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

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

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

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