Properties

Label 6010.2.a.h
Level 6010
Weight 2
Character orbit 6010.a
Self dual Yes
Analytic conductor 47.990
Analytic rank 0
Dimension 28
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: \(28\)
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.

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

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 −3.20632 1.00000 −1.00000 −3.20632 −2.43054 1.00000 7.28047 −1.00000
1.2 1.00000 −2.95613 1.00000 −1.00000 −2.95613 −3.28957 1.00000 5.73868 −1.00000
1.3 1.00000 −2.81740 1.00000 −1.00000 −2.81740 −2.15395 1.00000 4.93776 −1.00000
1.4 1.00000 −2.80565 1.00000 −1.00000 −2.80565 2.92877 1.00000 4.87166 −1.00000
1.5 1.00000 −2.45664 1.00000 −1.00000 −2.45664 3.60299 1.00000 3.03507 −1.00000
1.6 1.00000 −2.33584 1.00000 −1.00000 −2.33584 4.65545 1.00000 2.45616 −1.00000
1.7 1.00000 −1.85629 1.00000 −1.00000 −1.85629 2.08107 1.00000 0.445825 −1.00000
1.8 1.00000 −1.73502 1.00000 −1.00000 −1.73502 −0.456244 1.00000 0.0103032 −1.00000
1.9 1.00000 −1.14577 1.00000 −1.00000 −1.14577 0.345550 1.00000 −1.68722 −1.00000
1.10 1.00000 −0.869813 1.00000 −1.00000 −0.869813 −1.24307 1.00000 −2.24343 −1.00000
1.11 1.00000 −0.734514 1.00000 −1.00000 −0.734514 0.223072 1.00000 −2.46049 −1.00000
1.12 1.00000 −0.503837 1.00000 −1.00000 −0.503837 −4.37336 1.00000 −2.74615 −1.00000
1.13 1.00000 −0.134464 1.00000 −1.00000 −0.134464 4.82249 1.00000 −2.98192 −1.00000
1.14 1.00000 0.184156 1.00000 −1.00000 0.184156 −4.92010 1.00000 −2.96609 −1.00000
1.15 1.00000 0.321033 1.00000 −1.00000 0.321033 −2.34471 1.00000 −2.89694 −1.00000
1.16 1.00000 0.519061 1.00000 −1.00000 0.519061 −3.03480 1.00000 −2.73058 −1.00000
1.17 1.00000 0.657748 1.00000 −1.00000 0.657748 4.85947 1.00000 −2.56737 −1.00000
1.18 1.00000 0.983549 1.00000 −1.00000 0.983549 0.242326 1.00000 −2.03263 −1.00000
1.19 1.00000 1.25977 1.00000 −1.00000 1.25977 3.22153 1.00000 −1.41297 −1.00000
1.20 1.00000 1.41587 1.00000 −1.00000 1.41587 2.06613 1.00000 −0.995326 −1.00000
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
\(2\) \(-1\)
\(5\) \(1\)
\(601\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3}^{28} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6010))\).