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
Inner twists 1

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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: \(55\)
Twist minimal: yes
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.

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

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 admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 6046.2.a.d 55
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6046.2.a.d 55 1.a even 1 1 trivial

Atkin-Lehner signs

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

Hecke kernels

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database