# Properties

 Label 80.3.p Level $80$ Weight $3$ Character orbit 80.p Rep. character $\chi_{80}(17,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $10$ Newform subspaces $4$ Sturm bound $36$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$80 = 2^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 80.p (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$36$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(80, [\chi])$$.

Total New Old
Modular forms 60 14 46
Cusp forms 36 10 26
Eisenstein series 24 4 20

## Trace form

 $$10 q + 2 q^{3} - 2 q^{5} + 2 q^{7} + O(q^{10})$$ $$10 q + 2 q^{3} - 2 q^{5} + 2 q^{7} + 4 q^{11} - 14 q^{13} + 50 q^{15} + 2 q^{17} + 12 q^{21} - 46 q^{23} - 14 q^{25} - 112 q^{27} - 60 q^{31} - 68 q^{33} - 46 q^{35} - 22 q^{37} + 12 q^{41} + 66 q^{43} + 108 q^{45} + 242 q^{47} + 292 q^{51} + 26 q^{53} + 148 q^{55} - 16 q^{57} - 36 q^{61} - 222 q^{63} + 122 q^{65} - 334 q^{67} - 412 q^{71} + 170 q^{73} - 302 q^{75} - 100 q^{77} + 34 q^{81} + 274 q^{83} - 142 q^{85} + 496 q^{87} + 580 q^{91} - 116 q^{93} + 240 q^{95} - 22 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(80, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
80.3.p.a $2$ $2.180$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$-6$$ $$14$$ $$q+(-1+i)q^{3}+(-3+4i)q^{5}+(7+7i)q^{7}+\cdots$$
80.3.p.b $2$ $2.180$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$10$$ $$6$$ $$q+(-1+i)q^{3}+5q^{5}+(3+3i)q^{7}+\cdots$$
80.3.p.c $2$ $2.180$ $$\Q(\sqrt{-1})$$ None $$0$$ $$4$$ $$0$$ $$-4$$ $$q+(2-2i)q^{3}-5iq^{5}+(-2-2i)q^{7}+\cdots$$
80.3.p.d $4$ $2.180$ $$\Q(i, \sqrt{41})$$ None $$0$$ $$2$$ $$-6$$ $$-14$$ $$q+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(80, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(80, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(10, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 2}$$