# Properties

 Label 504.2.bs Level 504 Weight 2 Character orbit bs Rep. character $$\chi_{504}(257,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 48 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.bs (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$63$$ Character field: $$\Q(\zeta_{6})$$ 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 208 48 160
Cusp forms 176 48 128
Eisenstein series 32 0 32

## Trace form

 $$48q - 4q^{9} + O(q^{10})$$ $$48q - 4q^{9} + 8q^{15} + 8q^{21} - 12q^{23} - 24q^{25} - 18q^{27} + 18q^{29} - 10q^{39} + 6q^{41} - 6q^{43} + 6q^{45} + 36q^{47} + 6q^{49} - 12q^{51} + 12q^{53} + 4q^{57} + 46q^{63} - 54q^{75} - 36q^{77} - 12q^{79} - 24q^{87} + 18q^{89} + 6q^{91} + 16q^{93} - 64q^{99} + O(q^{100})$$

## 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.bs.a $$48$$ $$4.024$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(504, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database