# Properties

 Label 1225.1.i Level $1225$ Weight $1$ Character orbit 1225.i Rep. character $\chi_{1225}(276,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $4$ Newform subspaces $2$ Sturm bound $140$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1225 = 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1225.i (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$140$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1225, [\chi])$$.

Total New Old
Modular forms 52 16 36
Cusp forms 4 4 0
Eisenstein series 48 12 36

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

## Trace form

 $$4q - 2q^{9} + O(q^{10})$$ $$4q - 2q^{9} + 2q^{11} + 2q^{16} - 4q^{29} - 2q^{46} + 4q^{64} - 4q^{71} - 2q^{74} + 2q^{79} - 2q^{81} - 2q^{86} - 4q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1225, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1225.1.i.a $$2$$ $$0.611$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-7})$$ None $$-1$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{6}^{2}q^{2}-q^{8}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots$$
1225.1.i.b $$2$$ $$0.611$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-7})$$ None $$1$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}^{2}q^{2}+q^{8}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots$$