Properties

Label 6034.2.a.r
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.

\(\operatorname{Tr}(f)(q) = \) \( 31q + 31q^{2} + 7q^{3} + 31q^{4} + 15q^{5} + 7q^{6} - 31q^{7} + 31q^{8} + 42q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 31q + 31q^{2} + 7q^{3} + 31q^{4} + 15q^{5} + 7q^{6} - 31q^{7} + 31q^{8} + 42q^{9} + 15q^{10} + 12q^{11} + 7q^{12} + 26q^{13} - 31q^{14} + 6q^{15} + 31q^{16} + 33q^{17} + 42q^{18} + 34q^{19} + 15q^{20} - 7q^{21} + 12q^{22} - 14q^{23} + 7q^{24} + 58q^{25} + 26q^{26} + 28q^{27} - 31q^{28} + 11q^{29} + 6q^{30} + 19q^{31} + 31q^{32} + 43q^{33} + 33q^{34} - 15q^{35} + 42q^{36} + 2q^{37} + 34q^{38} - 16q^{39} + 15q^{40} + 53q^{41} - 7q^{42} + 22q^{43} + 12q^{44} + 43q^{45} - 14q^{46} + 27q^{47} + 7q^{48} + 31q^{49} + 58q^{50} + 17q^{51} + 26q^{52} + 11q^{53} + 28q^{54} + 19q^{55} - 31q^{56} + 45q^{57} + 11q^{58} + 54q^{59} + 6q^{60} + 41q^{61} + 19q^{62} - 42q^{63} + 31q^{64} + 30q^{65} + 43q^{66} + 13q^{67} + 33q^{68} + 17q^{69} - 15q^{70} + 43q^{71} + 42q^{72} + 42q^{73} + 2q^{74} + 62q^{75} + 34q^{76} - 12q^{77} - 16q^{78} - 12q^{79} + 15q^{80} + 63q^{81} + 53q^{82} + 35q^{83} - 7q^{84} + 16q^{85} + 22q^{86} - 4q^{87} + 12q^{88} + 115q^{89} + 43q^{90} - 26q^{91} - 14q^{92} + q^{93} + 27q^{94} - 13q^{95} + 7q^{96} + 32q^{97} + 31q^{98} + 34q^{99} + O(q^{100}) \)

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 −3.29198 1.00000 −1.58360 −3.29198 −1.00000 1.00000 7.83715 −1.58360
1.2 1.00000 −3.19812 1.00000 3.31602 −3.19812 −1.00000 1.00000 7.22798 3.31602
1.3 1.00000 −2.74816 1.00000 3.57738 −2.74816 −1.00000 1.00000 4.55238 3.57738
1.4 1.00000 −2.34364 1.00000 −2.37141 −2.34364 −1.00000 1.00000 2.49264 −2.37141
1.5 1.00000 −2.29462 1.00000 1.21852 −2.29462 −1.00000 1.00000 2.26529 1.21852
1.6 1.00000 −2.15124 1.00000 −0.116889 −2.15124 −1.00000 1.00000 1.62782 −0.116889
1.7 1.00000 −1.78656 1.00000 −1.18496 −1.78656 −1.00000 1.00000 0.191811 −1.18496
1.8 1.00000 −1.76695 1.00000 2.46864 −1.76695 −1.00000 1.00000 0.122112 2.46864
1.9 1.00000 −1.69299 1.00000 −2.70073 −1.69299 −1.00000 1.00000 −0.133772 −2.70073
1.10 1.00000 −1.40540 1.00000 2.72818 −1.40540 −1.00000 1.00000 −1.02486 2.72818
1.11 1.00000 −0.820659 1.00000 4.15538 −0.820659 −1.00000 1.00000 −2.32652 4.15538
1.12 1.00000 −0.585502 1.00000 −3.38680 −0.585502 −1.00000 1.00000 −2.65719 −3.38680
1.13 1.00000 −0.307546 1.00000 −1.88818 −0.307546 −1.00000 1.00000 −2.90542 −1.88818
1.14 1.00000 −0.217225 1.00000 0.607550 −0.217225 −1.00000 1.00000 −2.95281 0.607550
1.15 1.00000 −0.118197 1.00000 −0.813929 −0.118197 −1.00000 1.00000 −2.98603 −0.813929
1.16 1.00000 0.239534 1.00000 −1.50535 0.239534 −1.00000 1.00000 −2.94262 −1.50535
1.17 1.00000 0.630504 1.00000 3.47508 0.630504 −1.00000 1.00000 −2.60246 3.47508
1.18 1.00000 0.718722 1.00000 3.07705 0.718722 −1.00000 1.00000 −2.48344 3.07705
1.19 1.00000 0.747767 1.00000 −1.63599 0.747767 −1.00000 1.00000 −2.44084 −1.63599
1.20 1.00000 1.15174 1.00000 2.73654 1.15174 −1.00000 1.00000 −1.67348 2.73654
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6034))\):

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