# Properties

 Label 40.3.l Level $40$ Weight $3$ Character orbit 40.l Rep. character $\chi_{40}(17,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $6$ Newform subspaces $2$ Sturm bound $18$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$40 = 2^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 40.l (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$18$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(40, [\chi])$$.

Total New Old
Modular forms 32 6 26
Cusp forms 16 6 10
Eisenstein series 16 0 16

## Trace form

 $$6 q + 4 q^{5} + 8 q^{7} + O(q^{10})$$ $$6 q + 4 q^{5} + 8 q^{7} - 8 q^{11} - 38 q^{13} - 72 q^{15} - 14 q^{17} + 56 q^{21} + 96 q^{23} + 50 q^{25} + 120 q^{27} - 16 q^{31} - 120 q^{33} - 72 q^{35} - 82 q^{37} + 56 q^{41} + 48 q^{43} + 154 q^{45} - 128 q^{47} - 240 q^{51} - 66 q^{53} - 88 q^{55} - 80 q^{57} - 24 q^{61} + 128 q^{63} + 134 q^{65} + 224 q^{67} + 272 q^{71} + 166 q^{73} + 264 q^{75} + 72 q^{77} - 46 q^{81} - 184 q^{83} - 198 q^{85} - 320 q^{87} - 352 q^{91} + 120 q^{93} - 104 q^{95} + 38 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(40, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
40.3.l.a $2$ $1.090$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$10$$ $$-6$$ $$q+(1-i)q^{3}+5q^{5}+(-3-3i)q^{7}+\cdots$$
40.3.l.b $4$ $1.090$ $$\Q(i, \sqrt{41})$$ None $$0$$ $$-2$$ $$-6$$ $$14$$ $$q+(-1+\beta _{2})q^{3}+(-1-2\beta _{1}+\beta _{3})q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(40, [\chi])$$ into lower level spaces

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