# Properties

 Label 260.2.bg Level $260$ Weight $2$ Character orbit 260.bg Rep. character $\chi_{260}(23,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $152$ Newform subspaces $3$ Sturm bound $84$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$260 = 2^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 260.bg (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$260$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$3$$ Sturm bound: $$84$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$, $$17$$

## Dimensions

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

Total New Old
Modular forms 184 184 0
Cusp forms 152 152 0
Eisenstein series 32 32 0

## Trace form

 $$152 q - 6 q^{2} - 12 q^{6} + O(q^{10})$$ $$152 q - 6 q^{2} - 12 q^{6} + 6 q^{10} - 12 q^{12} - 6 q^{13} + 4 q^{16} - 14 q^{17} - 30 q^{20} - 12 q^{22} - 36 q^{25} - 32 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 52 q^{36} + 18 q^{37} - 16 q^{38} + 68 q^{40} - 24 q^{41} + 40 q^{42} - 102 q^{45} - 12 q^{46} - 40 q^{48} + 78 q^{50} - 50 q^{52} - 12 q^{53} - 20 q^{56} + 66 q^{58} - 8 q^{61} - 44 q^{62} - 12 q^{65} + 96 q^{66} - 44 q^{68} - 54 q^{72} - 12 q^{76} + 40 q^{77} - 100 q^{78} + 24 q^{80} + 4 q^{81} - 58 q^{82} - 12 q^{85} - 10 q^{88} - 20 q^{90} + 100 q^{92} - 48 q^{93} - 12 q^{97} - 162 q^{98} + O(q^{100})$$

## 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.bg.a $4$ $2.076$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-1})$$ $$-2$$ $$0$$ $$4$$ $$0$$ $$q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2\zeta_{12}+\cdots)q^{4}+\cdots$$
260.2.bg.b $4$ $2.076$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-1})$$ $$2$$ $$0$$ $$-4$$ $$0$$ $$q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{4}+\cdots$$
260.2.bg.c $144$ $2.076$ None $$-6$$ $$0$$ $$0$$ $$0$$