# Properties

 Label 260.2.i Level $260$ Weight $2$ Character orbit 260.i Rep. character $\chi_{260}(61,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $8$ Newform subspaces $4$ Sturm bound $84$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$260 = 2^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 260.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$4$$ Sturm bound: $$84$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$, $$19$$

## Dimensions

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

Total New Old
Modular forms 96 8 88
Cusp forms 72 8 64
Eisenstein series 24 0 24

## Trace form

 $$8 q + 2 q^{3} - 6 q^{7} + O(q^{10})$$ $$8 q + 2 q^{3} - 6 q^{7} - 4 q^{11} + 4 q^{13} + 2 q^{15} + 14 q^{17} + 4 q^{19} - 32 q^{21} - 2 q^{23} + 8 q^{25} - 28 q^{27} + 12 q^{29} - 2 q^{33} + 2 q^{35} + 10 q^{37} + 12 q^{39} + 4 q^{41} - 6 q^{43} - 8 q^{45} + 40 q^{47} - 8 q^{49} + 32 q^{51} - 8 q^{53} - 8 q^{55} - 4 q^{57} + 8 q^{61} - 12 q^{63} + 4 q^{65} - 14 q^{67} - 24 q^{69} - 16 q^{71} - 24 q^{73} + 2 q^{75} - 44 q^{77} + 8 q^{79} - 12 q^{81} + 24 q^{83} + 6 q^{85} - 10 q^{87} - 32 q^{89} - 8 q^{91} - 16 q^{93} + 8 q^{95} - 10 q^{97} + 32 q^{99} + O(q^{100})$$

## 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.i.a $2$ $2.076$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-2$$ $$1$$ $$q+(-1+\zeta_{6})q^{3}-q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$$
260.2.i.b $2$ $2.076$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$2$$ $$1$$ $$q+(-1+\zeta_{6})q^{3}+q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$$
260.2.i.c $2$ $2.076$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-2$$ $$-5$$ $$q+(1-\zeta_{6})q^{3}-q^{5}-5\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$$
260.2.i.d $2$ $2.076$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$2$$ $$-3$$ $$q+(3-3\zeta_{6})q^{3}+q^{5}-3\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(260, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(52, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 2}$$