# Properties

 Label 2100.2.da Level 2100 Weight 2 Character orbit da Rep. character $$\chi_{2100}(31,\cdot)$$ Character field $$\Q(\zeta_{30})$$ Dimension 1920 Sturm bound 960

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2100.da (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$700$$ Character field: $$\Q(\zeta_{30})$$ Sturm bound: $$960$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2100, [\chi])$$.

Total New Old
Modular forms 3904 1920 1984
Cusp forms 3776 1920 1856
Eisenstein series 128 0 128

## Trace form

 $$1920q + 36q^{8} + 240q^{9} + O(q^{10})$$ $$1920q + 36q^{8} + 240q^{9} + 18q^{10} + 12q^{14} + 4q^{25} - 20q^{28} + 32q^{30} + 24q^{33} + 54q^{38} + 30q^{40} - 20q^{42} + 20q^{46} - 8q^{49} - 156q^{50} + 162q^{52} - 36q^{56} + 52q^{58} + 22q^{60} + 12q^{64} + 132q^{68} - 34q^{70} - 18q^{72} + 44q^{74} - 48q^{77} + 48q^{78} + 72q^{80} + 240q^{81} + 60q^{82} - 48q^{84} + 64q^{85} - 30q^{88} - 108q^{92} + 64q^{93} + 90q^{96} - 136q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2100, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(2100, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2100, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(700, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database