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Properties

Label 1849.4.c
Level $1849$
Weight $4$
Character orbit 1849.c
Rep. character $\chi_{1849}(423,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $862$
Sturm bound $630$

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Defining parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(630\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1849, [\chi])\).

Total New Old
Modular forms 990 942 48
Cusp forms 902 862 40
Eisenstein series 88 80 8

Trace form

\( 862 q + 2 q^{2} + 5 q^{3} + 3282 q^{4} + 19 q^{5} - 15 q^{6} + 51 q^{7} + 72 q^{8} - 3474 q^{9} + O(q^{10}) \) \( 862 q + 2 q^{2} + 5 q^{3} + 3282 q^{4} + 19 q^{5} - 15 q^{6} + 51 q^{7} + 72 q^{8} - 3474 q^{9} - 27 q^{10} - 74 q^{11} + 72 q^{12} + 19 q^{13} - 96 q^{14} - 65 q^{15} + 11962 q^{16} + 74 q^{17} - 247 q^{18} - 78 q^{19} + 495 q^{20} + 18 q^{21} - 380 q^{22} + 35 q^{23} - 202 q^{24} - 8774 q^{25} + 21 q^{26} + 194 q^{27} + 794 q^{28} + 53 q^{29} - 627 q^{30} - 303 q^{31} + 798 q^{32} + 424 q^{33} + 231 q^{34} - 710 q^{35} - 11004 q^{36} + 129 q^{37} + 854 q^{38} - 1382 q^{39} - 1345 q^{40} - 622 q^{41} - 62 q^{42} - 1158 q^{44} - 1888 q^{45} + 40 q^{46} + 420 q^{47} + 2401 q^{48} - 15320 q^{49} - 424 q^{50} - 1590 q^{51} + 628 q^{52} - 889 q^{53} - 1848 q^{54} + 1242 q^{55} + 1581 q^{56} + 765 q^{57} - 1328 q^{58} + 3006 q^{59} + 1565 q^{60} - 437 q^{61} - 1509 q^{62} + 2222 q^{63} + 39108 q^{64} + 2126 q^{65} - 1245 q^{66} + 484 q^{67} + 924 q^{68} + 3503 q^{69} + 170 q^{70} + 1545 q^{71} - 3834 q^{72} - 1292 q^{73} + 2134 q^{74} - 164 q^{75} + 252 q^{76} - 1448 q^{77} - 5644 q^{78} + 1145 q^{79} + 3157 q^{80} - 23087 q^{81} - 6608 q^{82} - 749 q^{83} - 6268 q^{84} - 1946 q^{85} - 4562 q^{87} + 5372 q^{88} + 2196 q^{89} - 668 q^{90} + 3513 q^{91} - 3045 q^{92} + 983 q^{93} - 9878 q^{94} + 739 q^{95} - 4562 q^{96} - 110 q^{97} + 213 q^{98} + 3631 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1849, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1849, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1849, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 2}\)