# Properties

 Label 2100.2.cs Level 2100 Weight 2 Character orbit cs Rep. character $$\chi_{2100}(127,\cdot)$$ Character field $$\Q(\zeta_{20})$$ Dimension 1440 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.cs (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$100$$ Character field: $$\Q(\zeta_{20})$$ Sturm bound: $$960$$

## Dimensions

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

Total New Old
Modular forms 3904 1440 2464
Cusp forms 3776 1440 2336
Eisenstein series 128 0 128

## Trace form

 $$1440q + O(q^{10})$$ $$1440q - 16q^{10} - 16q^{12} - 8q^{13} - 40q^{17} + 40q^{20} + 24q^{22} - 40q^{25} + 16q^{30} + 40q^{32} + 8q^{37} + 56q^{38} + 144q^{40} + 280q^{44} + 8q^{45} + 40q^{50} + 16q^{52} + 8q^{53} + 248q^{58} + 160q^{62} + 40q^{65} + 56q^{68} + 104q^{73} - 24q^{78} + 80q^{80} + 360q^{81} + 16q^{82} + 32q^{85} - 112q^{88} + 520q^{89} - 360q^{92} + 64q^{93} - 80q^{94} + 40q^{96} + 40q^{97} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(2100, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(300, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(700, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database