Properties

Label 6010.2.a.g
Level 6010
Weight 2
Character orbit 6010.a
Self dual Yes
Analytic conductor 47.990
Analytic rank 0
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9900916148\)
Analytic rank: \(0\)
Dimension: \(27\)
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.

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

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 −1.00000 −3.12246 1.00000 1.00000 3.12246 −0.227875 −1.00000 6.74974 −1.00000
1.2 −1.00000 −2.89176 1.00000 1.00000 2.89176 4.20794 −1.00000 5.36230 −1.00000
1.3 −1.00000 −2.88499 1.00000 1.00000 2.88499 0.210491 −1.00000 5.32318 −1.00000
1.4 −1.00000 −2.52918 1.00000 1.00000 2.52918 −2.70859 −1.00000 3.39676 −1.00000
1.5 −1.00000 −2.12852 1.00000 1.00000 2.12852 −4.55968 −1.00000 1.53060 −1.00000
1.6 −1.00000 −2.00989 1.00000 1.00000 2.00989 −0.566476 −1.00000 1.03966 −1.00000
1.7 −1.00000 −1.92694 1.00000 1.00000 1.92694 −3.44591 −1.00000 0.713113 −1.00000
1.8 −1.00000 −1.21224 1.00000 1.00000 1.21224 2.32820 −1.00000 −1.53047 −1.00000
1.9 −1.00000 −1.11003 1.00000 1.00000 1.11003 1.51458 −1.00000 −1.76783 −1.00000
1.10 −1.00000 −0.805731 1.00000 1.00000 0.805731 2.46129 −1.00000 −2.35080 −1.00000
1.11 −1.00000 −0.716010 1.00000 1.00000 0.716010 3.53027 −1.00000 −2.48733 −1.00000
1.12 −1.00000 −0.409284 1.00000 1.00000 0.409284 −1.22599 −1.00000 −2.83249 −1.00000
1.13 −1.00000 −0.114121 1.00000 1.00000 0.114121 −3.33992 −1.00000 −2.98698 −1.00000
1.14 −1.00000 −0.0770650 1.00000 1.00000 0.0770650 −1.82853 −1.00000 −2.99406 −1.00000
1.15 −1.00000 1.03782 1.00000 1.00000 −1.03782 −3.65688 −1.00000 −1.92294 −1.00000
1.16 −1.00000 1.08273 1.00000 1.00000 −1.08273 3.52082 −1.00000 −1.82769 −1.00000
1.17 −1.00000 1.23890 1.00000 1.00000 −1.23890 −4.00661 −1.00000 −1.46513 −1.00000
1.18 −1.00000 1.45178 1.00000 1.00000 −1.45178 3.96566 −1.00000 −0.892348 −1.00000
1.19 −1.00000 1.60467 1.00000 1.00000 −1.60467 −3.11642 −1.00000 −0.425041 −1.00000
1.20 −1.00000 1.83794 1.00000 1.00000 −1.83794 2.63564 −1.00000 0.378009 −1.00000
See all 27 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.27
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(5\) \(-1\)
\(601\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3}^{27} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6010))\).