Properties

Label 6021.2.a.t
Level 6021
Weight 2
Character orbit 6021.a
Self dual Yes
Analytic conductor 48.078
Analytic rank 0
Dimension 40
CM No

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Newspace parameters

Level: \( N \) = \( 6021 = 3^{3} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.077927057\)
Analytic rank: \(0\)
Dimension: \(40\)
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.

\(\operatorname{Tr}(f)(q) = \) \(40q \) \(\mathstrut +\mathstrut 46q^{4} \) \(\mathstrut +\mathstrut 16q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(40q \) \(\mathstrut +\mathstrut 46q^{4} \) \(\mathstrut +\mathstrut 16q^{7} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 50q^{16} \) \(\mathstrut +\mathstrut 64q^{19} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 40q^{25} \) \(\mathstrut +\mathstrut 48q^{28} \) \(\mathstrut +\mathstrut 54q^{31} \) \(\mathstrut +\mathstrut 32q^{34} \) \(\mathstrut +\mathstrut 24q^{37} \) \(\mathstrut +\mathstrut 40q^{40} \) \(\mathstrut +\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 52q^{46} \) \(\mathstrut +\mathstrut 64q^{49} \) \(\mathstrut +\mathstrut 18q^{52} \) \(\mathstrut +\mathstrut 36q^{55} \) \(\mathstrut +\mathstrut 8q^{58} \) \(\mathstrut +\mathstrut 58q^{61} \) \(\mathstrut +\mathstrut 120q^{64} \) \(\mathstrut +\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 30q^{70} \) \(\mathstrut +\mathstrut 50q^{73} \) \(\mathstrut +\mathstrut 112q^{76} \) \(\mathstrut +\mathstrut 60q^{79} \) \(\mathstrut +\mathstrut 50q^{82} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 16q^{88} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 44q^{94} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.70299 0 5.30613 −3.42111 0 −1.82484 −8.93642 0 9.24720
1.2 −2.69102 0 5.24161 −2.40662 0 2.96509 −8.72327 0 6.47626
1.3 −2.65109 0 5.02828 1.58126 0 −3.54711 −8.02824 0 −4.19207
1.4 −2.63563 0 4.94652 3.15326 0 2.40096 −7.76593 0 −8.31081
1.5 −2.32144 0 3.38909 −1.08423 0 4.03069 −3.22470 0 2.51697
1.6 −2.16137 0 2.67154 −3.69668 0 0.733541 −1.45144 0 7.98990
1.7 −2.08210 0 2.33515 0.145427 0 4.41479 −0.697822 0 −0.302795
1.8 −2.00467 0 2.01871 4.10087 0 1.86508 −0.0375024 0 −8.22090
1.9 −1.74618 0 1.04913 −3.84450 0 0.0845192 1.66038 0 6.71318
1.10 −1.69867 0 0.885473 −0.550686 0 0.164494 1.89321 0 0.935432
1.11 −1.47084 0 0.163365 −1.43270 0 −5.26244 2.70139 0 2.10726
1.12 −1.37704 0 −0.103765 2.60531 0 −2.14080 2.89697 0 −3.58761
1.13 −1.35612 0 −0.160951 −1.12934 0 −1.90121 2.93050 0 1.53151
1.14 −1.23529 0 −0.474050 1.76412 0 −1.12531 3.05618 0 −2.17920
1.15 −1.01187 0 −0.976110 −1.54012 0 4.83269 3.01145 0 1.55841
1.16 −0.968595 0 −1.06182 2.59691 0 3.83305 2.96567 0 −2.51535
1.17 −0.538428 0 −1.71010 −1.52796 0 0.425996 1.99762 0 0.822698
1.18 −0.536475 0 −1.71219 −2.69435 0 −1.96571 1.99150 0 1.44545
1.19 −0.323417 0 −1.89540 3.36365 0 3.36190 1.25984 0 −1.08786
1.20 −0.243699 0 −1.94061 −0.214655 0 −3.34538 0.960324 0 0.0523112
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.40
Significant digits:
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Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(223\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6021))\):

\(T_{2}^{40} - \cdots\)
\(T_{5}^{40} - \cdots\)