# Properties

 Label 1352.1.p Level $1352$ Weight $1$ Character orbit 1352.p Rep. character $\chi_{1352}(147,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $3$ Sturm bound $182$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1352 = 2^{3} \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1352.p (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$104$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$182$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1352, [\chi])$$.

Total New Old
Modular forms 44 36 8
Cusp forms 16 16 0
Eisenstein series 28 20 8

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 16 0 0 0

## Trace form

 $$16 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + O(q^{10})$$ $$16 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + 2 q^{10} - 4 q^{14} - 8 q^{16} + 2 q^{22} - 12 q^{25} - 4 q^{27} - 2 q^{30} - 2 q^{35} + 4 q^{36} + 4 q^{38} - 4 q^{40} - 2 q^{42} + 4 q^{48} + 6 q^{49} + 12 q^{51} + 2 q^{56} - 4 q^{62} - 8 q^{64} - 8 q^{66} + 4 q^{68} + 2 q^{74} - 2 q^{75} - 2 q^{82} - 2 q^{88} + 2 q^{94} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1352, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1352.1.p.a $2$ $0.675$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-26})$$ None $$-1$$ $$1$$ $$-2$$ $$1$$ $$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-q^{5}-\zeta_{6}^{2}q^{6}+\cdots$$
1352.1.p.b $2$ $0.675$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-26})$$ None $$1$$ $$1$$ $$2$$ $$-1$$ $$q+\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}^{2}q^{6}+\cdots$$
1352.1.p.c $12$ $0.675$ 12.0.$$\cdots$$.1 $D_{7}$ $$\Q(\sqrt{-2})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}-\beta _{9}q^{3}+\beta _{7}q^{4}+\beta _{11}q^{6}+\cdots$$