Properties

Label 6026.2.a.l
Level 6026
Weight 2
Character orbit 6026.a
Self dual Yes
Analytic conductor 48.118
Analytic rank 0
Dimension 36
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(0\)
Dimension: \(36\)
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.

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

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 −3.41962 1.00000 −1.05998 3.41962 −0.874431 −1.00000 8.69383 1.05998
1.2 −1.00000 −3.00646 1.00000 2.50601 3.00646 −2.50762 −1.00000 6.03882 −2.50601
1.3 −1.00000 −2.95632 1.00000 1.44309 2.95632 4.32514 −1.00000 5.73985 −1.44309
1.4 −1.00000 −2.75069 1.00000 −4.14565 2.75069 −3.93457 −1.00000 4.56631 4.14565
1.5 −1.00000 −2.51058 1.00000 −0.511257 2.51058 2.88576 −1.00000 3.30300 0.511257
1.6 −1.00000 −2.27426 1.00000 0.325199 2.27426 −2.71769 −1.00000 2.17227 −0.325199
1.7 −1.00000 −2.19697 1.00000 0.174713 2.19697 3.49233 −1.00000 1.82670 −0.174713
1.8 −1.00000 −2.09135 1.00000 2.51915 2.09135 −0.00923183 −1.00000 1.37373 −2.51915
1.9 −1.00000 −2.07888 1.00000 2.71554 2.07888 −2.97474 −1.00000 1.32176 −2.71554
1.10 −1.00000 −1.66763 1.00000 1.81504 1.66763 3.25466 −1.00000 −0.218995 −1.81504
1.11 −1.00000 −1.53572 1.00000 −3.94419 1.53572 4.26764 −1.00000 −0.641564 3.94419
1.12 −1.00000 −1.53570 1.00000 −3.27140 1.53570 1.87914 −1.00000 −0.641618 3.27140
1.13 −1.00000 −0.919839 1.00000 −1.90352 0.919839 0.476690 −1.00000 −2.15390 1.90352
1.14 −1.00000 −0.633980 1.00000 3.82144 0.633980 0.499597 −1.00000 −2.59807 −3.82144
1.15 −1.00000 −0.478528 1.00000 −0.306849 0.478528 −3.45315 −1.00000 −2.77101 0.306849
1.16 −1.00000 −0.303391 1.00000 0.0493123 0.303391 −2.29306 −1.00000 −2.90795 −0.0493123
1.17 −1.00000 −0.179106 1.00000 0.789963 0.179106 −0.160696 −1.00000 −2.96792 −0.789963
1.18 −1.00000 0.325322 1.00000 −2.89999 −0.325322 0.0543655 −1.00000 −2.89417 2.89999
1.19 −1.00000 0.372945 1.00000 −2.66658 −0.372945 3.34934 −1.00000 −2.86091 2.66658
1.20 −1.00000 0.455108 1.00000 −2.88071 −0.455108 −3.99338 −1.00000 −2.79288 2.88071
See all 36 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.36
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(23\) \(1\)
\(131\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):

\(T_{3}^{36} - \cdots\)
\(T_{5}^{36} - \cdots\)