# Properties

 Label 1352.1.n Level $1352$ Weight $1$ Character orbit 1352.n Rep. character $\chi_{1352}(315,\cdot)$ 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.n (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.n.a $4$ $0.675$ $$\Q(\zeta_{12})$$ $D_{3}$ $$\Q(\sqrt{-26})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots$$
1352.1.n.b $6$ $0.675$ 6.0.64827.1 $D_{7}$ $$\Q(\sqrt{-2})$$ None $$-3$$ $$1$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots$$
1352.1.n.c $6$ $0.675$ 6.0.64827.1 $D_{7}$ $$\Q(\sqrt{-2})$$ None $$3$$ $$1$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots$$