# Properties

 Label 504.2.j Level 504 Weight 2 Character orbit j Rep. character $$\chi_{504}(323,\cdot)$$ Character field $$\Q$$ Dimension 24 Newform subspaces 1 Sturm bound 192 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$504 = 2^{3} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 504.j (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$24$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$192$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(504, [\chi])$$.

Total New Old
Modular forms 104 24 80
Cusp forms 88 24 64
Eisenstein series 16 0 16

## Trace form

 $$24q - 8q^{4} + O(q^{10})$$ $$24q - 8q^{4} + 24q^{10} + 12q^{16} + 32q^{19} + 12q^{22} + 24q^{25} + 4q^{28} - 8q^{40} - 64q^{43} - 12q^{46} - 24q^{49} - 16q^{52} - 12q^{58} + 16q^{64} + 16q^{67} + 24q^{70} + 8q^{76} + 24q^{82} - 84q^{88} - 72q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(504, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
504.2.j.a $$24$$ $$4.024$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(504, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(504, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database