Properties

Label 6022.2.a.c
Level 6022
Weight 2
Character orbit 6022.a
Self dual Yes
Analytic conductor 48.086
Analytic rank 0
Dimension 61
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: \(61\)
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.

\(\operatorname{Tr}(f)(q) = \) \(61q \) \(\mathstrut -\mathstrut 61q^{2} \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 61q^{8} \) \(\mathstrut +\mathstrut 67q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(61q \) \(\mathstrut -\mathstrut 61q^{2} \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 61q^{8} \) \(\mathstrut +\mathstrut 67q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut 8q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 61q^{16} \) \(\mathstrut +\mathstrut 60q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 29q^{19} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut +\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 39q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 61q^{25} \) \(\mathstrut -\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 2q^{28} \) \(\mathstrut +\mathstrut 36q^{29} \) \(\mathstrut -\mathstrut 40q^{31} \) \(\mathstrut -\mathstrut 61q^{32} \) \(\mathstrut +\mathstrut 28q^{33} \) \(\mathstrut -\mathstrut 60q^{34} \) \(\mathstrut +\mathstrut 55q^{35} \) \(\mathstrut +\mathstrut 67q^{36} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut +\mathstrut 17q^{39} \) \(\mathstrut -\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 44q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut +\mathstrut 52q^{45} \) \(\mathstrut -\mathstrut 39q^{46} \) \(\mathstrut +\mathstrut 64q^{47} \) \(\mathstrut +\mathstrut 8q^{48} \) \(\mathstrut +\mathstrut 49q^{49} \) \(\mathstrut -\mathstrut 61q^{50} \) \(\mathstrut +\mathstrut 15q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 65q^{53} \) \(\mathstrut -\mathstrut 32q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 2q^{56} \) \(\mathstrut +\mathstrut 9q^{57} \) \(\mathstrut -\mathstrut 36q^{58} \) \(\mathstrut +\mathstrut 2q^{59} \) \(\mathstrut +\mathstrut 45q^{61} \) \(\mathstrut +\mathstrut 40q^{62} \) \(\mathstrut +\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 61q^{64} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut -\mathstrut 28q^{66} \) \(\mathstrut -\mathstrut 20q^{67} \) \(\mathstrut +\mathstrut 60q^{68} \) \(\mathstrut +\mathstrut 21q^{69} \) \(\mathstrut -\mathstrut 55q^{70} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut -\mathstrut 67q^{72} \) \(\mathstrut +\mathstrut 25q^{73} \) \(\mathstrut -\mathstrut 20q^{74} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut -\mathstrut 29q^{76} \) \(\mathstrut +\mathstrut 131q^{77} \) \(\mathstrut -\mathstrut 17q^{78} \) \(\mathstrut -\mathstrut 17q^{79} \) \(\mathstrut +\mathstrut 16q^{80} \) \(\mathstrut +\mathstrut 85q^{81} \) \(\mathstrut -\mathstrut 44q^{82} \) \(\mathstrut +\mathstrut 104q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 22q^{86} \) \(\mathstrut +\mathstrut 86q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut +\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 52q^{90} \) \(\mathstrut -\mathstrut 68q^{91} \) \(\mathstrut +\mathstrut 39q^{92} \) \(\mathstrut +\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut +\mathstrut 58q^{95} \) \(\mathstrut -\mathstrut 8q^{96} \) \(\mathstrut +\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 49q^{98} \) \(\mathstrut +\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.31019 1.00000 1.46037 3.31019 −0.428308 −1.00000 7.95734 −1.46037
1.2 −1.00000 −3.29982 1.00000 3.94529 3.29982 1.75060 −1.00000 7.88881 −3.94529
1.3 −1.00000 −2.88590 1.00000 −3.47728 2.88590 −4.98917 −1.00000 5.32845 3.47728
1.4 −1.00000 −2.85737 1.00000 −1.73685 2.85737 −2.09511 −1.00000 5.16453 1.73685
1.5 −1.00000 −2.74236 1.00000 0.141045 2.74236 −0.820556 −1.00000 4.52053 −0.141045
1.6 −1.00000 −2.71725 1.00000 0.844160 2.71725 4.53942 −1.00000 4.38347 −0.844160
1.7 −1.00000 −2.65789 1.00000 −1.96173 2.65789 1.75208 −1.00000 4.06439 1.96173
1.8 −1.00000 −2.60317 1.00000 2.24226 2.60317 −4.82749 −1.00000 3.77649 −2.24226
1.9 −1.00000 −2.51016 1.00000 1.21389 2.51016 4.01976 −1.00000 3.30092 −1.21389
1.10 −1.00000 −2.42852 1.00000 2.56237 2.42852 −2.36456 −1.00000 2.89773 −2.56237
1.11 −1.00000 −2.37453 1.00000 3.86248 2.37453 −2.00027 −1.00000 2.63837 −3.86248
1.12 −1.00000 −2.35686 1.00000 −2.52767 2.35686 0.0751824 −1.00000 2.55481 2.52767
1.13 −1.00000 −1.81947 1.00000 −2.66446 1.81947 1.39987 −1.00000 0.310478 2.66446
1.14 −1.00000 −1.69347 1.00000 −1.85965 1.69347 −0.879374 −1.00000 −0.132168 1.85965
1.15 −1.00000 −1.57891 1.00000 −2.16938 1.57891 −1.92539 −1.00000 −0.507029 2.16938
1.16 −1.00000 −1.42902 1.00000 1.04628 1.42902 2.47786 −1.00000 −0.957895 −1.04628
1.17 −1.00000 −1.39055 1.00000 1.34087 1.39055 −2.43238 −1.00000 −1.06637 −1.34087
1.18 −1.00000 −1.34981 1.00000 0.909179 1.34981 3.61244 −1.00000 −1.17801 −0.909179
1.19 −1.00000 −1.27129 1.00000 2.47111 1.27129 −1.62843 −1.00000 −1.38382 −2.47111
1.20 −1.00000 −1.13476 1.00000 3.93476 1.13476 4.57427 −1.00000 −1.71231 −3.93476
See all 61 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.61
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 \(T_{3}^{61} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6022))\).