Properties

Label 6043.2.a.b
Level 6043
Weight 2
Character orbit 6043.a
Self dual Yes
Analytic conductor 48.254
Analytic rank 1
Dimension 243
CM No

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Newspace parameters

Level: \( N \) = \( 6043 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2535979415\)
Analytic rank: \(1\)
Dimension: \(243\)
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.

\(\operatorname{Tr}(f)(q) = \) \(243q \) \(\mathstrut -\mathstrut 40q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 232q^{4} \) \(\mathstrut -\mathstrut 85q^{5} \) \(\mathstrut -\mathstrut 20q^{6} \) \(\mathstrut -\mathstrut 28q^{7} \) \(\mathstrut -\mathstrut 114q^{8} \) \(\mathstrut +\mathstrut 210q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(243q \) \(\mathstrut -\mathstrut 40q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 232q^{4} \) \(\mathstrut -\mathstrut 85q^{5} \) \(\mathstrut -\mathstrut 20q^{6} \) \(\mathstrut -\mathstrut 28q^{7} \) \(\mathstrut -\mathstrut 114q^{8} \) \(\mathstrut +\mathstrut 210q^{9} \) \(\mathstrut -\mathstrut 24q^{10} \) \(\mathstrut -\mathstrut 37q^{11} \) \(\mathstrut -\mathstrut 74q^{12} \) \(\mathstrut -\mathstrut 113q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut -\mathstrut 34q^{15} \) \(\mathstrut +\mathstrut 218q^{16} \) \(\mathstrut -\mathstrut 125q^{17} \) \(\mathstrut -\mathstrut 108q^{18} \) \(\mathstrut -\mathstrut 46q^{19} \) \(\mathstrut -\mathstrut 157q^{20} \) \(\mathstrut -\mathstrut 113q^{21} \) \(\mathstrut -\mathstrut 16q^{22} \) \(\mathstrut -\mathstrut 60q^{23} \) \(\mathstrut -\mathstrut 49q^{24} \) \(\mathstrut +\mathstrut 208q^{25} \) \(\mathstrut -\mathstrut 52q^{26} \) \(\mathstrut -\mathstrut 90q^{27} \) \(\mathstrut -\mathstrut 70q^{28} \) \(\mathstrut -\mathstrut 137q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 258q^{32} \) \(\mathstrut -\mathstrut 153q^{33} \) \(\mathstrut -\mathstrut 23q^{34} \) \(\mathstrut -\mathstrut 77q^{35} \) \(\mathstrut +\mathstrut 180q^{36} \) \(\mathstrut -\mathstrut 108q^{37} \) \(\mathstrut -\mathstrut 122q^{38} \) \(\mathstrut -\mathstrut 32q^{39} \) \(\mathstrut -\mathstrut 57q^{40} \) \(\mathstrut -\mathstrut 186q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 54q^{43} \) \(\mathstrut -\mathstrut 90q^{44} \) \(\mathstrut -\mathstrut 233q^{45} \) \(\mathstrut -\mathstrut 42q^{46} \) \(\mathstrut -\mathstrut 188q^{47} \) \(\mathstrut -\mathstrut 149q^{48} \) \(\mathstrut +\mathstrut 189q^{49} \) \(\mathstrut -\mathstrut 146q^{50} \) \(\mathstrut -\mathstrut 34q^{51} \) \(\mathstrut -\mathstrut 195q^{52} \) \(\mathstrut -\mathstrut 196q^{53} \) \(\mathstrut -\mathstrut 36q^{54} \) \(\mathstrut -\mathstrut 57q^{55} \) \(\mathstrut -\mathstrut 63q^{56} \) \(\mathstrut -\mathstrut 76q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 137q^{59} \) \(\mathstrut -\mathstrut 73q^{60} \) \(\mathstrut -\mathstrut 96q^{61} \) \(\mathstrut -\mathstrut 167q^{62} \) \(\mathstrut -\mathstrut 113q^{63} \) \(\mathstrut +\mathstrut 224q^{64} \) \(\mathstrut -\mathstrut 131q^{65} \) \(\mathstrut -\mathstrut 11q^{66} \) \(\mathstrut -\mathstrut 71q^{67} \) \(\mathstrut -\mathstrut 260q^{68} \) \(\mathstrut -\mathstrut 162q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 77q^{71} \) \(\mathstrut -\mathstrut 290q^{72} \) \(\mathstrut -\mathstrut 160q^{73} \) \(\mathstrut -\mathstrut 34q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 84q^{76} \) \(\mathstrut -\mathstrut 416q^{77} \) \(\mathstrut -\mathstrut 59q^{78} \) \(\mathstrut -\mathstrut 17q^{79} \) \(\mathstrut -\mathstrut 268q^{80} \) \(\mathstrut +\mathstrut 147q^{81} \) \(\mathstrut -\mathstrut 28q^{82} \) \(\mathstrut -\mathstrut 238q^{83} \) \(\mathstrut -\mathstrut 184q^{84} \) \(\mathstrut -\mathstrut 108q^{85} \) \(\mathstrut -\mathstrut 61q^{86} \) \(\mathstrut -\mathstrut 127q^{87} \) \(\mathstrut -\mathstrut 47q^{88} \) \(\mathstrut -\mathstrut 183q^{89} \) \(\mathstrut -\mathstrut 56q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut -\mathstrut 109q^{92} \) \(\mathstrut -\mathstrut 206q^{93} \) \(\mathstrut +\mathstrut q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 127q^{97} \) \(\mathstrut -\mathstrut 294q^{98} \) \(\mathstrut -\mathstrut 66q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.82300 0.597654 5.96933 −3.72082 −1.68718 −3.33856 −11.2054 −2.64281 10.5039
1.2 −2.80165 −0.611503 5.84923 2.20797 1.71322 −5.04593 −10.7842 −2.62606 −6.18596
1.3 −2.79141 −3.08096 5.79195 −0.513295 8.60020 −1.76306 −10.5849 6.49230 1.43282
1.4 −2.78744 0.620034 5.76982 0.534830 −1.72831 −0.323304 −10.5081 −2.61556 −1.49081
1.5 −2.77909 1.09974 5.72334 2.87165 −3.05629 2.58870 −10.3475 −1.79056 −7.98057
1.6 −2.76632 −1.35744 5.65252 −2.91911 3.75510 1.53004 −10.1040 −1.15737 8.07518
1.7 −2.76265 1.82603 5.63224 −3.05466 −5.04467 4.94747 −10.0346 0.334370 8.43896
1.8 −2.75980 −3.38147 5.61647 1.70872 9.33216 5.00632 −9.98072 8.43432 −4.71572
1.9 −2.72028 −2.17990 5.39995 −3.45469 5.92994 1.90963 −9.24882 1.75196 9.39775
1.10 −2.71539 −2.22479 5.37337 1.62014 6.04118 −3.35178 −9.16003 1.94968 −4.39933
1.11 −2.71243 2.12328 5.35728 1.35121 −5.75926 0.0653501 −9.10638 1.50834 −3.66505
1.12 −2.70932 3.28141 5.34043 −1.89583 −8.89039 0.209771 −9.05031 7.76762 5.13641
1.13 −2.64143 −1.28560 4.97716 2.15419 3.39581 3.78416 −7.86396 −1.34724 −5.69015
1.14 −2.64136 2.66871 4.97680 3.42573 −7.04902 −3.32847 −7.86280 4.12199 −9.04859
1.15 −2.63490 3.27029 4.94268 −2.75610 −8.61687 −4.50836 −7.75365 7.69478 7.26204
1.16 −2.56275 2.38749 4.56769 −3.37811 −6.11854 0.794528 −6.58035 2.70010 8.65725
1.17 −2.55204 −3.15051 4.51292 −4.10943 8.04024 −3.50763 −6.41307 6.92573 10.4874
1.18 −2.55150 0.112762 4.51017 −1.14524 −0.287713 −1.83176 −6.40472 −2.98728 2.92209
1.19 −2.55008 −1.24259 4.50293 −2.88473 3.16871 −3.99948 −6.38267 −1.45597 7.35631
1.20 −2.53808 −2.96165 4.44184 −3.22634 7.51690 0.844603 −6.19757 5.77138 8.18871
See next 80 embeddings (of 243 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.243
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

\( p \) Sign
\(6043\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{243} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6043))\).