# Properties

 Label 1040.2.k Level $1040$ Weight $2$ Character orbit 1040.k Rep. character $\chi_{1040}(961,\cdot)$ Character field $\Q$ Dimension $28$ Newform subspaces $5$ 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.k (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$5$$ 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 180 28 152
Cusp forms 156 28 128
Eisenstein series 24 0 24

## Trace form

 $$28 q - 4 q^{3} + 28 q^{9} + O(q^{10})$$ $$28 q - 4 q^{3} + 28 q^{9} - 12 q^{23} - 28 q^{25} + 8 q^{27} - 12 q^{35} + 28 q^{39} + 44 q^{43} - 4 q^{49} - 24 q^{51} - 8 q^{53} + 8 q^{55} - 8 q^{61} - 4 q^{65} + 32 q^{69} + 4 q^{75} - 24 q^{77} + 16 q^{79} + 28 q^{81} - 20 q^{91} - 16 q^{95} + O(q^{100})$$

## 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.k.a $2$ $8.304$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-2q^{3}-iq^{5}+q^{9}+(2+3i)q^{13}+\cdots$$
1040.2.k.b $6$ $8.304$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots$$
1040.2.k.c $6$ $8.304$ 6.0.9144576.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}-\beta _{2}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots$$
1040.2.k.d $6$ $8.304$ 6.0.5089536.1 None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(1+\beta _{1})q^{3}+\beta _{4}q^{5}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$$
1040.2.k.e $8$ $8.304$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1040, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(52, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(104, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(208, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(260, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(520, [\chi])$$$$^{\oplus 2}$$