# Properties

 Label 1156.1.c Level $1156$ Weight $1$ Character orbit 1156.c Rep. character $\chi_{1156}(579,\cdot)$ Character field $\Q$ Dimension $3$ Newform subspaces $2$ Sturm bound $153$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1156 = 2^{2} \cdot 17^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1156.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$153$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1156, [\chi])$$.

Total New Old
Modular forms 21 18 3
Cusp forms 3 3 0
Eisenstein series 18 15 3

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 3 0 0 0

## Trace form

 $$3 q - q^{2} + 3 q^{4} - q^{8} + 3 q^{9} + O(q^{10})$$ $$3 q - q^{2} + 3 q^{4} - q^{8} + 3 q^{9} - 2 q^{13} + 3 q^{16} - q^{18} + q^{25} - 2 q^{26} - q^{32} + 3 q^{36} + 3 q^{49} - 3 q^{50} - 2 q^{52} - 2 q^{53} + 3 q^{64} - q^{72} + 3 q^{81} - 2 q^{89} - q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1156, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1156.1.c.a $1$ $0.577$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-17})$$ $$\Q(\sqrt{17})$$ $$1$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}+q^{8}+q^{9}-2q^{13}+q^{16}+\cdots$$
1156.1.c.b $2$ $0.577$ $$\Q(\sqrt{2})$$ $D_{4}$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}-\beta q^{5}-q^{8}+q^{9}+\beta q^{10}+\cdots$$