# Properties

 Label 1352.1.g Level $1352$ Weight $1$ Character orbit 1352.g Rep. character $\chi_{1352}(339,\cdot)$ Character field $\Q$ Dimension $8$ 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.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ 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 22 19 3
Cusp forms 8 8 0
Eisenstein series 14 11 3

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 8 0 0 0

## Trace form

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

## 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.g.a $2$ $0.675$ $$\Q(\sqrt{-1})$$ $D_{3}$ $$\Q(\sqrt{-26})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}-iq^{7}+\cdots$$
1352.1.g.b $3$ $0.675$ $$\Q(\zeta_{14})^+$$ $D_{7}$ $$\Q(\sqrt{-2})$$ None $$-3$$ $$-1$$ $$0$$ $$0$$ $$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-q^{8}+\cdots$$
1352.1.g.c $3$ $0.675$ $$\Q(\zeta_{14})^+$$ $D_{7}$ $$\Q(\sqrt{-2})$$ None $$3$$ $$-1$$ $$0$$ $$0$$ $$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+q^{8}+\cdots$$