Properties

Label 6022.2.a.e
Level 6022
Weight 2
Character orbit 6022.a
Self dual Yes
Analytic conductor 48.086
Analytic rank 0
Dimension 68
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: \(0\)
Dimension: \(68\)
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.

\(\operatorname{Tr}(f)(q) = \) \(68q \) \(\mathstrut +\mathstrut 68q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 68q^{4} \) \(\mathstrut +\mathstrut 20q^{5} \) \(\mathstrut +\mathstrut 25q^{6} \) \(\mathstrut +\mathstrut 29q^{7} \) \(\mathstrut +\mathstrut 68q^{8} \) \(\mathstrut +\mathstrut 87q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(68q \) \(\mathstrut +\mathstrut 68q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 68q^{4} \) \(\mathstrut +\mathstrut 20q^{5} \) \(\mathstrut +\mathstrut 25q^{6} \) \(\mathstrut +\mathstrut 29q^{7} \) \(\mathstrut +\mathstrut 68q^{8} \) \(\mathstrut +\mathstrut 87q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut +\mathstrut 46q^{11} \) \(\mathstrut +\mathstrut 25q^{12} \) \(\mathstrut +\mathstrut 30q^{13} \) \(\mathstrut +\mathstrut 29q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 68q^{16} \) \(\mathstrut +\mathstrut 73q^{17} \) \(\mathstrut +\mathstrut 87q^{18} \) \(\mathstrut +\mathstrut 56q^{19} \) \(\mathstrut +\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 46q^{22} \) \(\mathstrut +\mathstrut 63q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 88q^{25} \) \(\mathstrut +\mathstrut 30q^{26} \) \(\mathstrut +\mathstrut 67q^{27} \) \(\mathstrut +\mathstrut 29q^{28} \) \(\mathstrut +\mathstrut 43q^{29} \) \(\mathstrut +\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 68q^{31} \) \(\mathstrut +\mathstrut 68q^{32} \) \(\mathstrut +\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 73q^{34} \) \(\mathstrut +\mathstrut 50q^{35} \) \(\mathstrut +\mathstrut 87q^{36} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 56q^{38} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 20q^{40} \) \(\mathstrut +\mathstrut 64q^{41} \) \(\mathstrut -\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 52q^{43} \) \(\mathstrut +\mathstrut 46q^{44} \) \(\mathstrut +\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 63q^{46} \) \(\mathstrut +\mathstrut 94q^{47} \) \(\mathstrut +\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 91q^{49} \) \(\mathstrut +\mathstrut 88q^{50} \) \(\mathstrut +\mathstrut 20q^{51} \) \(\mathstrut +\mathstrut 30q^{52} \) \(\mathstrut +\mathstrut 38q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 29q^{56} \) \(\mathstrut +\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 43q^{58} \) \(\mathstrut +\mathstrut 84q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 68q^{62} \) \(\mathstrut +\mathstrut 22q^{63} \) \(\mathstrut +\mathstrut 68q^{64} \) \(\mathstrut -\mathstrut 20q^{65} \) \(\mathstrut +\mathstrut 26q^{66} \) \(\mathstrut +\mathstrut 54q^{67} \) \(\mathstrut +\mathstrut 73q^{68} \) \(\mathstrut -\mathstrut 11q^{69} \) \(\mathstrut +\mathstrut 50q^{70} \) \(\mathstrut +\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 87q^{72} \) \(\mathstrut +\mathstrut 62q^{73} \) \(\mathstrut +\mathstrut 8q^{74} \) \(\mathstrut +\mathstrut 54q^{75} \) \(\mathstrut +\mathstrut 56q^{76} \) \(\mathstrut +\mathstrut 67q^{77} \) \(\mathstrut +\mathstrut 6q^{78} \) \(\mathstrut +\mathstrut 67q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 120q^{81} \) \(\mathstrut +\mathstrut 64q^{82} \) \(\mathstrut +\mathstrut 130q^{83} \) \(\mathstrut -\mathstrut 5q^{84} \) \(\mathstrut -\mathstrut 24q^{85} \) \(\mathstrut +\mathstrut 52q^{86} \) \(\mathstrut +\mathstrut 72q^{87} \) \(\mathstrut +\mathstrut 46q^{88} \) \(\mathstrut +\mathstrut 61q^{89} \) \(\mathstrut +\mathstrut 7q^{90} \) \(\mathstrut +\mathstrut 43q^{91} \) \(\mathstrut +\mathstrut 63q^{92} \) \(\mathstrut +\mathstrut 40q^{93} \) \(\mathstrut +\mathstrut 94q^{94} \) \(\mathstrut +\mathstrut 55q^{95} \) \(\mathstrut +\mathstrut 25q^{96} \) \(\mathstrut +\mathstrut 41q^{97} \) \(\mathstrut +\mathstrut 91q^{98} \) \(\mathstrut +\mathstrut 106q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.35476 1.00000 −3.57894 −3.35476 1.79257 1.00000 8.25439 −3.57894
1.2 1.00000 −3.25636 1.00000 2.14369 −3.25636 −2.21695 1.00000 7.60391 2.14369
1.3 1.00000 −3.01193 1.00000 3.00375 −3.01193 5.03538 1.00000 6.07172 3.00375
1.4 1.00000 −2.72056 1.00000 −0.689023 −2.72056 0.199511 1.00000 4.40143 −0.689023
1.5 1.00000 −2.64273 1.00000 −1.57154 −2.64273 −2.07612 1.00000 3.98402 −1.57154
1.6 1.00000 −2.61602 1.00000 −0.861265 −2.61602 0.881327 1.00000 3.84357 −0.861265
1.7 1.00000 −2.49368 1.00000 −0.272983 −2.49368 −4.45268 1.00000 3.21842 −0.272983
1.8 1.00000 −2.49125 1.00000 3.68938 −2.49125 1.92510 1.00000 3.20631 3.68938
1.9 1.00000 −2.43949 1.00000 −1.96660 −2.43949 4.60253 1.00000 2.95113 −1.96660
1.10 1.00000 −2.32468 1.00000 2.75364 −2.32468 1.28652 1.00000 2.40413 2.75364
1.11 1.00000 −2.31895 1.00000 2.61531 −2.31895 1.26807 1.00000 2.37754 2.61531
1.12 1.00000 −2.31495 1.00000 −4.12889 −2.31495 −1.35948 1.00000 2.35897 −4.12889
1.13 1.00000 −2.26646 1.00000 2.42379 −2.26646 −1.89494 1.00000 2.13682 2.42379
1.14 1.00000 −2.24505 1.00000 −1.17279 −2.24505 1.15296 1.00000 2.04026 −1.17279
1.15 1.00000 −1.47177 1.00000 0.895866 −1.47177 0.963361 1.00000 −0.833884 0.895866
1.16 1.00000 −1.21963 1.00000 −1.41374 −1.21963 −2.00566 1.00000 −1.51249 −1.41374
1.17 1.00000 −1.15681 1.00000 1.22743 −1.15681 3.85871 1.00000 −1.66179 1.22743
1.18 1.00000 −1.15100 1.00000 1.71186 −1.15100 3.72563 1.00000 −1.67520 1.71186
1.19 1.00000 −1.02270 1.00000 3.27073 −1.02270 4.67919 1.00000 −1.95408 3.27073
1.20 1.00000 −0.927049 1.00000 −3.29749 −0.927049 4.05370 1.00000 −2.14058 −3.29749
See all 68 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.68
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 \(T_{3}^{68} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6022))\).