# Properties

 Label 2100.2.w Level 2100 Weight 2 Character orbit w Rep. character $$\chi_{2100}(1007,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 560 Sturm bound 960

# Learn more about

## Defining parameters

 Level: $$N$$ $$=$$ $$2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2100.w (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$420$$ Character field: $$\Q(i)$$ Sturm bound: $$960$$

## Dimensions

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

Total New Old
Modular forms 1008 592 416
Cusp forms 912 560 352
Eisenstein series 96 32 64

## Trace form

 $$560q + O(q^{10})$$ $$560q - 16q^{16} + 12q^{18} + 8q^{21} + 24q^{22} + 36q^{28} + 24q^{36} + 16q^{37} + 16q^{42} - 16q^{46} + 32q^{58} + 16q^{72} - 116q^{78} + 144q^{81} + 96q^{88} + 32q^{93} + O(q^{100})$$

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

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

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

$$S_{2}^{\mathrm{old}}(2100, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(420, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database