# Properties

 Label 1849.4.g Level $1849$ Weight $4$ Character orbit 1849.g Rep. character $\chi_{1849}(210,\cdot)$ Character field $\Q(\zeta_{21})$ Dimension $5172$ Sturm bound $630$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1849 = 43^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1849.g (of order $$21$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$43$$ Character field: $$\Q(\zeta_{21})$$ Sturm bound: $$630$$

## Dimensions

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

Total New Old
Modular forms 5940 5652 288
Cusp forms 5412 5172 240
Eisenstein series 528 480 48

## Trace form

 $$5172q + 12q^{2} + 9q^{3} - 3268q^{4} - 5q^{5} + 22q^{6} + 54q^{7} - 2q^{8} + 3390q^{9} + O(q^{10})$$ $$5172q + 12q^{2} + 9q^{3} - 3268q^{4} - 5q^{5} + 22q^{6} + 54q^{7} - 2q^{8} + 3390q^{9} + 41q^{10} + 88q^{11} - 114q^{12} + 163q^{13} - 254q^{14} + 163q^{15} - 11752q^{16} - 60q^{17} + 72q^{18} + 407q^{19} - 621q^{20} - 193q^{21} + 520q^{22} + 245q^{23} - 1072q^{24} + 9012q^{25} + 133q^{26} - 180q^{27} - 1228q^{28} + 17q^{29} + 1796q^{30} + 1003q^{31} + 2730q^{32} - 473q^{33} + 1043q^{34} + 241q^{35} - 72401q^{36} + 228q^{37} - 1512q^{38} - 1250q^{39} - 2673q^{40} + 76q^{41} - 5286q^{42} + 332q^{44} - 856q^{45} - 4331q^{46} - 714q^{47} - 5243q^{48} - 91346q^{49} + 3273q^{50} + 4803q^{51} + 3474q^{52} + 1491q^{53} + 4130q^{54} + 1460q^{55} + 2647q^{56} + 719q^{57} - 142q^{58} - 1242q^{59} - 4533q^{60} - 837q^{61} + 3959q^{62} - 3279q^{63} - 43350q^{64} - 54q^{65} + 3219q^{66} - 1226q^{67} + 875q^{68} + 4715q^{69} + 2553q^{70} + 1619q^{71} + 20137q^{72} + 3630q^{73} + 5104q^{74} + 1186q^{75} - 1092q^{76} - 3515q^{77} - 2980q^{78} - 5982q^{79} + 1610q^{80} + 26202q^{81} - 5292q^{82} - 10192q^{83} - 18435q^{84} - 8666q^{85} - 13218q^{87} - 7290q^{88} - 11478q^{89} - 26961q^{90} - 11920q^{91} - 5782q^{92} + 4q^{93} + 14736q^{94} + 1151q^{95} + 7222q^{96} - 1276q^{97} + 5254q^{98} + 6967q^{99} + O(q^{100})$$

## 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

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