# Properties

 Label 260.2.p Level $260$ Weight $2$ Character orbit 260.p Rep. character $\chi_{260}(103,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $76$ Newform subspaces $4$ 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.p (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$260$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$84$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$, $$7$$, $$37$$

## Dimensions

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

Total New Old
Modular forms 92 92 0
Cusp forms 76 76 0
Eisenstein series 16 16 0

## Trace form

 $$76 q + O(q^{10})$$ $$76 q - 12 q^{10} - 24 q^{12} - 6 q^{13} + 8 q^{16} - 28 q^{17} - 24 q^{22} + 12 q^{25} + 20 q^{26} + 24 q^{30} - 8 q^{36} + 4 q^{38} - 56 q^{40} + 8 q^{42} - 44 q^{48} + 44 q^{52} - 12 q^{53} + 8 q^{56} - 16 q^{61} - 28 q^{62} - 30 q^{65} - 24 q^{66} - 40 q^{68} - 64 q^{77} - 20 q^{78} - 28 q^{81} + 52 q^{82} - 116 q^{88} + 8 q^{90} - 4 q^{92} + O(q^{100})$$

## 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.p.a $2$ $2.076$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$-2$$ $$0$$ $$4$$ $$0$$ $$q+(-1+i)q^{2}-2iq^{4}+(2+i)q^{5}+\cdots$$
260.2.p.b $2$ $2.076$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$2$$ $$0$$ $$-4$$ $$0$$ $$q+(1-i)q^{2}-2iq^{4}+(-2-i)q^{5}+\cdots$$
260.2.p.c $8$ $2.076$ 8.0.3317760000.5 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots$$
260.2.p.d $64$ $2.076$ None $$0$$ $$0$$ $$0$$ $$0$$