Properties

Label 6026.2.a.g
Level 6026
Weight 2
Character orbit 6026.a
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 21
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: \(1\)
Dimension: \(21\)
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.

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

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 −3.25554 1.00000 0.398003 −3.25554 0.686920 1.00000 7.59851 0.398003
1.2 1.00000 −2.96739 1.00000 −0.775054 −2.96739 0.413858 1.00000 5.80542 −0.775054
1.3 1.00000 −2.37676 1.00000 −2.07688 −2.37676 −0.108208 1.00000 2.64897 −2.07688
1.4 1.00000 −1.87480 1.00000 0.417125 −1.87480 −3.88487 1.00000 0.514862 0.417125
1.5 1.00000 −1.74967 1.00000 2.79997 −1.74967 0.229508 1.00000 0.0613311 2.79997
1.6 1.00000 −1.31043 1.00000 −3.45176 −1.31043 −4.90131 1.00000 −1.28277 −3.45176
1.7 1.00000 −1.30046 1.00000 −2.98653 −1.30046 2.26537 1.00000 −1.30880 −2.98653
1.8 1.00000 −1.08114 1.00000 0.379081 −1.08114 0.614832 1.00000 −1.83113 0.379081
1.9 1.00000 −0.293262 1.00000 2.91518 −0.293262 −1.20061 1.00000 −2.91400 2.91518
1.10 1.00000 −0.104929 1.00000 −0.922657 −0.104929 4.49446 1.00000 −2.98899 −0.922657
1.11 1.00000 0.104111 1.00000 1.37645 0.104111 −2.65513 1.00000 −2.98916 1.37645
1.12 1.00000 0.775060 1.00000 0.913280 0.775060 −1.54834 1.00000 −2.39928 0.913280
1.13 1.00000 0.780842 1.00000 −0.582778 0.780842 2.23605 1.00000 −2.39029 −0.582778
1.14 1.00000 0.825726 1.00000 −2.91252 0.825726 −1.72528 1.00000 −2.31818 −2.91252
1.15 1.00000 0.938474 1.00000 0.929839 0.938474 −1.00873 1.00000 −2.11927 0.929839
1.16 1.00000 1.13204 1.00000 −3.67213 1.13204 −0.943976 1.00000 −1.71848 −3.67213
1.17 1.00000 1.44805 1.00000 3.26245 1.44805 −3.72778 1.00000 −0.903151 3.26245
1.18 1.00000 1.90172 1.00000 −3.81206 1.90172 1.69979 1.00000 0.616557 −3.81206
1.19 1.00000 2.43324 1.00000 −0.544807 2.43324 −1.90449 1.00000 2.92064 −0.544807
1.20 1.00000 2.71715 1.00000 −1.49550 2.71715 −4.64653 1.00000 4.38289 −1.49550
See all 21 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.21
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):

\(T_{3}^{21} - \cdots\)
\(T_{5}^{21} + \cdots\)