# Properties

 Label 80.4.c Level $80$ Weight $4$ Character orbit 80.c Rep. character $\chi_{80}(49,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $3$ Sturm bound $48$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$80 = 2^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 80.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$48$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(80, [\chi])$$.

Total New Old
Modular forms 42 10 32
Cusp forms 30 8 22
Eisenstein series 12 2 10

## Trace form

 $$8 q - 56 q^{9} + O(q^{10})$$ $$8 q - 56 q^{9} - 64 q^{11} - 32 q^{15} + 128 q^{19} - 16 q^{21} + 72 q^{25} + 112 q^{29} + 320 q^{31} - 64 q^{35} - 640 q^{39} - 32 q^{41} - 144 q^{45} + 360 q^{49} - 448 q^{51} + 1056 q^{55} + 1408 q^{59} + 64 q^{61} - 544 q^{65} - 720 q^{69} + 64 q^{71} - 2688 q^{75} - 3008 q^{79} + 56 q^{81} + 1088 q^{85} - 752 q^{89} - 704 q^{91} + 3232 q^{95} + 6400 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(80, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
80.4.c.a $2$ $4.720$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-10$$ $$0$$ $$q+iq^{3}+(-5-5i)q^{5}-13iq^{7}+23q^{9}+\cdots$$
80.4.c.b $2$ $4.720$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$14$$ $$0$$ $$q-\beta q^{3}+(7-\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots$$
80.4.c.c $4$ $4.720$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(80, [\chi])$$ into lower level spaces

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