# Properties

 Label 1040.2.dh Level $1040$ Weight $2$ Character orbit 1040.dh Rep. character $\chi_{1040}(289,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $80$ Newform subspaces $4$ Sturm bound $336$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1040 = 2^{4} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1040.dh (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$336$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1040, [\chi])$$.

Total New Old
Modular forms 360 88 272
Cusp forms 312 80 232
Eisenstein series 48 8 40

## Trace form

 $$80 q - 2 q^{5} + 34 q^{9} + O(q^{10})$$ $$80 q - 2 q^{5} + 34 q^{9} + 2 q^{11} - 2 q^{15} + 2 q^{19} - 20 q^{21} - 2 q^{25} + 8 q^{31} - 4 q^{35} - 2 q^{39} - 8 q^{41} - 7 q^{45} + 22 q^{49} + 92 q^{51} + 2 q^{55} - 6 q^{59} - 12 q^{61} - 7 q^{65} - 14 q^{69} - 26 q^{71} + 6 q^{75} - 36 q^{81} - 7 q^{85} + 14 q^{89} - 14 q^{91} + 8 q^{95} - 104 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1040, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1040.2.dh.a $12$ $8.304$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$-6$$ $$0$$ $$q+(-\beta _{1}+\beta _{10})q^{3}+(\beta _{6}+\beta _{7})q^{5}+\beta _{2}q^{7}+\cdots$$
1040.2.dh.b $12$ $8.304$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{5}+\beta _{9})q^{3}+(-\beta _{1}-\beta _{7})q^{5}+(-2\beta _{3}+\cdots)q^{7}+\cdots$$
1040.2.dh.c $12$ $8.304$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{2}-\beta _{10})q^{3}-\beta _{9}q^{5}+\beta _{1}q^{7}+(1+\cdots)q^{9}+\cdots$$
1040.2.dh.d $44$ $8.304$ None $$0$$ $$0$$ $$4$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1040, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1040, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(260, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(520, [\chi])$$$$^{\oplus 2}$$