# Properties

 Label 1215.1.h Level $1215$ Weight $1$ Character orbit 1215.h Rep. character $\chi_{1215}(404,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $12$ 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.h (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$45$$ Character field: $$\Q(\zeta_{6})$$ 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 56 12 44
Cusp forms 20 12 8
Eisenstein series 36 0 36

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 12 0 0 0

## Trace form

 $$12 q - 6 q^{4} + O(q^{10})$$ $$12 q - 6 q^{4} - 6 q^{16} - 6 q^{25} + 6 q^{34} + 6 q^{40} - 12 q^{46} - 6 q^{49} + 6 q^{76} + O(q^{100})$$

## 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.h.a $6$ $0.606$ $$\Q(\zeta_{18})$$ $D_{9}$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$-3$$ $$0$$ $$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots$$
1215.1.h.b $6$ $0.606$ $$\Q(\zeta_{18})$$ $D_{9}$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$3$$ $$0$$ $$q+(\zeta_{18}-\zeta_{18}^{2})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$$

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

$$S_{1}^{\mathrm{old}}(1215, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(405, [\chi])$$$$^{\oplus 2}$$