Properties

Label 6046.2.a.d
Level 6046
Weight 2
Character orbit 6046.a
Self dual Yes
Analytic conductor 48.278
Analytic rank 1
Dimension 55
CM No

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Newspace parameters

Level: \( N \) = \( 6046 = 2 \cdot 3023 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2775530621\)
Analytic rank: \(1\)
Dimension: \(55\)
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.

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

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 −3.14242 1.00000 1.46177 3.14242 −0.391407 −1.00000 6.87480 −1.46177
1.2 −1.00000 −3.11598 1.00000 −1.88193 3.11598 −1.15467 −1.00000 6.70936 1.88193
1.3 −1.00000 −2.90391 1.00000 −2.93195 2.90391 1.22051 −1.00000 5.43272 2.93195
1.4 −1.00000 −2.84928 1.00000 3.68221 2.84928 3.75882 −1.00000 5.11842 −3.68221
1.5 −1.00000 −2.76458 1.00000 −3.35839 2.76458 2.59254 −1.00000 4.64289 3.35839
1.6 −1.00000 −2.68677 1.00000 2.41964 2.68677 0.726544 −1.00000 4.21874 −2.41964
1.7 −1.00000 −2.59616 1.00000 0.628601 2.59616 3.52393 −1.00000 3.74004 −0.628601
1.8 −1.00000 −2.51732 1.00000 1.76331 2.51732 1.11201 −1.00000 3.33688 −1.76331
1.9 −1.00000 −2.34064 1.00000 0.439606 2.34064 −1.53111 −1.00000 2.47858 −0.439606
1.10 −1.00000 −2.07899 1.00000 −2.29890 2.07899 −3.17260 −1.00000 1.32220 2.29890
1.11 −1.00000 −2.05889 1.00000 −2.17707 2.05889 −2.39868 −1.00000 1.23901 2.17707
1.12 −1.00000 −1.88890 1.00000 −2.81426 1.88890 4.34333 −1.00000 0.567942 2.81426
1.13 −1.00000 −1.82825 1.00000 −1.60206 1.82825 1.75337 −1.00000 0.342490 1.60206
1.14 −1.00000 −1.81717 1.00000 2.05072 1.81717 1.90646 −1.00000 0.302089 −2.05072
1.15 −1.00000 −1.56981 1.00000 3.21985 1.56981 −0.392480 −1.00000 −0.535687 −3.21985
1.16 −1.00000 −1.49688 1.00000 2.53302 1.49688 −3.95759 −1.00000 −0.759363 −2.53302
1.17 −1.00000 −1.42034 1.00000 1.09471 1.42034 4.85520 −1.00000 −0.982644 −1.09471
1.18 −1.00000 −1.39612 1.00000 −2.68054 1.39612 −4.55830 −1.00000 −1.05084 2.68054
1.19 −1.00000 −0.961298 1.00000 0.560610 0.961298 −3.48762 −1.00000 −2.07591 −0.560610
1.20 −1.00000 −0.859002 1.00000 0.293314 0.859002 1.77335 −1.00000 −2.26211 −0.293314
See all 55 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.55
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3023\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6046))\):

\(T_{3}^{55} + \cdots\)
\(T_{11}^{55} + \cdots\)