Properties

Label 6026.2.a.j
Level 6026
Weight 2
Character orbit 6026.a
Self dual Yes
Analytic conductor 48.118
Analytic rank 0
Dimension 33
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: \(33\)
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.

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

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 −3.30495 1.00000 3.30220 3.30495 3.90022 −1.00000 7.92270 −3.30220
1.2 −1.00000 −2.92506 1.00000 0.618794 2.92506 −2.50272 −1.00000 5.55600 −0.618794
1.3 −1.00000 −2.90304 1.00000 −1.99628 2.90304 −0.299170 −1.00000 5.42764 1.99628
1.4 −1.00000 −2.82338 1.00000 −3.52183 2.82338 3.82891 −1.00000 4.97150 3.52183
1.5 −1.00000 −2.71066 1.00000 −2.38566 2.71066 −4.13924 −1.00000 4.34767 2.38566
1.6 −1.00000 −2.31184 1.00000 −1.83764 2.31184 0.291912 −1.00000 2.34459 1.83764
1.7 −1.00000 −1.90551 1.00000 3.90912 1.90551 1.35086 −1.00000 0.630974 −3.90912
1.8 −1.00000 −1.82570 1.00000 −3.75704 1.82570 0.299528 −1.00000 0.333191 3.75704
1.9 −1.00000 −1.80561 1.00000 −1.32735 1.80561 −4.32567 −1.00000 0.260232 1.32735
1.10 −1.00000 −1.47729 1.00000 2.55278 1.47729 −3.54262 −1.00000 −0.817604 −2.55278
1.11 −1.00000 −1.46112 1.00000 2.24970 1.46112 −0.440676 −1.00000 −0.865116 −2.24970
1.12 −1.00000 −0.987482 1.00000 −4.26130 0.987482 0.584751 −1.00000 −2.02488 4.26130
1.13 −1.00000 −0.968563 1.00000 −0.0731928 0.968563 −0.501115 −1.00000 −2.06189 0.0731928
1.14 −1.00000 −0.909549 1.00000 0.734986 0.909549 5.27401 −1.00000 −2.17272 −0.734986
1.15 −1.00000 −0.471999 1.00000 1.82038 0.471999 −1.64482 −1.00000 −2.77722 −1.82038
1.16 −1.00000 −0.0820624 1.00000 −3.26458 0.0820624 −0.430136 −1.00000 −2.99327 3.26458
1.17 −1.00000 0.189963 1.00000 2.89176 −0.189963 3.54124 −1.00000 −2.96391 −2.89176
1.18 −1.00000 0.214096 1.00000 2.53148 −0.214096 4.82861 −1.00000 −2.95416 −2.53148
1.19 −1.00000 0.539204 1.00000 −2.22740 −0.539204 4.94386 −1.00000 −2.70926 2.22740
1.20 −1.00000 0.581698 1.00000 −2.21086 −0.581698 1.23881 −1.00000 −2.66163 2.21086
See all 33 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.33
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):

\(T_{3}^{33} - \cdots\)
\(T_{5}^{33} + \cdots\)