# Properties

 Label 504.2.w Level 504 Weight 2 Character orbit w Rep. character $$\chi_{504}(205,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 184 Newform subspaces 1 Sturm bound 192 Trace bound 0

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## Defining parameters

 Level: $$N$$ = $$504 = 2^{3} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 504.w (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

 $$184q + q^{2} + q^{4} - 2q^{6} - 2q^{7} - 8q^{8} - 2q^{9} + O(q^{10})$$ $$184q + q^{2} + q^{4} - 2q^{6} - 2q^{7} - 8q^{8} - 2q^{9} + 2q^{10} - 17q^{12} - 7q^{14} - 2q^{15} + q^{16} - 4q^{17} + 13q^{18} + 6q^{20} + 2q^{22} - 4q^{23} + 12q^{24} - 156q^{25} - 4q^{26} - 8q^{28} - 18q^{30} + 2q^{31} + q^{32} + 22q^{33} - 18q^{36} + 10q^{38} - 14q^{39} + 8q^{40} - 4q^{41} + 3q^{42} + 17q^{44} - 6q^{46} + 42q^{47} - 3q^{48} - 2q^{49} - 31q^{50} - 18q^{52} - 58q^{54} + 4q^{55} - 34q^{56} - 20q^{57} - 10q^{58} + 26q^{60} + 32q^{62} + 50q^{63} - 8q^{64} + 22q^{65} + 79q^{66} + 24q^{68} + 8q^{70} - 16q^{71} - 27q^{72} - 4q^{73} - 38q^{74} - 6q^{76} - 47q^{78} + 2q^{79} - 11q^{80} + 6q^{81} + q^{84} + 46q^{86} + 4q^{87} + 14q^{88} + 4q^{89} - 35q^{90} - 48q^{92} + 9q^{94} + 22q^{95} - 16q^{96} - 4q^{97} - 83q^{98} + O(q^{100})$$

## 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.w.a $$184$$ $$4.024$$ None $$1$$ $$0$$ $$0$$ $$-2$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database