# Properties

 Label 1156.1.f Level $1156$ Weight $1$ Character orbit 1156.f Rep. character $\chi_{1156}(251,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $4$ Newform subspaces $2$ Sturm bound $153$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1156 = 2^{2} \cdot 17^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1156.f (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$68$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$153$$ Trace bound: $$5$$

## Dimensions

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

Total New Old
Modular forms 44 32 12
Cusp forms 8 4 4
Eisenstein series 36 28 8

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

 $$4q - 4q^{4} + 2q^{5} + O(q^{10})$$ $$4q - 4q^{4} + 2q^{5} - 2q^{10} + 4q^{13} + 4q^{16} - 2q^{20} - 2q^{29} + 2q^{37} + 2q^{40} - 2q^{41} - 2q^{45} - 4q^{50} - 4q^{52} + 2q^{58} + 2q^{61} - 4q^{64} - 2q^{73} - 2q^{74} + 2q^{80} - 4q^{81} - 2q^{82} + 4q^{89} - 2q^{90} + 2q^{97} + O(q^{100})$$

## 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.f.a $$2$$ $$0.577$$ $$\Q(\sqrt{-1})$$ $$D_{2}$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-17})$$ $$\Q(\sqrt{17})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}-iq^{8}-iq^{9}+q^{13}+\cdots$$
1156.1.f.b $$2$$ $$0.577$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-iq^{2}-q^{4}+(1-i)q^{5}+iq^{8}-iq^{9}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(1156, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(1156, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(68, [\chi])$$$$^{\oplus 2}$$