# Properties

 Label 2100.2.cp Level 2100 Weight 2 Character orbit cp Rep. character $$\chi_{2100}(83,\cdot)$$ Character field $$\Q(\zeta_{20})$$ Dimension 3776 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.cp (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$2100$$ 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 3904 0
Cusp forms 3776 3776 0
Eisenstein series 128 128 0

## Trace form

 $$3776q - 40q^{4} - 40q^{9} + O(q^{10})$$ $$3776q - 40q^{4} - 40q^{9} - 24q^{16} - 8q^{18} - 12q^{21} - 16q^{22} - 64q^{25} + 16q^{28} - 16q^{30} - 44q^{36} - 64q^{37} + 6q^{42} - 24q^{46} - 40q^{57} - 8q^{58} - 80q^{60} - 40q^{64} + 32q^{70} - 4q^{72} - 76q^{78} - 24q^{81} - 10q^{84} - 64q^{85} - 64q^{88} - 8q^{93} + O(q^{100})$$

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

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

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database