# Properties

 Label 260.2.bk Level $260$ Weight $2$ Character orbit 260.bk Rep. character $\chi_{260}(33,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $28$ Newform subspaces $3$ Sturm bound $84$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$260 = 2^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 260.bk (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$3$$ Sturm bound: $$84$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(260, [\chi])$$.

Total New Old
Modular forms 192 28 164
Cusp forms 144 28 116
Eisenstein series 48 0 48

## Trace form

 $$28 q - 12 q^{9} + O(q^{10})$$ $$28 q - 12 q^{9} + 12 q^{13} - 12 q^{15} - 2 q^{17} + 12 q^{19} + 12 q^{21} - 12 q^{23} + 2 q^{25} - 24 q^{27} + 24 q^{31} - 4 q^{33} - 12 q^{35} - 18 q^{37} + 12 q^{39} + 22 q^{41} - 12 q^{45} + 26 q^{49} + 6 q^{53} + 4 q^{55} - 56 q^{57} - 8 q^{59} - 12 q^{61} - 12 q^{63} - 30 q^{65} + 32 q^{67} - 16 q^{69} - 100 q^{73} - 44 q^{75} + 8 q^{77} - 6 q^{81} + 26 q^{85} + 4 q^{87} - 30 q^{89} - 16 q^{91} - 36 q^{93} - 12 q^{95} + 56 q^{97} + 56 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(260, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
260.2.bk.a $4$ $2.076$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$-8$$ $$-12$$ $$q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(-2+\zeta_{12}^{3})q^{5}+\cdots$$
260.2.bk.b $4$ $2.076$ $$\Q(\zeta_{12})$$ None $$0$$ $$4$$ $$-4$$ $$6$$ $$q+(1+\zeta_{12})q^{3}+(-1-2\zeta_{12}^{3})q^{5}+\cdots$$
260.2.bk.c $20$ $2.076$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$-2$$ $$12$$ $$6$$ $$q+(\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+2\beta _{7}+\cdots)q^{3}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(260, [\chi])$$ into lower level spaces

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