# Properties

 Label 2850.2.i Level $2850$ Weight $2$ Character orbit 2850.i Rep. character $\chi_{2850}(2101,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $124$ Sturm bound $1200$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2850.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Sturm bound: $$1200$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2850, [\chi])$$.

Total New Old
Modular forms 1248 124 1124
Cusp forms 1152 124 1028
Eisenstein series 96 0 96

## Trace form

 $$124q + 2q^{3} - 62q^{4} + 12q^{7} - 62q^{9} + O(q^{10})$$ $$124q + 2q^{3} - 62q^{4} + 12q^{7} - 62q^{9} - 4q^{12} - 6q^{13} + 12q^{14} - 62q^{16} - 12q^{17} - 24q^{19} - 14q^{21} + 4q^{22} + 8q^{23} + 24q^{26} - 4q^{27} - 6q^{28} + 12q^{29} + 4q^{31} + 8q^{33} - 12q^{34} - 62q^{36} - 12q^{37} - 8q^{38} + 28q^{39} - 4q^{42} - 14q^{43} + 32q^{46} - 4q^{47} + 2q^{48} + 120q^{49} - 4q^{51} - 6q^{52} - 24q^{56} + 6q^{57} + 8q^{58} - 28q^{59} - 6q^{61} + 12q^{62} - 6q^{63} + 124q^{64} + 4q^{66} + 2q^{67} + 24q^{68} + 16q^{69} - 2q^{73} + 12q^{74} + 18q^{76} - 48q^{77} + 12q^{78} + 22q^{79} - 62q^{81} + 16q^{82} + 24q^{83} + 28q^{84} + 24q^{87} - 8q^{88} - 36q^{89} + 18q^{91} + 8q^{92} - 18q^{93} + 48q^{94} + 28q^{97} - 8q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2850, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(2850, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2850, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(475, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(570, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(950, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1425, [\chi])$$$$^{\oplus 2}$$