# Properties

 Label 40.4.c Level $40$ Weight $4$ Character orbit 40.c Rep. character $\chi_{40}(9,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $1$ Sturm bound $24$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$40 = 2^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 40.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$24$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(40, [\chi])$$.

Total New Old
Modular forms 22 4 18
Cusp forms 14 4 10
Eisenstein series 8 0 8

## Trace form

 $$4 q - 4 q^{5} - 4 q^{9} + O(q^{10})$$ $$4 q - 4 q^{5} - 4 q^{9} + 80 q^{11} - 80 q^{15} - 80 q^{19} - 272 q^{21} + 276 q^{25} + 280 q^{29} + 384 q^{31} - 304 q^{35} - 224 q^{39} - 1048 q^{41} + 772 q^{45} + 492 q^{49} + 1920 q^{51} - 1616 q^{55} - 1392 q^{59} - 1384 q^{61} + 608 q^{65} + 112 q^{69} + 1376 q^{71} + 160 q^{75} + 1472 q^{79} - 1484 q^{81} + 1152 q^{85} + 1320 q^{89} + 992 q^{91} - 1456 q^{95} - 3152 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(40, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
40.4.c.a $4$ $2.360$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(40, [\chi])$$ into lower level spaces

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