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.

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

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 −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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6034))\):

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