Properties

Label 6022.2.a.b
Level 6022
Weight 2
Character orbit 6022.a
Self dual Yes
Analytic conductor 48.086
Analytic rank 1
Dimension 54
CM No

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Newspace parameters

Level: \( N \) = \( 6022 = 2 \cdot 3011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6022.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0859120972\)
Analytic rank: \(1\)
Dimension: \(54\)
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.

\(\operatorname{Tr}(f)(q) = \) \(54q \) \(\mathstrut +\mathstrut 54q^{2} \) \(\mathstrut -\mathstrut 22q^{3} \) \(\mathstrut +\mathstrut 54q^{4} \) \(\mathstrut -\mathstrut 14q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 20q^{7} \) \(\mathstrut +\mathstrut 54q^{8} \) \(\mathstrut +\mathstrut 32q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(54q \) \(\mathstrut +\mathstrut 54q^{2} \) \(\mathstrut -\mathstrut 22q^{3} \) \(\mathstrut +\mathstrut 54q^{4} \) \(\mathstrut -\mathstrut 14q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 20q^{7} \) \(\mathstrut +\mathstrut 54q^{8} \) \(\mathstrut +\mathstrut 32q^{9} \) \(\mathstrut -\mathstrut 14q^{10} \) \(\mathstrut -\mathstrut 22q^{11} \) \(\mathstrut -\mathstrut 22q^{12} \) \(\mathstrut -\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 20q^{14} \) \(\mathstrut -\mathstrut 32q^{15} \) \(\mathstrut +\mathstrut 54q^{16} \) \(\mathstrut -\mathstrut 67q^{17} \) \(\mathstrut +\mathstrut 32q^{18} \) \(\mathstrut -\mathstrut 54q^{19} \) \(\mathstrut -\mathstrut 14q^{20} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 22q^{22} \) \(\mathstrut -\mathstrut 52q^{23} \) \(\mathstrut -\mathstrut 22q^{24} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut -\mathstrut 24q^{26} \) \(\mathstrut -\mathstrut 82q^{27} \) \(\mathstrut -\mathstrut 20q^{28} \) \(\mathstrut -\mathstrut 30q^{29} \) \(\mathstrut -\mathstrut 32q^{30} \) \(\mathstrut -\mathstrut 78q^{31} \) \(\mathstrut +\mathstrut 54q^{32} \) \(\mathstrut -\mathstrut 48q^{33} \) \(\mathstrut -\mathstrut 67q^{34} \) \(\mathstrut -\mathstrut 71q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut -\mathstrut 54q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut -\mathstrut 14q^{40} \) \(\mathstrut -\mathstrut 61q^{41} \) \(\mathstrut -\mathstrut 18q^{42} \) \(\mathstrut -\mathstrut 53q^{43} \) \(\mathstrut -\mathstrut 22q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 52q^{46} \) \(\mathstrut -\mathstrut 96q^{47} \) \(\mathstrut -\mathstrut 22q^{48} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 13q^{51} \) \(\mathstrut -\mathstrut 24q^{52} \) \(\mathstrut -\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 82q^{54} \) \(\mathstrut -\mathstrut 75q^{55} \) \(\mathstrut -\mathstrut 20q^{56} \) \(\mathstrut -\mathstrut 17q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 78q^{59} \) \(\mathstrut -\mathstrut 32q^{60} \) \(\mathstrut -\mathstrut 23q^{61} \) \(\mathstrut -\mathstrut 78q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 54q^{64} \) \(\mathstrut -\mathstrut 43q^{65} \) \(\mathstrut -\mathstrut 48q^{66} \) \(\mathstrut -\mathstrut 54q^{67} \) \(\mathstrut -\mathstrut 67q^{68} \) \(\mathstrut +\mathstrut 7q^{69} \) \(\mathstrut -\mathstrut 71q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut +\mathstrut 32q^{72} \) \(\mathstrut -\mathstrut 62q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 81q^{75} \) \(\mathstrut -\mathstrut 54q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 45q^{79} \) \(\mathstrut -\mathstrut 14q^{80} \) \(\mathstrut +\mathstrut 22q^{81} \) \(\mathstrut -\mathstrut 61q^{82} \) \(\mathstrut -\mathstrut 117q^{83} \) \(\mathstrut -\mathstrut 18q^{84} \) \(\mathstrut -\mathstrut 53q^{86} \) \(\mathstrut -\mathstrut 84q^{87} \) \(\mathstrut -\mathstrut 22q^{88} \) \(\mathstrut -\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 60q^{91} \) \(\mathstrut -\mathstrut 52q^{92} \) \(\mathstrut +\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 96q^{94} \) \(\mathstrut -\mathstrut 44q^{95} \) \(\mathstrut -\mathstrut 22q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.41232 1.00000 −1.85663 −3.41232 3.02838 1.00000 8.64394 −1.85663
1.2 1.00000 −3.40089 1.00000 3.63611 −3.40089 −2.39111 1.00000 8.56603 3.63611
1.3 1.00000 −3.18590 1.00000 −1.36832 −3.18590 −3.72265 1.00000 7.14997 −1.36832
1.4 1.00000 −3.17082 1.00000 0.413863 −3.17082 −1.62952 1.00000 7.05407 0.413863
1.5 1.00000 −3.06406 1.00000 3.64593 −3.06406 0.427453 1.00000 6.38849 3.64593
1.6 1.00000 −2.86198 1.00000 −0.548157 −2.86198 2.20032 1.00000 5.19094 −0.548157
1.7 1.00000 −2.75819 1.00000 0.593272 −2.75819 4.20000 1.00000 4.60761 0.593272
1.8 1.00000 −2.72056 1.00000 1.67549 −2.72056 −1.89176 1.00000 4.40146 1.67549
1.9 1.00000 −2.71927 1.00000 −3.84841 −2.71927 −3.35161 1.00000 4.39444 −3.84841
1.10 1.00000 −2.46224 1.00000 −1.05561 −2.46224 2.87810 1.00000 3.06261 −1.05561
1.11 1.00000 −2.44368 1.00000 2.22438 −2.44368 −3.70978 1.00000 2.97155 2.22438
1.12 1.00000 −2.44169 1.00000 −4.13245 −2.44169 3.61005 1.00000 2.96185 −4.13245
1.13 1.00000 −1.92077 1.00000 3.09656 −1.92077 −3.07737 1.00000 0.689347 3.09656
1.14 1.00000 −1.82742 1.00000 −0.665814 −1.82742 1.40743 1.00000 0.339448 −0.665814
1.15 1.00000 −1.65622 1.00000 3.86194 −1.65622 0.0747047 1.00000 −0.256946 3.86194
1.16 1.00000 −1.62746 1.00000 2.10353 −1.62746 −4.91169 1.00000 −0.351369 2.10353
1.17 1.00000 −1.61281 1.00000 1.01065 −1.61281 0.302486 1.00000 −0.398851 1.01065
1.18 1.00000 −1.59103 1.00000 −2.29870 −1.59103 −3.52840 1.00000 −0.468610 −2.29870
1.19 1.00000 −1.52904 1.00000 −3.77354 −1.52904 0.908453 1.00000 −0.662042 −3.77354
1.20 1.00000 −1.50713 1.00000 −3.56652 −1.50713 −0.922198 1.00000 −0.728548 −3.56652
See all 54 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.54
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3011\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3}^{54} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6022))\).