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

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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: \(67\)
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.

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

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 −3.37105 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 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6046))\):

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