Properties

Label 6034.2.a.n
Level 6034
Weight 2
Character orbit 6034.a
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
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.

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

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 −2.83864 1.00000 0.330019 2.83864 −1.00000 −1.00000 5.05788 −0.330019
1.2 −1.00000 −2.67063 1.00000 3.15601 2.67063 −1.00000 −1.00000 4.13228 −3.15601
1.3 −1.00000 −2.58057 1.00000 −2.90281 2.58057 −1.00000 −1.00000 3.65935 2.90281
1.4 −1.00000 −1.92027 1.00000 −2.53143 1.92027 −1.00000 −1.00000 0.687441 2.53143
1.5 −1.00000 −1.91791 1.00000 0.374562 1.91791 −1.00000 −1.00000 0.678384 −0.374562
1.6 −1.00000 −1.69422 1.00000 3.76480 1.69422 −1.00000 −1.00000 −0.129635 −3.76480
1.7 −1.00000 −1.44122 1.00000 −2.06061 1.44122 −1.00000 −1.00000 −0.922894 2.06061
1.8 −1.00000 −0.920246 1.00000 2.96551 0.920246 −1.00000 −1.00000 −2.15315 −2.96551
1.9 −1.00000 −0.797155 1.00000 1.40867 0.797155 −1.00000 −1.00000 −2.36454 −1.40867
1.10 −1.00000 −0.0752307 1.00000 −2.78876 0.0752307 −1.00000 −1.00000 −2.99434 2.78876
1.11 −1.00000 0.0287183 1.00000 1.06252 −0.0287183 −1.00000 −1.00000 −2.99918 −1.06252
1.12 −1.00000 0.430787 1.00000 1.34011 −0.430787 −1.00000 −1.00000 −2.81442 −1.34011
1.13 −1.00000 0.632516 1.00000 −0.321740 −0.632516 −1.00000 −1.00000 −2.59992 0.321740
1.14 −1.00000 0.685916 1.00000 1.44966 −0.685916 −1.00000 −1.00000 −2.52952 −1.44966
1.15 −1.00000 1.20386 1.00000 −2.97794 −1.20386 −1.00000 −1.00000 −1.55072 2.97794
1.16 −1.00000 1.44853 1.00000 −1.26403 −1.44853 −1.00000 −1.00000 −0.901751 1.26403
1.17 −1.00000 1.52105 1.00000 −3.19164 −1.52105 −1.00000 −1.00000 −0.686407 3.19164
1.18 −1.00000 1.56085 1.00000 −1.28710 −1.56085 −1.00000 −1.00000 −0.563752 1.28710
1.19 −1.00000 2.10114 1.00000 4.16694 −2.10114 −1.00000 −1.00000 1.41477 −4.16694
1.20 −1.00000 2.39691 1.00000 1.79254 −2.39691 −1.00000 −1.00000 2.74520 −1.79254
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(7\) \(1\)
\(431\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6034))\):

\(T_{3}^{24} - \cdots\)
\(T_{5}^{24} - \cdots\)
\(T_{11}^{24} - \cdots\)