Properties

Label 6046.2.a.f
Level 6046
Weight 2
Character orbit 6046.a
Self dual yes
Analytic conductor 48.278
Analytic rank 0
Dimension 67
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: \(0\)
Dimension: \(67\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 67q + 67q^{2} + 21q^{3} + 67q^{4} + 21q^{5} + 21q^{6} + 38q^{7} + 67q^{8} + 90q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 67q + 67q^{2} + 21q^{3} + 67q^{4} + 21q^{5} + 21q^{6} + 38q^{7} + 67q^{8} + 90q^{9} + 21q^{10} + 56q^{11} + 21q^{12} + 33q^{13} + 38q^{14} + 25q^{15} + 67q^{16} + 30q^{17} + 90q^{18} + 36q^{19} + 21q^{20} + 20q^{21} + 56q^{22} + 65q^{23} + 21q^{24} + 72q^{25} + 33q^{26} + 57q^{27} + 38q^{28} + 84q^{29} + 25q^{30} + 52q^{31} + 67q^{32} - 9q^{33} + 30q^{34} + 30q^{35} + 90q^{36} + 52q^{37} + 36q^{38} + 41q^{39} + 21q^{40} + 46q^{41} + 20q^{42} + 61q^{43} + 56q^{44} + 23q^{45} + 65q^{46} + 51q^{47} + 21q^{48} + 81q^{49} + 72q^{50} + 33q^{51} + 33q^{52} + 72q^{53} + 57q^{54} + 14q^{55} + 38q^{56} - 26q^{57} + 84q^{58} + 71q^{59} + 25q^{60} + 42q^{61} + 52q^{62} + 63q^{63} + 67q^{64} - 2q^{65} - 9q^{66} + 70q^{67} + 30q^{68} + 21q^{69} + 30q^{70} + 104q^{71} + 90q^{72} - 31q^{73} + 52q^{74} + 69q^{75} + 36q^{76} + 48q^{77} + 41q^{78} + 79q^{79} + 21q^{80} + 123q^{81} + 46q^{82} + 41q^{83} + 20q^{84} + 6q^{85} + 61q^{86} + 19q^{87} + 56q^{88} + 58q^{89} + 23q^{90} + 31q^{91} + 65q^{92} + 13q^{93} + 51q^{94} + 77q^{95} + 21q^{96} - 8q^{97} + 81q^{98} + 129q^{99} + O(q^{100}) \)

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 −3.37105 1.00000 3.37148 −3.37105 1.10661 1.00000 8.36395 3.37148
1.2 1.00000 −3.14488 1.00000 −1.06232 −3.14488 −3.74953 1.00000 6.89025 −1.06232
1.3 1.00000 −3.02893 1.00000 −3.61003 −3.02893 0.772328 1.00000 6.17443 −3.61003
1.4 1.00000 −3.02873 1.00000 −2.84681 −3.02873 −0.956843 1.00000 6.17323 −2.84681
1.5 1.00000 −2.76774 1.00000 −2.60035 −2.76774 3.45506 1.00000 4.66041 −2.60035
1.6 1.00000 −2.74369 1.00000 0.0184852 −2.74369 0.788378 1.00000 4.52782 0.0184852
1.7 1.00000 −2.73291 1.00000 −0.132829 −2.73291 3.97016 1.00000 4.46882 −0.132829
1.8 1.00000 −2.66695 1.00000 2.34176 −2.66695 3.40715 1.00000 4.11263 2.34176
1.9 1.00000 −2.41094 1.00000 0.848657 −2.41094 −1.16640 1.00000 2.81262 0.848657
1.10 1.00000 −2.39039 1.00000 0.762400 −2.39039 −3.68654 1.00000 2.71398 0.762400
1.11 1.00000 −2.34396 1.00000 3.11002 −2.34396 1.16030 1.00000 2.49414 3.11002
1.12 1.00000 −2.14148 1.00000 3.02625 −2.14148 4.90651 1.00000 1.58595 3.02625
1.13 1.00000 −2.08665 1.00000 −0.513266 −2.08665 0.880996 1.00000 1.35412 −0.513266
1.14 1.00000 −1.75304 1.00000 −0.582580 −1.75304 −2.67925 1.00000 0.0731519 −0.582580
1.15 1.00000 −1.55218 1.00000 3.12516 −1.55218 2.04511 1.00000 −0.590743 3.12516
1.16 1.00000 −1.49577 1.00000 −3.91198 −1.49577 2.85048 1.00000 −0.762675 −3.91198
1.17 1.00000 −1.35974 1.00000 1.23410 −1.35974 −3.50749 1.00000 −1.15110 1.23410
1.18 1.00000 −1.34907 1.00000 0.876974 −1.34907 −1.47730 1.00000 −1.18002 0.876974
1.19 1.00000 −1.25114 1.00000 3.81116 −1.25114 −1.42946 1.00000 −1.43464 3.81116
1.20 1.00000 −1.23522 1.00000 −0.854459 −1.23522 4.26002 1.00000 −1.47423 −0.854459
See all 67 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.67
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.f 67
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6046.2.a.f 67 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6046))\):

\(T_{3}^{67} - \cdots\)
\(T_{11}^{67} - \cdots\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database