# Properties

 Label 504.2.cy Level 504 Weight 2 Character orbit cy Rep. character $$\chi_{504}(347,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 184 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.cy (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$504$$ 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 200 200 0
Cusp forms 184 184 0
Eisenstein series 16 16 0

## Trace form

 $$184q - 3q^{2} - 2q^{3} + q^{4} - 2q^{6} - 2q^{9} + O(q^{10})$$ $$184q - 3q^{2} - 2q^{3} + q^{4} - 2q^{6} - 2q^{9} - 6q^{10} - 5q^{12} - 3q^{14} + q^{16} + 5q^{18} - 4q^{19} - 6q^{20} + 2q^{22} - 8q^{24} + 148q^{25} + 6q^{26} - 8q^{27} + 24q^{30} - 33q^{32} + 22q^{33} - 4q^{34} - 30q^{35} - 38q^{36} - 12q^{40} - 12q^{41} + 7q^{42} - 4q^{43} - 9q^{44} - 6q^{46} - 5q^{48} - 2q^{49} - 21q^{50} + 26q^{51} - 18q^{52} - 40q^{54} + 18q^{56} + 4q^{57} + 6q^{58} - 6q^{59} - 2q^{60} - 8q^{64} - 6q^{65} + 43q^{66} + 2q^{67} - 18q^{70} - 11q^{72} - 4q^{73} - 36q^{75} + 2q^{76} - 29q^{78} - 87q^{80} - 10q^{81} - 4q^{82} - 72q^{83} - 65q^{84} + 14q^{88} + 24q^{89} - 49q^{90} - 36q^{91} - 36q^{92} + 9q^{94} - 88q^{96} - 4q^{97} - 57q^{98} + 10q^{99} + O(q^{100})$$

## 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.cy.a $$184$$ $$4.024$$ None $$-3$$ $$-2$$ $$0$$ $$0$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database