Properties

Label 6034.2.a.q
Level 6034
Weight 2
Character orbit 6034.a
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 31
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: \(31\)
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.

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

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 −3.16461 1.00000 3.38179 −3.16461 1.00000 1.00000 7.01477 3.38179
1.2 1.00000 −2.89830 1.00000 −2.40071 −2.89830 1.00000 1.00000 5.40017 −2.40071
1.3 1.00000 −2.89657 1.00000 −0.704468 −2.89657 1.00000 1.00000 5.39012 −0.704468
1.4 1.00000 −2.80916 1.00000 1.77691 −2.80916 1.00000 1.00000 4.89139 1.77691
1.5 1.00000 −2.64787 1.00000 −3.70858 −2.64787 1.00000 1.00000 4.01123 −3.70858
1.6 1.00000 −2.45055 1.00000 −1.39178 −2.45055 1.00000 1.00000 3.00517 −1.39178
1.7 1.00000 −2.05592 1.00000 0.0511127 −2.05592 1.00000 1.00000 1.22679 0.0511127
1.8 1.00000 −1.92779 1.00000 4.40026 −1.92779 1.00000 1.00000 0.716369 4.40026
1.9 1.00000 −1.44788 1.00000 2.75672 −1.44788 1.00000 1.00000 −0.903639 2.75672
1.10 1.00000 −1.34024 1.00000 2.37980 −1.34024 1.00000 1.00000 −1.20375 2.37980
1.11 1.00000 −1.32232 1.00000 −1.62109 −1.32232 1.00000 1.00000 −1.25146 −1.62109
1.12 1.00000 −0.827780 1.00000 −4.23980 −0.827780 1.00000 1.00000 −2.31478 −4.23980
1.13 1.00000 −0.676569 1.00000 1.60949 −0.676569 1.00000 1.00000 −2.54225 1.60949
1.14 1.00000 −0.368112 1.00000 1.13454 −0.368112 1.00000 1.00000 −2.86449 1.13454
1.15 1.00000 −0.120971 1.00000 3.54943 −0.120971 1.00000 1.00000 −2.98537 3.54943
1.16 1.00000 −0.111656 1.00000 −1.58993 −0.111656 1.00000 1.00000 −2.98753 −1.58993
1.17 1.00000 −0.0841654 1.00000 3.03532 −0.0841654 1.00000 1.00000 −2.99292 3.03532
1.18 1.00000 0.510622 1.00000 −1.22941 0.510622 1.00000 1.00000 −2.73927 −1.22941
1.19 1.00000 0.603112 1.00000 −3.65115 0.603112 1.00000 1.00000 −2.63626 −3.65115
1.20 1.00000 0.913939 1.00000 −2.72754 0.913939 1.00000 1.00000 −2.16472 −2.72754
See all 31 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.31
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6034))\):

\(T_{3}^{31} - \cdots\)
\(T_{5}^{31} - \cdots\)
\(T_{11}^{31} - \cdots\)