Properties

Label 6026.2.a.m
Level 6026
Weight 2
Character orbit 6026.a
Self dual Yes
Analytic conductor 48.118
Analytic rank 0
Dimension 41
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(0\)
Dimension: \(41\)
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.

\(\operatorname{Tr}(f)(q) = \) \(41q \) \(\mathstrut +\mathstrut 41q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 41q^{4} \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 41q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(41q \) \(\mathstrut +\mathstrut 41q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 41q^{4} \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 41q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut 9q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 4q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 41q^{16} \) \(\mathstrut +\mathstrut 10q^{17} \) \(\mathstrut +\mathstrut 63q^{18} \) \(\mathstrut +\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 41q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 76q^{25} \) \(\mathstrut +\mathstrut 16q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut +\mathstrut 12q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut 41q^{32} \) \(\mathstrut +\mathstrut 5q^{33} \) \(\mathstrut +\mathstrut 10q^{34} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 63q^{36} \) \(\mathstrut +\mathstrut 26q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut +\mathstrut 50q^{39} \) \(\mathstrut +\mathstrut 9q^{40} \) \(\mathstrut +\mathstrut 27q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 44q^{45} \) \(\mathstrut +\mathstrut 41q^{46} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 87q^{49} \) \(\mathstrut +\mathstrut 76q^{50} \) \(\mathstrut +\mathstrut 24q^{51} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut +\mathstrut 63q^{53} \) \(\mathstrut +\mathstrut 7q^{54} \) \(\mathstrut +\mathstrut 18q^{55} \) \(\mathstrut +\mathstrut 12q^{56} \) \(\mathstrut -\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 28q^{58} \) \(\mathstrut +\mathstrut 33q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 25q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 41q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut -\mathstrut 9q^{67} \) \(\mathstrut +\mathstrut 10q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 36q^{71} \) \(\mathstrut +\mathstrut 63q^{72} \) \(\mathstrut +\mathstrut 36q^{73} \) \(\mathstrut +\mathstrut 26q^{74} \) \(\mathstrut +\mathstrut 6q^{75} \) \(\mathstrut +\mathstrut 16q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut +\mathstrut 51q^{79} \) \(\mathstrut +\mathstrut 9q^{80} \) \(\mathstrut +\mathstrut 149q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut -\mathstrut 27q^{83} \) \(\mathstrut +\mathstrut 16q^{84} \) \(\mathstrut +\mathstrut 52q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 3q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 68q^{89} \) \(\mathstrut +\mathstrut 44q^{90} \) \(\mathstrut +\mathstrut 22q^{91} \) \(\mathstrut +\mathstrut 41q^{92} \) \(\mathstrut +\mathstrut 45q^{93} \) \(\mathstrut +\mathstrut 18q^{94} \) \(\mathstrut +\mathstrut 46q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 16q^{97} \) \(\mathstrut +\mathstrut 87q^{98} \) \(\mathstrut -\mathstrut 10q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.33099 1.00000 −3.73356 −3.33099 2.28084 1.00000 8.09549 −3.73356
1.2 1.00000 −3.25480 1.00000 3.43025 −3.25480 2.34297 1.00000 7.59373 3.43025
1.3 1.00000 −3.22313 1.00000 −0.601968 −3.22313 −4.66050 1.00000 7.38856 −0.601968
1.4 1.00000 −3.13493 1.00000 2.02213 −3.13493 −2.34132 1.00000 6.82778 2.02213
1.5 1.00000 −2.99315 1.00000 −2.87948 −2.99315 −2.15668 1.00000 5.95893 −2.87948
1.6 1.00000 −2.68141 1.00000 3.69693 −2.68141 1.66171 1.00000 4.18994 3.69693
1.7 1.00000 −2.35219 1.00000 0.827343 −2.35219 0.166684 1.00000 2.53280 0.827343
1.8 1.00000 −2.27206 1.00000 0.0411842 −2.27206 3.26699 1.00000 2.16224 0.0411842
1.9 1.00000 −2.27011 1.00000 −1.81074 −2.27011 2.75406 1.00000 2.15338 −1.81074
1.10 1.00000 −2.01222 1.00000 −2.36434 −2.01222 3.66472 1.00000 1.04902 −2.36434
1.11 1.00000 −1.56181 1.00000 1.51273 −1.56181 2.72551 1.00000 −0.560757 1.51273
1.12 1.00000 −1.30065 1.00000 2.66833 −1.30065 −4.20545 1.00000 −1.30832 2.66833
1.13 1.00000 −1.27958 1.00000 2.95127 −1.27958 4.74723 1.00000 −1.36266 2.95127
1.14 1.00000 −1.08669 1.00000 −0.588357 −1.08669 −3.89024 1.00000 −1.81911 −0.588357
1.15 1.00000 −0.990574 1.00000 4.23904 −0.990574 −4.18696 1.00000 −2.01876 4.23904
1.16 1.00000 −0.830898 1.00000 −1.41489 −0.830898 −0.234026 1.00000 −2.30961 −1.41489
1.17 1.00000 −0.425330 1.00000 2.71720 −0.425330 −0.709481 1.00000 −2.81909 2.71720
1.18 1.00000 −0.356133 1.00000 3.98743 −0.356133 1.62862 1.00000 −2.87317 3.98743
1.19 1.00000 −0.352298 1.00000 −1.51534 −0.352298 −1.04103 1.00000 −2.87589 −1.51534
1.20 1.00000 −0.148340 1.00000 −1.78404 −0.148340 −0.469198 1.00000 −2.97800 −1.78404
See all 41 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.41
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(23\) \(-1\)
\(131\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):

\(T_{3}^{41} - \cdots\)
\(T_{5}^{41} - \cdots\)