Properties

Label 6047.2.a.b
Level 6047
Weight 2
Character orbit 6047.a
Self dual Yes
Analytic conductor 48.286
Analytic rank 0
Dimension 287
CM No

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Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(0\)
Dimension: \(287\)
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.

\(\operatorname{Tr}(f)(q) = \) \(287q \) \(\mathstrut +\mathstrut 21q^{2} \) \(\mathstrut +\mathstrut 29q^{3} \) \(\mathstrut +\mathstrut 319q^{4} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 60q^{8} \) \(\mathstrut +\mathstrut 352q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(287q \) \(\mathstrut +\mathstrut 21q^{2} \) \(\mathstrut +\mathstrut 29q^{3} \) \(\mathstrut +\mathstrut 319q^{4} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 60q^{8} \) \(\mathstrut +\mathstrut 352q^{9} \) \(\mathstrut +\mathstrut 38q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 80q^{12} \) \(\mathstrut +\mathstrut 86q^{13} \) \(\mathstrut +\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 375q^{16} \) \(\mathstrut +\mathstrut 59q^{17} \) \(\mathstrut +\mathstrut 93q^{18} \) \(\mathstrut +\mathstrut 39q^{19} \) \(\mathstrut +\mathstrut 27q^{20} \) \(\mathstrut +\mathstrut 51q^{21} \) \(\mathstrut +\mathstrut 99q^{22} \) \(\mathstrut +\mathstrut 68q^{23} \) \(\mathstrut +\mathstrut 31q^{24} \) \(\mathstrut +\mathstrut 492q^{25} \) \(\mathstrut +\mathstrut 19q^{26} \) \(\mathstrut +\mathstrut 107q^{27} \) \(\mathstrut +\mathstrut 142q^{28} \) \(\mathstrut +\mathstrut 39q^{29} \) \(\mathstrut +\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 104q^{31} \) \(\mathstrut +\mathstrut 131q^{32} \) \(\mathstrut +\mathstrut 139q^{33} \) \(\mathstrut +\mathstrut 71q^{34} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 410q^{36} \) \(\mathstrut +\mathstrut 298q^{37} \) \(\mathstrut +\mathstrut 19q^{38} \) \(\mathstrut +\mathstrut 37q^{39} \) \(\mathstrut +\mathstrut 98q^{40} \) \(\mathstrut +\mathstrut 90q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 85q^{44} \) \(\mathstrut +\mathstrut 73q^{45} \) \(\mathstrut +\mathstrut 97q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 161q^{48} \) \(\mathstrut +\mathstrut 473q^{49} \) \(\mathstrut +\mathstrut 85q^{50} \) \(\mathstrut +\mathstrut 34q^{51} \) \(\mathstrut +\mathstrut 179q^{52} \) \(\mathstrut +\mathstrut 95q^{53} \) \(\mathstrut +\mathstrut 28q^{54} \) \(\mathstrut +\mathstrut 62q^{55} \) \(\mathstrut +\mathstrut 16q^{56} \) \(\mathstrut +\mathstrut 247q^{57} \) \(\mathstrut +\mathstrut 247q^{58} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 51q^{60} \) \(\mathstrut +\mathstrut 106q^{61} \) \(\mathstrut +\mathstrut 22q^{62} \) \(\mathstrut +\mathstrut 104q^{63} \) \(\mathstrut +\mathstrut 480q^{64} \) \(\mathstrut +\mathstrut 150q^{65} \) \(\mathstrut -\mathstrut 27q^{66} \) \(\mathstrut +\mathstrut 232q^{67} \) \(\mathstrut +\mathstrut 88q^{68} \) \(\mathstrut +\mathstrut 57q^{69} \) \(\mathstrut +\mathstrut 123q^{70} \) \(\mathstrut +\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 240q^{72} \) \(\mathstrut +\mathstrut 372q^{73} \) \(\mathstrut +\mathstrut 13q^{74} \) \(\mathstrut +\mathstrut 81q^{75} \) \(\mathstrut +\mathstrut 82q^{76} \) \(\mathstrut +\mathstrut 65q^{77} \) \(\mathstrut +\mathstrut 154q^{78} \) \(\mathstrut +\mathstrut 143q^{79} \) \(\mathstrut +\mathstrut 17q^{80} \) \(\mathstrut +\mathstrut 519q^{81} \) \(\mathstrut +\mathstrut 98q^{82} \) \(\mathstrut +\mathstrut 49q^{83} \) \(\mathstrut +\mathstrut 79q^{84} \) \(\mathstrut +\mathstrut 236q^{85} \) \(\mathstrut +\mathstrut 61q^{86} \) \(\mathstrut +\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 254q^{88} \) \(\mathstrut +\mathstrut 114q^{89} \) \(\mathstrut +\mathstrut 36q^{90} \) \(\mathstrut +\mathstrut 96q^{91} \) \(\mathstrut +\mathstrut 151q^{92} \) \(\mathstrut +\mathstrut 189q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 30q^{95} \) \(\mathstrut +\mathstrut 23q^{96} \) \(\mathstrut +\mathstrut 503q^{97} \) \(\mathstrut +\mathstrut 91q^{98} \) \(\mathstrut +\mathstrut 130q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.82393 0.966727 5.97458 −3.10169 −2.72997 3.62589 −11.2239 −2.06544 8.75895
1.2 −2.77891 2.72758 5.72233 3.39937 −7.57970 2.40965 −10.3440 4.43971 −9.44654
1.3 −2.77777 −0.912476 5.71599 −2.85880 2.53465 1.63814 −10.3222 −2.16739 7.94108
1.4 −2.77436 2.72832 5.69705 0.314782 −7.56934 −2.82964 −10.2569 4.44375 −0.873318
1.5 −2.72275 −2.45696 5.41335 −2.55614 6.68969 2.46431 −9.29370 3.03667 6.95973
1.6 −2.69892 0.321066 5.28419 −2.61974 −0.866532 −2.02949 −8.86379 −2.89692 7.07048
1.7 −2.69592 −1.00544 5.26800 3.45607 2.71058 −2.60868 −8.81026 −1.98909 −9.31730
1.8 −2.69052 −1.22455 5.23892 3.48449 3.29468 4.74165 −8.71440 −1.50048 −9.37511
1.9 −2.65594 2.26002 5.05400 −1.82444 −6.00248 −0.589488 −8.11124 2.10770 4.84561
1.10 −2.65477 2.03227 5.04782 −0.522833 −5.39521 4.81464 −8.09128 1.13010 1.38800
1.11 −2.63049 −1.81721 4.91948 0.465740 4.78015 0.973946 −7.67967 0.302245 −1.22512
1.12 −2.60365 1.57080 4.77897 2.08285 −4.08981 −3.47220 −7.23545 −0.532582 −5.42301
1.13 −2.59725 −1.79883 4.74569 3.88835 4.67200 −2.12607 −7.13122 0.235784 −10.0990
1.14 −2.59707 −2.63415 4.74475 −0.775653 6.84106 2.06715 −7.12830 3.93875 2.01442
1.15 −2.59210 −2.49236 4.71900 2.95307 6.46045 −0.174259 −7.04794 3.21184 −7.65466
1.16 −2.58681 1.99218 4.69158 0.151026 −5.15340 −4.97386 −6.96259 0.968794 −0.390675
1.17 −2.58121 2.05935 4.66263 −2.01171 −5.31560 −0.352944 −6.87281 1.24091 5.19265
1.18 −2.56224 3.46263 4.56507 −4.38158 −8.87209 2.36597 −6.57231 8.98983 11.2266
1.19 −2.56189 −1.33145 4.56327 1.10606 3.41103 1.45032 −6.56680 −1.22724 −2.83359
1.20 −2.54598 0.470310 4.48203 0.162012 −1.19740 3.47622 −6.31920 −2.77881 −0.412479
See next 80 embeddings (of 287 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.287
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(6047\) \(-1\)