Properties

Label 6037.2.a.b
Level 6037
Weight 2
Character orbit 6037.a
Self dual Yes
Analytic conductor 48.206
Analytic rank 0
Dimension 259
CM No

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Newspace parameters

Level: \( N \) = \( 6037 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6037.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2056877002\)
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.

\(\operatorname{Tr}(f)(q) = \) \(259q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 29q^{3} \) \(\mathstrut +\mathstrut 273q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 24q^{6} \) \(\mathstrut +\mathstrut 42q^{7} \) \(\mathstrut +\mathstrut 141q^{8} \) \(\mathstrut +\mathstrut 286q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(259q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 29q^{3} \) \(\mathstrut +\mathstrut 273q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 24q^{6} \) \(\mathstrut +\mathstrut 42q^{7} \) \(\mathstrut +\mathstrut 141q^{8} \) \(\mathstrut +\mathstrut 286q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 108q^{11} \) \(\mathstrut +\mathstrut 46q^{12} \) \(\mathstrut +\mathstrut 33q^{13} \) \(\mathstrut +\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 40q^{15} \) \(\mathstrut +\mathstrut 301q^{16} \) \(\mathstrut +\mathstrut 67q^{17} \) \(\mathstrut +\mathstrut 117q^{18} \) \(\mathstrut +\mathstrut 69q^{19} \) \(\mathstrut +\mathstrut 103q^{20} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut +\mathstrut 42q^{22} \) \(\mathstrut +\mathstrut 162q^{23} \) \(\mathstrut +\mathstrut 45q^{24} \) \(\mathstrut +\mathstrut 291q^{25} \) \(\mathstrut +\mathstrut 41q^{26} \) \(\mathstrut +\mathstrut 101q^{27} \) \(\mathstrut +\mathstrut 87q^{28} \) \(\mathstrut +\mathstrut 78q^{29} \) \(\mathstrut +\mathstrut 48q^{30} \) \(\mathstrut +\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut 314q^{32} \) \(\mathstrut +\mathstrut 67q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut +\mathstrut 252q^{35} \) \(\mathstrut +\mathstrut 337q^{36} \) \(\mathstrut +\mathstrut 49q^{37} \) \(\mathstrut +\mathstrut 59q^{38} \) \(\mathstrut +\mathstrut 93q^{39} \) \(\mathstrut +\mathstrut 44q^{40} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 38q^{42} \) \(\mathstrut +\mathstrut 178q^{43} \) \(\mathstrut +\mathstrut 171q^{44} \) \(\mathstrut +\mathstrut 67q^{45} \) \(\mathstrut +\mathstrut 43q^{46} \) \(\mathstrut +\mathstrut 185q^{47} \) \(\mathstrut +\mathstrut 67q^{48} \) \(\mathstrut +\mathstrut 273q^{49} \) \(\mathstrut +\mathstrut 204q^{50} \) \(\mathstrut +\mathstrut 145q^{51} \) \(\mathstrut +\mathstrut 83q^{52} \) \(\mathstrut +\mathstrut 112q^{53} \) \(\mathstrut +\mathstrut 60q^{54} \) \(\mathstrut +\mathstrut 57q^{55} \) \(\mathstrut +\mathstrut 93q^{56} \) \(\mathstrut +\mathstrut 109q^{57} \) \(\mathstrut +\mathstrut 63q^{58} \) \(\mathstrut +\mathstrut 228q^{59} \) \(\mathstrut +\mathstrut 53q^{60} \) \(\mathstrut +\mathstrut 20q^{61} \) \(\mathstrut +\mathstrut 126q^{62} \) \(\mathstrut +\mathstrut 153q^{63} \) \(\mathstrut +\mathstrut 345q^{64} \) \(\mathstrut +\mathstrut 113q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut +\mathstrut 208q^{67} \) \(\mathstrut +\mathstrut 166q^{68} \) \(\mathstrut +\mathstrut 10q^{69} \) \(\mathstrut +\mathstrut 69q^{70} \) \(\mathstrut +\mathstrut 150q^{71} \) \(\mathstrut +\mathstrut 331q^{72} \) \(\mathstrut +\mathstrut 75q^{73} \) \(\mathstrut +\mathstrut 84q^{74} \) \(\mathstrut +\mathstrut 72q^{75} \) \(\mathstrut +\mathstrut 102q^{76} \) \(\mathstrut +\mathstrut 166q^{77} \) \(\mathstrut +\mathstrut 69q^{78} \) \(\mathstrut +\mathstrut 52q^{79} \) \(\mathstrut +\mathstrut 180q^{80} \) \(\mathstrut +\mathstrut 327q^{81} \) \(\mathstrut +\mathstrut 43q^{82} \) \(\mathstrut +\mathstrut 434q^{83} \) \(\mathstrut +\mathstrut 75q^{85} \) \(\mathstrut +\mathstrut 133q^{86} \) \(\mathstrut +\mathstrut 144q^{87} \) \(\mathstrut +\mathstrut 111q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut -\mathstrut 8q^{90} \) \(\mathstrut +\mathstrut 35q^{91} \) \(\mathstrut +\mathstrut 372q^{92} \) \(\mathstrut +\mathstrut 160q^{93} \) \(\mathstrut +\mathstrut 36q^{94} \) \(\mathstrut +\mathstrut 154q^{95} \) \(\mathstrut +\mathstrut 60q^{96} \) \(\mathstrut +\mathstrut 35q^{97} \) \(\mathstrut +\mathstrut 254q^{98} \) \(\mathstrut +\mathstrut 234q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.75717 −1.09794 5.60201 2.84974 3.02722 3.79647 −9.93137 −1.79452 −7.85722
1.2 −2.66503 2.65532 5.10237 −0.476820 −7.07650 −1.66384 −8.26789 4.05073 1.27074
1.3 −2.65823 −1.47107 5.06620 −0.123247 3.91044 −2.04180 −8.15068 −0.835960 0.327620
1.4 −2.65707 2.92115 5.06000 0.928477 −7.76170 3.41739 −8.13063 5.53314 −2.46702
1.5 −2.64523 1.84208 4.99727 3.41959 −4.87275 2.32041 −7.92847 0.393274 −9.04562
1.6 −2.61164 1.28286 4.82065 −1.11903 −3.35038 −4.20141 −7.36653 −1.35426 2.92250
1.7 −2.60200 −2.50808 4.77039 0.421972 6.52603 −1.06326 −7.20855 3.29049 −1.09797
1.8 −2.60071 −0.749599 4.76372 −3.60076 1.94949 −2.40322 −7.18764 −2.43810 9.36455
1.9 −2.58809 −2.19108 4.69820 0.221659 5.67071 0.704833 −6.98319 1.80083 −0.573673
1.10 −2.58711 −3.26786 4.69312 2.66521 8.45431 2.69955 −6.96738 7.67894 −6.89517
1.11 −2.58398 0.626068 4.67694 −1.39938 −1.61774 0.699914 −6.91715 −2.60804 3.61596
1.12 −2.56682 2.69132 4.58858 1.90137 −6.90815 −1.37100 −6.64441 4.24322 −4.88048
1.13 −2.47379 −1.46896 4.11964 2.18568 3.63389 −2.37075 −5.24354 −0.842162 −5.40693
1.14 −2.46629 1.74062 4.08257 −1.65001 −4.29287 1.73775 −5.13620 0.0297629 4.06940
1.15 −2.46237 −0.199276 4.06325 −0.688498 0.490692 0.363231 −5.08049 −2.96029 1.69534
1.16 −2.44806 0.638947 3.99301 2.71697 −1.56418 −2.58742 −4.87901 −2.59175 −6.65132
1.17 −2.42988 0.381455 3.90430 −2.17078 −0.926887 −2.70764 −4.62721 −2.85449 5.27472
1.18 −2.42952 −2.16225 3.90258 −1.13309 5.25323 1.20579 −4.62237 1.67531 2.75288
1.19 −2.38315 −2.49497 3.67942 −2.67299 5.94590 −2.23204 −4.00231 3.22488 6.37013
1.20 −2.38263 −0.344809 3.67692 0.273793 0.821552 0.727572 −3.99549 −2.88111 −0.652346
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
\(6037\) \(-1\)