Properties

Label 6043.2.a.c
Level 6043
Weight 2
Character orbit 6043.a
Self dual Yes
Analytic conductor 48.254
Analytic rank 0
Dimension 259
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: \(0\)
Dimension: \(259\)
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.

\(\operatorname{Tr}(f)(q) = \) \(259q \) \(\mathstrut +\mathstrut 39q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 271q^{4} \) \(\mathstrut +\mathstrut 83q^{5} \) \(\mathstrut +\mathstrut 18q^{6} \) \(\mathstrut +\mathstrut 26q^{7} \) \(\mathstrut +\mathstrut 111q^{8} \) \(\mathstrut +\mathstrut 286q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(259q \) \(\mathstrut +\mathstrut 39q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 271q^{4} \) \(\mathstrut +\mathstrut 83q^{5} \) \(\mathstrut +\mathstrut 18q^{6} \) \(\mathstrut +\mathstrut 26q^{7} \) \(\mathstrut +\mathstrut 111q^{8} \) \(\mathstrut +\mathstrut 286q^{9} \) \(\mathstrut +\mathstrut 36q^{10} \) \(\mathstrut +\mathstrut 35q^{11} \) \(\mathstrut +\mathstrut 58q^{12} \) \(\mathstrut +\mathstrut 109q^{13} \) \(\mathstrut +\mathstrut 31q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 287q^{16} \) \(\mathstrut +\mathstrut 124q^{17} \) \(\mathstrut +\mathstrut 97q^{18} \) \(\mathstrut +\mathstrut 42q^{19} \) \(\mathstrut +\mathstrut 149q^{20} \) \(\mathstrut +\mathstrut 99q^{21} \) \(\mathstrut +\mathstrut 22q^{22} \) \(\mathstrut +\mathstrut 63q^{23} \) \(\mathstrut +\mathstrut 53q^{24} \) \(\mathstrut +\mathstrut 308q^{25} \) \(\mathstrut +\mathstrut 86q^{26} \) \(\mathstrut +\mathstrut 82q^{27} \) \(\mathstrut +\mathstrut 52q^{28} \) \(\mathstrut +\mathstrut 131q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut +\mathstrut 29q^{31} \) \(\mathstrut +\mathstrut 251q^{32} \) \(\mathstrut +\mathstrut 147q^{33} \) \(\mathstrut +\mathstrut 24q^{34} \) \(\mathstrut +\mathstrut 79q^{35} \) \(\mathstrut +\mathstrut 315q^{36} \) \(\mathstrut +\mathstrut 108q^{37} \) \(\mathstrut +\mathstrut 124q^{38} \) \(\mathstrut +\mathstrut 48q^{39} \) \(\mathstrut +\mathstrut 87q^{40} \) \(\mathstrut +\mathstrut 190q^{41} \) \(\mathstrut +\mathstrut 28q^{42} \) \(\mathstrut +\mathstrut 36q^{43} \) \(\mathstrut +\mathstrut 70q^{44} \) \(\mathstrut +\mathstrut 211q^{45} \) \(\mathstrut +\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 186q^{47} \) \(\mathstrut +\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 297q^{49} \) \(\mathstrut +\mathstrut 161q^{50} \) \(\mathstrut +\mathstrut 20q^{51} \) \(\mathstrut +\mathstrut 173q^{52} \) \(\mathstrut +\mathstrut 213q^{53} \) \(\mathstrut +\mathstrut 56q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 99q^{56} \) \(\mathstrut +\mathstrut 80q^{57} \) \(\mathstrut +\mathstrut 32q^{58} \) \(\mathstrut +\mathstrut 135q^{59} \) \(\mathstrut +\mathstrut 23q^{60} \) \(\mathstrut +\mathstrut 83q^{61} \) \(\mathstrut +\mathstrut 172q^{62} \) \(\mathstrut +\mathstrut 85q^{63} \) \(\mathstrut +\mathstrut 297q^{64} \) \(\mathstrut +\mathstrut 177q^{65} \) \(\mathstrut +\mathstrut 41q^{66} \) \(\mathstrut +\mathstrut 30q^{67} \) \(\mathstrut +\mathstrut 271q^{68} \) \(\mathstrut +\mathstrut 168q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut +\mathstrut 63q^{71} \) \(\mathstrut +\mathstrut 241q^{72} \) \(\mathstrut +\mathstrut 152q^{73} \) \(\mathstrut +\mathstrut 32q^{74} \) \(\mathstrut +\mathstrut 36q^{75} \) \(\mathstrut +\mathstrut 92q^{76} \) \(\mathstrut +\mathstrut 396q^{77} \) \(\mathstrut +\mathstrut 21q^{78} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut 242q^{80} \) \(\mathstrut +\mathstrut 343q^{81} \) \(\mathstrut +\mathstrut 40q^{82} \) \(\mathstrut +\mathstrut 236q^{83} \) \(\mathstrut +\mathstrut 92q^{84} \) \(\mathstrut +\mathstrut 124q^{85} \) \(\mathstrut +\mathstrut 55q^{86} \) \(\mathstrut +\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 7q^{88} \) \(\mathstrut +\mathstrut 214q^{89} \) \(\mathstrut +\mathstrut 100q^{90} \) \(\mathstrut +\mathstrut 2q^{91} \) \(\mathstrut +\mathstrut 176q^{92} \) \(\mathstrut +\mathstrut 228q^{93} \) \(\mathstrut +\mathstrut 51q^{94} \) \(\mathstrut +\mathstrut 96q^{95} \) \(\mathstrut +\mathstrut 48q^{96} \) \(\mathstrut +\mathstrut 135q^{97} \) \(\mathstrut +\mathstrut 261q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.74821 2.62862 5.55264 2.51369 −7.22400 −0.922798 −9.76337 3.90966 −6.90814
1.2 −2.71457 −1.54009 5.36892 −1.75287 4.18068 1.37518 −9.14518 −0.628138 4.75830
1.3 −2.69191 2.00966 5.24636 −1.44990 −5.40981 0.895791 −8.73889 1.03872 3.90300
1.4 −2.66716 0.658905 5.11375 −0.783297 −1.75741 −0.338104 −8.30489 −2.56584 2.08918
1.5 −2.66509 0.277531 5.10272 0.539093 −0.739647 3.78634 −8.26903 −2.92298 −1.43673
1.6 −2.66120 −0.520492 5.08201 3.83583 1.38513 −0.144514 −8.20186 −2.72909 −10.2079
1.7 −2.63895 −2.10254 4.96408 0.468058 5.54852 −0.663333 −7.82206 1.42069 −1.23518
1.8 −2.62452 −2.36333 4.88811 3.68491 6.20260 1.44250 −7.57990 2.58531 −9.67113
1.9 −2.58624 1.73815 4.68864 −2.85125 −4.49526 −1.90278 −6.95348 0.0211502 7.37403
1.10 −2.57414 1.55511 4.62619 −0.336132 −4.00307 −3.88876 −6.76018 −0.581626 0.865250
1.11 −2.53746 −1.57895 4.43871 2.23521 4.00652 −0.788927 −6.18813 −0.506916 −5.67175
1.12 −2.52420 −2.07136 4.37157 −1.62373 5.22852 0.688788 −5.98631 1.29054 4.09861
1.13 −2.51764 −0.610944 4.33849 0.176769 1.53813 −3.05611 −5.88747 −2.62675 −0.445041
1.14 −2.51568 2.81970 4.32863 2.54444 −7.09345 1.96405 −5.85808 4.95070 −6.40100
1.15 −2.51359 −1.58136 4.31814 −2.14765 3.97489 −4.03310 −5.82684 −0.499302 5.39832
1.16 −2.50362 3.44242 4.26813 0.601384 −8.61852 3.68483 −5.67855 8.85024 −1.50564
1.17 −2.45883 0.759848 4.04584 3.80282 −1.86834 2.58562 −5.03037 −2.42263 −9.35049
1.18 −2.44655 2.77282 3.98563 −0.534926 −6.78385 0.576903 −4.85795 4.68851 1.30873
1.19 −2.43851 1.58144 3.94631 0.896601 −3.85634 −4.81539 −4.74608 −0.499059 −2.18637
1.20 −2.43000 −2.97934 3.90490 2.39158 7.23980 −4.31478 −4.62892 5.87647 −5.81153
See next 80 embeddings (of 259 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.259
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 \(T_{2}^{259} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6043))\).