Properties

Label 6026.2.a.k
Level 6026
Weight 2
Character orbit 6026.a
Self dual Yes
Analytic conductor 48.118
Analytic rank 0
Dimension 35
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: \(35\)
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.

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

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 −3.43871 1.00000 −4.28403 −3.43871 1.96690 1.00000 8.82470 −4.28403
1.2 1.00000 −3.36223 1.00000 2.69270 −3.36223 −4.35375 1.00000 8.30456 2.69270
1.3 1.00000 −3.00053 1.00000 0.314170 −3.00053 4.93238 1.00000 6.00320 0.314170
1.4 1.00000 −2.88440 1.00000 3.48712 −2.88440 4.69814 1.00000 5.31979 3.48712
1.5 1.00000 −2.84834 1.00000 3.81635 −2.84834 −2.03504 1.00000 5.11302 3.81635
1.6 1.00000 −2.77524 1.00000 −2.60760 −2.77524 −2.68280 1.00000 4.70196 −2.60760
1.7 1.00000 −2.41881 1.00000 −3.09594 −2.41881 0.393889 1.00000 2.85065 −3.09594
1.8 1.00000 −2.41686 1.00000 −1.19985 −2.41686 −1.78090 1.00000 2.84122 −1.19985
1.9 1.00000 −2.05490 1.00000 0.786161 −2.05490 −2.31145 1.00000 1.22260 0.786161
1.10 1.00000 −1.74363 1.00000 1.36417 −1.74363 0.246249 1.00000 0.0402388 1.36417
1.11 1.00000 −1.69112 1.00000 −3.34531 −1.69112 0.398747 1.00000 −0.140113 −3.34531
1.12 1.00000 −1.65659 1.00000 −0.00351955 −1.65659 −4.74512 1.00000 −0.255700 −0.00351955
1.13 1.00000 −1.52794 1.00000 1.80988 −1.52794 2.28195 1.00000 −0.665396 1.80988
1.14 1.00000 −0.824185 1.00000 2.25531 −0.824185 4.15544 1.00000 −2.32072 2.25531
1.15 1.00000 −0.783973 1.00000 4.00344 −0.783973 0.255131 1.00000 −2.38539 4.00344
1.16 1.00000 −0.711607 1.00000 −3.74432 −0.711607 2.05633 1.00000 −2.49362 −3.74432
1.17 1.00000 −0.339838 1.00000 −2.83329 −0.339838 −3.26036 1.00000 −2.88451 −2.83329
1.18 1.00000 0.0639197 1.00000 0.144901 0.0639197 −1.36969 1.00000 −2.99591 0.144901
1.19 1.00000 0.0851442 1.00000 −0.378458 0.0851442 4.38766 1.00000 −2.99275 −0.378458
1.20 1.00000 0.671472 1.00000 3.81346 0.671472 3.17342 1.00000 −2.54913 3.81346
See all 35 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.35
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):

\(T_{3}^{35} + \cdots\)
\(T_{5}^{35} - \cdots\)