Properties

Label 6015.2.a.b
Level 6015
Weight 2
Character orbit 6015.a
Self dual Yes
Analytic conductor 48.030
Analytic rank 1
Dimension 23
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: \(23\)
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.

\(\operatorname{Tr}(f)(q) = \) \(23q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(23q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 23q^{15} \) \(\mathstrut -\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 35q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut -\mathstrut 11q^{22} \) \(\mathstrut -\mathstrut 14q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 23q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut +\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 26q^{28} \) \(\mathstrut -\mathstrut 43q^{29} \) \(\mathstrut -\mathstrut 5q^{30} \) \(\mathstrut -\mathstrut 21q^{31} \) \(\mathstrut -\mathstrut 14q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut -\mathstrut 12q^{34} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 9q^{36} \) \(\mathstrut -\mathstrut 18q^{37} \) \(\mathstrut +\mathstrut 6q^{38} \) \(\mathstrut -\mathstrut 18q^{39} \) \(\mathstrut -\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 45q^{41} \) \(\mathstrut -\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 43q^{43} \) \(\mathstrut -\mathstrut 11q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut -\mathstrut 29q^{46} \) \(\mathstrut -\mathstrut 14q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut -\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 34q^{51} \) \(\mathstrut -\mathstrut 20q^{52} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 3q^{56} \) \(\mathstrut -\mathstrut 35q^{57} \) \(\mathstrut +\mathstrut 10q^{58} \) \(\mathstrut -\mathstrut 9q^{59} \) \(\mathstrut +\mathstrut 9q^{60} \) \(\mathstrut -\mathstrut 67q^{61} \) \(\mathstrut -\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 8q^{64} \) \(\mathstrut -\mathstrut 18q^{65} \) \(\mathstrut -\mathstrut 11q^{66} \) \(\mathstrut -\mathstrut 32q^{67} \) \(\mathstrut -\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 14q^{69} \) \(\mathstrut -\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 8q^{71} \) \(\mathstrut -\mathstrut 12q^{72} \) \(\mathstrut -\mathstrut 39q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut -\mathstrut 48q^{76} \) \(\mathstrut -\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 59q^{79} \) \(\mathstrut -\mathstrut 11q^{80} \) \(\mathstrut +\mathstrut 23q^{81} \) \(\mathstrut -\mathstrut q^{82} \) \(\mathstrut -\mathstrut 23q^{83} \) \(\mathstrut -\mathstrut 26q^{84} \) \(\mathstrut -\mathstrut 34q^{85} \) \(\mathstrut -\mathstrut 7q^{86} \) \(\mathstrut -\mathstrut 43q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 51q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 37q^{91} \) \(\mathstrut +\mathstrut 11q^{92} \) \(\mathstrut -\mathstrut 21q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 35q^{95} \) \(\mathstrut -\mathstrut 14q^{96} \) \(\mathstrut -\mathstrut 29q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 13q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.62638 1.00000 4.89789 1.00000 −2.62638 −0.417980 −7.61099 1.00000 −2.62638
1.2 −2.46180 1.00000 4.06045 1.00000 −2.46180 −1.67554 −5.07240 1.00000 −2.46180
1.3 −2.22931 1.00000 2.96981 1.00000 −2.22931 −0.230360 −2.16201 1.00000 −2.22931
1.4 −2.14529 1.00000 2.60225 1.00000 −2.14529 −2.89107 −1.29200 1.00000 −2.14529
1.5 −1.79507 1.00000 1.22228 1.00000 −1.79507 3.49730 1.39607 1.00000 −1.79507
1.6 −1.63766 1.00000 0.681937 1.00000 −1.63766 −0.197583 2.15854 1.00000 −1.63766
1.7 −1.27466 1.00000 −0.375250 1.00000 −1.27466 −0.831191 3.02763 1.00000 −1.27466
1.8 −1.13202 1.00000 −0.718528 1.00000 −1.13202 −1.31252 3.07743 1.00000 −1.13202
1.9 −1.12824 1.00000 −0.727075 1.00000 −1.12824 −4.89351 3.07679 1.00000 −1.12824
1.10 −0.791085 1.00000 −1.37418 1.00000 −0.791085 2.45382 2.66927 1.00000 −0.791085
1.11 −0.762017 1.00000 −1.41933 1.00000 −0.762017 2.32113 2.60559 1.00000 −0.762017
1.12 −0.108293 1.00000 −1.98827 1.00000 −0.108293 −2.69972 0.431901 1.00000 −0.108293
1.13 0.0493063 1.00000 −1.99757 1.00000 0.0493063 2.05010 −0.197105 1.00000 0.0493063
1.14 0.186838 1.00000 −1.96509 1.00000 0.186838 −4.07485 −0.740831 1.00000 0.186838
1.15 0.592282 1.00000 −1.64920 1.00000 0.592282 −0.542800 −2.16136 1.00000 0.592282
1.16 0.783438 1.00000 −1.38623 1.00000 0.783438 −0.845679 −2.65290 1.00000 0.783438
1.17 1.02584 1.00000 −0.947645 1.00000 1.02584 0.748026 −3.02382 1.00000 1.02584
1.18 1.03713 1.00000 −0.924357 1.00000 1.03713 2.93887 −3.03294 1.00000 1.03713
1.19 1.60756 1.00000 0.584262 1.00000 1.60756 0.859599 −2.27589 1.00000 1.60756
1.20 1.75959 1.00000 1.09616 1.00000 1.75959 −3.35674 −1.59039 1.00000 1.75959
See all 23 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.23
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 \(T_{2}^{23} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6015))\).