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

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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: \(56\)
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.

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

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 −3.35147 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 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6046))\):

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