71814 1.00000 5.38826 1.00000 −2.71814 −4.08781 −9.20975 1.00000 −2.71814
1.3 −2.63729 1.00000 4.95532 1.00000 −2.63729 3.21800 −7.79405 1.00000 −2.63729
1.4 −2.53504 1.00000 4.42643 1.00000 −2.53504 3.85984 −6.15109 1.00000 −2.53504
1.5 −2.53356 1.00000 4.41894 1.00000 −2.53356 1.97049 −6.12853 1.00000 −2.53356
1.6 −2.26589 1.00000 3.13426 1.00000 −2.26589 −0.747264 −2.57010 1.00000 −2.26589
1.7 −2.07772 1.00000 2.31692 1.00000 −2.07772 −4.42665 −0.658463 1.00000 −2.07772
1.8 −1.89266 1.00000 1.58218 1.00000 −1.89266 −3.83242 0.790801 1.00000 −1.89266
1.9 −1.87550 1.00000 1.51750 1.00000 −1.87550 3.82548 0.904923 1.00000 −1.87550
1.10 −1.83425 1.00000 1.36446 1.00000 −1.83425 0.959721 1.16574 1.00000 −1.83425
1.11 −1.80049 1.00000 1.24176 1.00000 −1.80049 −4.47883 1.36520 1.00000 −1.80049
1.12 −1.69499 1.00000 0.872981 1.00000 −1.69499 4.08936 1.91028 1.00000 −1.69499
1.13 −1.41364 1.00000 −0.00162729 1.00000 −1.41364 −1.83352 2.82958 1.00000 −1.41364
1.14 −1.30521 1.00000 −0.296439 1.00000 −1.30521 1.84814 2.99732 1.00000 −1.30521
1.15 −1.15381 1.00000 −0.668729 1.00000 −1.15381 −0.585541 3.07920 1.00000 −1.15381
1.16 −0.979152 1.00000 −1.04126 1.00000 −0.979152 4.18408 2.97786 1.00000 −0.979152
1.17 −0.762858 1.00000 −1.41805 1.00000 −0.762858 −2.97870 2.60748 1.00000 −0.762858
1.18 −0.497996 1.00000 −1.75200 1.00000 −0.497996 2.05942 1.86848 1.00000 −0.497996
1.19 −0.439798 1.00000 −1.80658 1.00000 −0.439798 −0.915251 1.67413 1.00000 −0.439798
1.20 −0.211503 1.00000 −1.95527 1.00000 −0.211503 3.03461 0.836552 1.00000 −0.211503
See all 43 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.43
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(5\) \(-1\)
\(401\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{43} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6015))\).