# Properties

 Label 225.2.w Level 225 Weight 2 Character orbit w Rep. character $$\chi_{225}(2,\cdot)$$ Character field $$\Q(\zeta_{60})$$ Dimension 448 Newform subspaces 1 Sturm bound 60 Trace bound 0

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## Defining parameters

 Level: $$N$$ = $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 225.w (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$225$$ Character field: $$\Q(\zeta_{60})$$ Newform subspaces: $$1$$ Sturm bound: $$60$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(225, [\chi])$$.

Total New Old
Modular forms 512 512 0
Cusp forms 448 448 0
Eisenstein series 64 64 0

## Trace form

 $$448q - 24q^{2} - 14q^{3} - 10q^{4} - 24q^{5} - 12q^{6} - 8q^{7} - 20q^{9} + O(q^{10})$$ $$448q - 24q^{2} - 14q^{3} - 10q^{4} - 24q^{5} - 12q^{6} - 8q^{7} - 20q^{9} - 32q^{10} - 18q^{11} - 14q^{12} - 8q^{13} - 30q^{14} - 14q^{15} - 50q^{16} - 56q^{18} - 40q^{19} - 48q^{20} - 12q^{21} - 48q^{23} + 16q^{25} - 38q^{27} - 24q^{28} - 30q^{29} - 50q^{30} - 6q^{31} - 60q^{32} - 8q^{33} - 10q^{34} + 4q^{36} - 44q^{37} - 60q^{39} - 16q^{40} - 18q^{41} + 174q^{42} - 8q^{43} - 64q^{45} - 24q^{46} - 18q^{47} - 100q^{48} + 24q^{50} - 32q^{51} + 24q^{52} - 150q^{54} - 24q^{55} - 18q^{56} - 94q^{57} - 4q^{58} + 202q^{60} - 6q^{61} - 46q^{63} - 40q^{64} - 96q^{65} + 12q^{66} - 14q^{67} + 288q^{68} + 50q^{69} - 28q^{70} + 102q^{72} - 32q^{73} + 18q^{75} - 32q^{76} + 216q^{77} + 182q^{78} - 10q^{79} - 32q^{81} - 72q^{82} + 36q^{83} + 100q^{84} - 32q^{85} - 18q^{86} + 48q^{87} - 28q^{88} + 106q^{90} - 24q^{91} + 30q^{92} + 8q^{93} - 130q^{94} + 6q^{95} - 60q^{96} - 38q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(225, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
225.2.w.a $$448$$ $$1.797$$ None $$-24$$ $$-14$$ $$-24$$ $$-8$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database