Properties

Label 6034.2.a.p
Level 6034
Weight 2
Character orbit 6034.a
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 27
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: \(27\)
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.

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

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 −3.22794 1.00000 1.50843 3.22794 1.00000 −1.00000 7.41957 −1.50843
1.2 −1.00000 −3.20972 1.00000 −3.26323 3.20972 1.00000 −1.00000 7.30232 3.26323
1.3 −1.00000 −3.03412 1.00000 1.18387 3.03412 1.00000 −1.00000 6.20591 −1.18387
1.4 −1.00000 −2.59011 1.00000 1.58456 2.59011 1.00000 −1.00000 3.70867 −1.58456
1.5 −1.00000 −2.42517 1.00000 2.60497 2.42517 1.00000 −1.00000 2.88143 −2.60497
1.6 −1.00000 −1.90367 1.00000 −3.72741 1.90367 1.00000 −1.00000 0.623956 3.72741
1.7 −1.00000 −1.81149 1.00000 −1.26479 1.81149 1.00000 −1.00000 0.281479 1.26479
1.8 −1.00000 −1.32317 1.00000 −0.695345 1.32317 1.00000 −1.00000 −1.24923 0.695345
1.9 −1.00000 −0.743500 1.00000 −1.77052 0.743500 1.00000 −1.00000 −2.44721 1.77052
1.10 −1.00000 −0.679472 1.00000 −2.19065 0.679472 1.00000 −1.00000 −2.53832 2.19065
1.11 −1.00000 −0.394534 1.00000 4.36123 0.394534 1.00000 −1.00000 −2.84434 −4.36123
1.12 −1.00000 −0.302933 1.00000 3.48262 0.302933 1.00000 −1.00000 −2.90823 −3.48262
1.13 −1.00000 −0.252343 1.00000 2.45924 0.252343 1.00000 −1.00000 −2.93632 −2.45924
1.14 −1.00000 −0.222181 1.00000 0.181430 0.222181 1.00000 −1.00000 −2.95064 −0.181430
1.15 −1.00000 0.396413 1.00000 −1.85319 −0.396413 1.00000 −1.00000 −2.84286 1.85319
1.16 −1.00000 0.482352 1.00000 2.96654 −0.482352 1.00000 −1.00000 −2.76734 −2.96654
1.17 −1.00000 0.975695 1.00000 −1.65902 −0.975695 1.00000 −1.00000 −2.04802 1.65902
1.18 −1.00000 1.58330 1.00000 −2.70248 −1.58330 1.00000 −1.00000 −0.493160 2.70248
1.19 −1.00000 1.64919 1.00000 0.930561 −1.64919 1.00000 −1.00000 −0.280182 −0.930561
1.20 −1.00000 1.94651 1.00000 3.30450 −1.94651 1.00000 −1.00000 0.788913 −3.30450
See all 27 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.27
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6034))\):

\(T_{3}^{27} - \cdots\)
\(T_{5}^{27} - \cdots\)
\(T_{11}^{27} - \cdots\)