# Properties

 Label 2100.2.dn Level 2100 Weight 2 Character orbit dn Rep. character $$\chi_{2100}(67,\cdot)$$ Character field $$\Q(\zeta_{60})$$ Dimension 3840 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.dn (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$700$$ Character field: $$\Q(\zeta_{60})$$ Sturm bound: $$960$$

## Dimensions

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

Total New Old
Modular forms 7808 3840 3968
Cusp forms 7552 3840 3712
Eisenstein series 256 0 256

## Trace form

 $$3840q - 24q^{8} + O(q^{10})$$ $$3840q - 24q^{8} + 44q^{28} - 8q^{33} - 48q^{38} - 20q^{40} + 20q^{42} + 32q^{48} + 288q^{50} - 104q^{52} + 40q^{58} + 20q^{60} + 144q^{62} + 120q^{64} + 44q^{68} + 80q^{70} + 12q^{72} - 16q^{73} + 48q^{77} + 48q^{78} + 36q^{80} - 480q^{81} - 4q^{82} + 160q^{84} + 96q^{85} - 140q^{88} - 96q^{90} + 72q^{92} + 64q^{93} + 320q^{97} + 416q^{98} + O(q^{100})$$

## 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