# Properties

 Label 2736.1.o Level $2736$ Weight $1$ Character orbit 2736.o Rep. character $\chi_{2736}(721,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $3$ Sturm bound $480$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2736 = 2^{4} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2736.o (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$480$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2736, [\chi])$$.

Total New Old
Modular forms 54 5 49
Cusp forms 30 4 26
Eisenstein series 24 1 23

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

 $$4 q + q^{5} + q^{7} + O(q^{10})$$ $$4 q + q^{5} + q^{7} - q^{11} + q^{17} + 2 q^{19} + 2 q^{23} + 3 q^{25} + q^{35} + q^{43} - q^{47} + 3 q^{49} + 5 q^{55} - q^{61} - q^{73} - q^{77} + 2 q^{83} - 5 q^{85} - q^{95} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2736, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2736.1.o.a $1$ $1.365$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-19})$$ $$\Q(\sqrt{57})$$ $$0$$ $$0$$ $$0$$ $$2$$ $$q+2q^{7}+q^{19}-q^{25}-2q^{43}+3q^{49}+\cdots$$
2736.1.o.b $1$ $1.365$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$1$$ $$1$$ $$q+q^{5}+q^{7}-q^{11}+q^{17}-q^{19}+2q^{23}+\cdots$$
2736.1.o.c $2$ $1.365$ $$\Q(\sqrt{3})$$ $D_{6}$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-\beta q^{5}-q^{7}-\beta q^{11}+\beta q^{17}+q^{19}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(2736, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(2736, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(304, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(684, [\chi])$$$$^{\oplus 3}$$