# Properties

 Label 1215.1.d Level $1215$ Weight $1$ Character orbit 1215.d Rep. character $\chi_{1215}(1214,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $2$ Sturm bound $162$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1215 = 3^{5} \cdot 5$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1215.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$162$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1215, [\chi])$$.

Total New Old
Modular forms 30 6 24
Cusp forms 12 6 6
Eisenstein series 18 0 18

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 0 0

## Trace form

 $$6 q + 6 q^{4} + O(q^{10})$$ $$6 q + 6 q^{4} + 6 q^{16} + 6 q^{25} - 6 q^{34} - 6 q^{40} - 6 q^{46} + 6 q^{49} - 6 q^{76} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1215, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1215.1.d.a $3$ $0.606$ $$\Q(\zeta_{18})^+$$ $D_{9}$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$-3$$ $$0$$ $$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{8}+\cdots$$
1215.1.d.b $3$ $0.606$ $$\Q(\zeta_{18})^+$$ $D_{9}$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$3$$ $$0$$ $$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1-\beta _{1}+\cdots)q^{8}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(1215, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(1215, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(135, [\chi])$$$$^{\oplus 3}$$