Properties

Label 6015.2.a.c
Level 6015
Weight 2
Character orbit 6015.a
Self dual Yes
Analytic conductor 48.030
Analytic rank 1
Dimension 28
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: \(1\)
Dimension: \(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \(28q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 28q^{3} \) \(\mathstrut +\mathstrut 21q^{4} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 20q^{7} \) \(\mathstrut +\mathstrut 28q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(28q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 28q^{3} \) \(\mathstrut +\mathstrut 21q^{4} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 20q^{7} \) \(\mathstrut +\mathstrut 28q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut q^{11} \) \(\mathstrut +\mathstrut 21q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 28q^{15} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut -\mathstrut 28q^{17} \) \(\mathstrut -\mathstrut q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 35q^{22} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut -\mathstrut 20q^{26} \) \(\mathstrut +\mathstrut 28q^{27} \) \(\mathstrut -\mathstrut 54q^{28} \) \(\mathstrut +\mathstrut 9q^{29} \) \(\mathstrut +\mathstrut q^{30} \) \(\mathstrut -\mathstrut 19q^{31} \) \(\mathstrut -\mathstrut 6q^{32} \) \(\mathstrut -\mathstrut q^{33} \) \(\mathstrut -\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 21q^{36} \) \(\mathstrut -\mathstrut 32q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 18q^{39} \) \(\mathstrut -\mathstrut 27q^{41} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut -\mathstrut 77q^{43} \) \(\mathstrut +\mathstrut q^{44} \) \(\mathstrut -\mathstrut 28q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 34q^{52} \) \(\mathstrut -\mathstrut 21q^{53} \) \(\mathstrut -\mathstrut q^{54} \) \(\mathstrut +\mathstrut q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut -\mathstrut 19q^{57} \) \(\mathstrut -\mathstrut 46q^{58} \) \(\mathstrut -\mathstrut 7q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 46q^{64} \) \(\mathstrut +\mathstrut 18q^{65} \) \(\mathstrut -\mathstrut 35q^{66} \) \(\mathstrut -\mathstrut 50q^{67} \) \(\mathstrut -\mathstrut 68q^{68} \) \(\mathstrut +\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut 4q^{70} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 87q^{73} \) \(\mathstrut +\mathstrut 4q^{74} \) \(\mathstrut +\mathstrut 28q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut -\mathstrut 65q^{79} \) \(\mathstrut +\mathstrut q^{80} \) \(\mathstrut +\mathstrut 28q^{81} \) \(\mathstrut -\mathstrut 41q^{82} \) \(\mathstrut +\mathstrut 13q^{83} \) \(\mathstrut -\mathstrut 54q^{84} \) \(\mathstrut +\mathstrut 28q^{85} \) \(\mathstrut -\mathstrut 17q^{86} \) \(\mathstrut +\mathstrut 9q^{87} \) \(\mathstrut -\mathstrut 117q^{88} \) \(\mathstrut -\mathstrut 33q^{89} \) \(\mathstrut +\mathstrut q^{90} \) \(\mathstrut -\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 19q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut -\mathstrut 75q^{97} \) \(\mathstrut -\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.60633 1.00000 4.79297 −1.00000 −2.60633 −3.84306 −7.27940 1.00000 2.60633
1.2 −2.51673 1.00000 4.33393 −1.00000 −2.51673 −0.0213252 −5.87387 1.00000 2.51673
1.3 −2.31182 1.00000 3.34451 −1.00000 −2.31182 −2.77511 −3.10826 1.00000 2.31182
1.4 −2.11452 1.00000 2.47118 −1.00000 −2.11452 1.95178 −0.996316 1.00000 2.11452
1.5 −1.92652 1.00000 1.71147 −1.00000 −1.92652 1.15268 0.555850 1.00000 1.92652
1.6 −1.85217 1.00000 1.43054 −1.00000 −1.85217 −4.50663 1.05474 1.00000 1.85217
1.7 −1.62087 1.00000 0.627218 −1.00000 −1.62087 2.78454 2.22510 1.00000 1.62087
1.8 −1.59553 1.00000 0.545711 −1.00000 −1.59553 −0.379773 2.32036 1.00000 1.59553
1.9 −1.45436 1.00000 0.115161 −1.00000 −1.45436 −2.79967 2.74123 1.00000 1.45436
1.10 −0.932405 1.00000 −1.13062 −1.00000 −0.932405 3.48092 2.91901 1.00000 0.932405
1.11 −0.711184 1.00000 −1.49422 −1.00000 −0.711184 −4.85706 2.48503 1.00000 0.711184
1.12 −0.549158 1.00000 −1.69842 −1.00000 −0.549158 0.129960 2.03102 1.00000 0.549158
1.13 −0.517037 1.00000 −1.73267 −1.00000 −0.517037 1.87988 1.92993 1.00000 0.517037
1.14 −0.327847 1.00000 −1.89252 −1.00000 −0.327847 −1.80659 1.27615 1.00000 0.327847
1.15 0.113161 1.00000 −1.98719 −1.00000 0.113161 2.66791 −0.451194 1.00000 −0.113161
1.16 0.344505 1.00000 −1.88132 −1.00000 0.344505 −3.88123 −1.33713 1.00000 −0.344505
1.17 0.403903 1.00000 −1.83686 −1.00000 0.403903 0.330671 −1.54972 1.00000 −0.403903
1.18 0.886913 1.00000 −1.21339 −1.00000 0.886913 2.28245 −2.84999 1.00000 −0.886913
1.19 0.894188 1.00000 −1.20043 −1.00000 0.894188 −1.23837 −2.86178 1.00000 −0.894188
1.20 0.902444 1.00000 −1.18560 −1.00000 0.902444 −2.02428 −2.87482 1.00000 −0.902444
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.28
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 \(T_{2}^{28} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6015))\).