# Properties

 Label 3520.1.cg Level $3520$ Weight $1$ Character orbit 3520.cg Rep. character $\chi_{3520}(1249,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $16$ Newform subspaces $2$ Sturm bound $576$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3520 = 2^{6} \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3520.cg (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$440$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$2$$ Sturm bound: $$576$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(3520, [\chi])$$.

Total New Old
Modular forms 112 16 96
Cusp forms 16 16 0
Eisenstein series 96 0 96

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

 $$16 q + 4 q^{9} + O(q^{10})$$ $$16 q + 4 q^{9} - 4 q^{25} - 20 q^{41} - 16 q^{49} - 4 q^{81} + 8 q^{89} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(3520, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3520.1.cg.a $8$ $1.757$ $$\Q(\zeta_{20})$$ $D_{10}$ $$\Q(\sqrt{-10})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\zeta_{20}^{8}q^{5}+(\zeta_{20}^{3}+\zeta_{20}^{5})q^{7}+\zeta_{20}^{2}q^{9}+\cdots$$
3520.1.cg.b $8$ $1.757$ $$\Q(\zeta_{20})$$ $D_{10}$ $$\Q(\sqrt{-10})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\zeta_{20}^{8}q^{5}+(\zeta_{20}^{3}+\zeta_{20}^{5})q^{7}+\zeta_{20}^{2}q^{9}+\cdots$$