# Properties

 Label 2004.2.h Level 2004 Weight 2 Character orbit h Rep. character $$\chi_{2004}(1001,\cdot)$$ Character field $$\Q$$ Dimension 56 Newform subspaces 1 Sturm bound 672 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2004 = 2^{2} \cdot 3 \cdot 167$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2004.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$501$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$672$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2004, [\chi])$$.

Total New Old
Modular forms 342 56 286
Cusp forms 330 56 274
Eisenstein series 12 0 12

## Trace form

 $$56q - 8q^{9} + O(q^{10})$$ $$56q - 8q^{9} - 4q^{19} + 4q^{21} + 52q^{25} + 12q^{27} + 4q^{31} - 8q^{33} + 32q^{49} + 24q^{57} + 28q^{61} - 26q^{63} - 54q^{75} - 24q^{81} + 8q^{85} + 14q^{87} - 20q^{93} + 36q^{97} + 32q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2004, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2004.2.h.a $$56$$ $$16.002$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2004, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2004, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(501, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1002, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database