Properties

Label 6046.2.a.e
Level 6046
Weight 2
Character orbit 6046.a
Self dual yes
Analytic conductor 48.278
Analytic rank 1
Dimension 56
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: \(56\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 56q + 56q^{2} - 18q^{3} + 56q^{4} - 17q^{5} - 18q^{6} - 35q^{7} + 56q^{8} + 34q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 56q + 56q^{2} - 18q^{3} + 56q^{4} - 17q^{5} - 18q^{6} - 35q^{7} + 56q^{8} + 34q^{9} - 17q^{10} - 53q^{11} - 18q^{12} - 21q^{13} - 35q^{14} - 36q^{15} + 56q^{16} - 22q^{17} + 34q^{18} - 31q^{19} - 17q^{20} - 23q^{21} - 53q^{22} - 59q^{23} - 18q^{24} + 41q^{25} - 21q^{26} - 63q^{27} - 35q^{28} - 88q^{29} - 36q^{30} - 44q^{31} + 56q^{32} + 4q^{33} - 22q^{34} - 51q^{35} + 34q^{36} - 60q^{37} - 31q^{38} - 62q^{39} - 17q^{40} - 39q^{41} - 23q^{42} - 66q^{43} - 53q^{44} - 34q^{45} - 59q^{46} - 51q^{47} - 18q^{48} + 41q^{49} + 41q^{50} - 48q^{51} - 21q^{52} - 75q^{53} - 63q^{54} - 41q^{55} - 35q^{56} - 12q^{57} - 88q^{58} - 77q^{59} - 36q^{60} - 43q^{61} - 44q^{62} - 88q^{63} + 56q^{64} - 54q^{65} + 4q^{66} - 62q^{67} - 22q^{68} - 48q^{69} - 51q^{70} - 122q^{71} + 34q^{72} - 7q^{73} - 60q^{74} - 63q^{75} - 31q^{76} - 39q^{77} - 62q^{78} - 91q^{79} - 17q^{80} + 8q^{81} - 39q^{82} - 51q^{83} - 23q^{84} - 72q^{85} - 66q^{86} - 19q^{87} - 53q^{88} - 62q^{89} - 34q^{90} - 48q^{91} - 59q^{92} - 41q^{93} - 51q^{94} - 120q^{95} - 18q^{96} + 6q^{97} + 41q^{98} - 128q^{99} + O(q^{100}) \)

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 −3.35147 1.00000 0.434868 −3.35147 3.30614 1.00000 8.23237 0.434868
1.2 1.00000 −3.31079 1.00000 −3.14984 −3.31079 −0.324393 1.00000 7.96133 −3.14984
1.3 1.00000 −3.25917 1.00000 −0.219000 −3.25917 −4.63324 1.00000 7.62218 −0.219000
1.4 1.00000 −3.18186 1.00000 3.25833 −3.18186 0.730955 1.00000 7.12426 3.25833
1.5 1.00000 −2.93762 1.00000 1.81603 −2.93762 −0.742842 1.00000 5.62960 1.81603
1.6 1.00000 −2.89764 1.00000 3.79029 −2.89764 −4.56649 1.00000 5.39633 3.79029
1.7 1.00000 −2.64315 1.00000 −1.33957 −2.64315 3.06951 1.00000 3.98626 −1.33957
1.8 1.00000 −2.45102 1.00000 0.781132 −2.45102 −0.0575638 1.00000 3.00749 0.781132
1.9 1.00000 −2.44881 1.00000 2.87933 −2.44881 −3.14262 1.00000 2.99666 2.87933
1.10 1.00000 −2.43348 1.00000 −1.73446 −2.43348 −1.67668 1.00000 2.92185 −1.73446
1.11 1.00000 −2.39212 1.00000 0.456785 −2.39212 2.48835 1.00000 2.72224 0.456785
1.12 1.00000 −2.37532 1.00000 −4.29598 −2.37532 −4.13959 1.00000 2.64215 −4.29598
1.13 1.00000 −2.14327 1.00000 4.37018 −2.14327 −1.18558 1.00000 1.59362 4.37018
1.14 1.00000 −2.05550 1.00000 −1.29697 −2.05550 0.414264 1.00000 1.22507 −1.29697
1.15 1.00000 −1.97472 1.00000 −3.51408 −1.97472 4.87260 1.00000 0.899523 −3.51408
1.16 1.00000 −1.79217 1.00000 −3.46015 −1.79217 −4.09544 1.00000 0.211861 −3.46015
1.17 1.00000 −1.73760 1.00000 −0.720137 −1.73760 −3.09490 1.00000 0.0192639 −0.720137
1.18 1.00000 −1.70174 1.00000 −3.77151 −1.70174 2.90105 1.00000 −0.104070 −3.77151
1.19 1.00000 −1.47034 1.00000 2.17542 −1.47034 −0.538935 1.00000 −0.838111 2.17542
1.20 1.00000 −1.44356 1.00000 1.04385 −1.44356 3.20508 1.00000 −0.916133 1.04385
See all 56 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.56
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.e 56
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6046.2.a.e 56 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6046))\):

\(T_{3}^{56} + \cdots\)
\(T_{11}^{56} + \cdots\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database