# Properties

 Label 1520.1.m Level $1520$ Weight $1$ Character orbit 1520.m Rep. character $\chi_{1520}(1329,\cdot)$ Character field $\Q$ Dimension $5$ Newform subspaces $3$ Sturm bound $240$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1520 = 2^{4} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1520.m (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$240$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1520, [\chi])$$.

Total New Old
Modular forms 38 7 31
Cusp forms 26 5 21
Eisenstein series 12 2 10

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 5 0 0 0

## Trace form

 $$5 q - 2 q^{5} - q^{9} + O(q^{10})$$ $$5 q - 2 q^{5} - q^{9} - q^{19} + 2 q^{25} + 3 q^{35} + 4 q^{39} - 2 q^{45} - q^{49} + 3 q^{55} + q^{81} + 3 q^{85} - 2 q^{95} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1520, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1520.1.m.a $1$ $0.759$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-19})$$, $$\Q(\sqrt{-95})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$1$$ $$0$$ $$q+q^{5}-q^{9}+2q^{11}-q^{19}+q^{25}+\cdots$$
1520.1.m.b $2$ $0.759$ $$\Q(\sqrt{2})$$ $D_{4}$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta q^{3}-q^{5}+q^{9}-\beta q^{13}+\beta q^{15}+\cdots$$
1520.1.m.c $2$ $0.759$ $$\Q(\sqrt{-3})$$ $D_{6}$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$0$$ $$q-\zeta_{6}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{9}-q^{11}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(1520, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(1520, [\chi]) \simeq$$ $$S_{1}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(380, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(760, [\chi])$$$$^{\oplus 2}$$