Properties

 Label 225.2.f Level $225$ Weight $2$ Character orbit 225.f Rep. character $\chi_{225}(107,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $12$ Newform subspaces $2$ Sturm bound $60$ Trace bound $1$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 225.f (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$60$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

Dimensions

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

Total New Old
Modular forms 84 12 72
Cusp forms 36 12 24
Eisenstein series 48 0 48

Trace form

 $$12 q + 8 q^{7} + O(q^{10})$$ $$12 q + 8 q^{7} - 4 q^{13} - 28 q^{16} - 8 q^{22} - 8 q^{28} - 8 q^{31} - 4 q^{37} + 32 q^{43} + 32 q^{46} - 4 q^{52} - 12 q^{58} - 24 q^{61} - 16 q^{67} - 4 q^{73} + 160 q^{76} + 4 q^{82} + 24 q^{88} - 88 q^{91} + 44 q^{97} + O(q^{100})$$

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.f.a $4$ $1.797$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(2-2\zeta_{8}^{2})q^{7}+\cdots$$
225.2.f.b $8$ $1.797$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{6}q^{2}-4\zeta_{24}^{2}q^{4}+\zeta_{24}q^{7}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(225, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(225, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$