# Properties

 Label 504.2.bu Level 504 Weight 2 Character orbit bu Rep. character $$\chi_{504}(41,\cdot)$$ 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.bu (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

 $$48q - 4q^{9} + O(q^{10})$$ $$48q - 4q^{9} + 8q^{15} - 4q^{21} + 12q^{23} - 24q^{25} - 36q^{29} + 32q^{39} + 12q^{43} + 6q^{49} + 24q^{51} + 28q^{57} - 14q^{63} + 36q^{65} - 60q^{77} - 12q^{79} - 36q^{81} - 12q^{91} + 16q^{93} - 108q^{95} + 44q^{99} + O(q^{100})$$

## 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.bu.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