Properties

Label 6034.2.a.m
Level 6034
Weight 2
Character orbit 6034.a
Self dual Yes
Analytic conductor 48.182
Analytic rank 1
Dimension 21
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: \(1\)
Dimension: \(21\)
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.

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

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 −3.34739 1.00000 1.24845 −3.34739 1.00000 1.00000 8.20504 1.24845
1.2 1.00000 −2.48749 1.00000 1.32783 −2.48749 1.00000 1.00000 3.18763 1.32783
1.3 1.00000 −2.30616 1.00000 −2.85291 −2.30616 1.00000 1.00000 2.31835 −2.85291
1.4 1.00000 −2.23818 1.00000 3.73239 −2.23818 1.00000 1.00000 2.00943 3.73239
1.5 1.00000 −2.23488 1.00000 0.812592 −2.23488 1.00000 1.00000 1.99468 0.812592
1.6 1.00000 −1.63595 1.00000 −2.93756 −1.63595 1.00000 1.00000 −0.323656 −2.93756
1.7 1.00000 −1.49715 1.00000 −0.207716 −1.49715 1.00000 1.00000 −0.758538 −0.207716
1.8 1.00000 −1.27918 1.00000 −0.808180 −1.27918 1.00000 1.00000 −1.36370 −0.808180
1.9 1.00000 −1.16337 1.00000 −3.30128 −1.16337 1.00000 1.00000 −1.64657 −3.30128
1.10 1.00000 −0.950934 1.00000 −2.70877 −0.950934 1.00000 1.00000 −2.09572 −2.70877
1.11 1.00000 −0.235507 1.00000 1.96765 −0.235507 1.00000 1.00000 −2.94454 1.96765
1.12 1.00000 −0.00804327 1.00000 3.67628 −0.00804327 1.00000 1.00000 −2.99994 3.67628
1.13 1.00000 0.402295 1.00000 1.29038 0.402295 1.00000 1.00000 −2.83816 1.29038
1.14 1.00000 0.584190 1.00000 0.414785 0.584190 1.00000 1.00000 −2.65872 0.414785
1.15 1.00000 0.800681 1.00000 −2.16386 0.800681 1.00000 1.00000 −2.35891 −2.16386
1.16 1.00000 0.893081 1.00000 0.353208 0.893081 1.00000 1.00000 −2.20241 0.353208
1.17 1.00000 1.34513 1.00000 −2.31517 1.34513 1.00000 1.00000 −1.19062 −2.31517
1.18 1.00000 1.87377 1.00000 −1.03478 1.87377 1.00000 1.00000 0.510997 −1.03478
1.19 1.00000 2.14514 1.00000 −0.309854 2.14514 1.00000 1.00000 1.60160 −0.309854
1.20 1.00000 2.28514 1.00000 −4.30862 2.28514 1.00000 1.00000 2.22188 −4.30862
See all 21 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.21
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6034))\):

\(T_{3}^{21} + \cdots\)
\(T_{5}^{21} + \cdots\)
\(T_{11}^{21} + \cdots\)