# Properties

 Label 21.3.d Level $21$ Weight $3$ Character orbit 21.d Rep. character $\chi_{21}(13,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $8$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$21 = 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 21.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$8$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(21, [\chi])$$.

Total New Old
Modular forms 8 2 6
Cusp forms 4 2 2
Eisenstein series 4 0 4

## Trace form

 $$2 q + 2 q^{2} - 6 q^{4} + 2 q^{7} - 14 q^{8} - 6 q^{9} + O(q^{10})$$ $$2 q + 2 q^{2} - 6 q^{4} + 2 q^{7} - 14 q^{8} - 6 q^{9} + 20 q^{11} + 2 q^{14} + 24 q^{15} + 10 q^{16} - 6 q^{18} - 24 q^{21} + 20 q^{22} - 28 q^{23} - 46 q^{25} - 6 q^{28} - 76 q^{29} + 24 q^{30} + 66 q^{32} + 96 q^{35} + 18 q^{36} + 52 q^{37} - 24 q^{39} - 24 q^{42} + 52 q^{43} - 60 q^{44} - 28 q^{46} - 94 q^{49} - 46 q^{50} + 20 q^{53} - 14 q^{56} + 72 q^{57} - 76 q^{58} - 72 q^{60} - 6 q^{63} + 26 q^{64} + 96 q^{65} + 148 q^{67} + 96 q^{70} - 124 q^{71} + 42 q^{72} + 52 q^{74} + 20 q^{77} - 24 q^{78} - 92 q^{79} + 18 q^{81} + 72 q^{84} + 52 q^{86} - 140 q^{88} - 96 q^{91} + 84 q^{92} - 96 q^{93} - 288 q^{95} - 94 q^{98} - 60 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(21, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
21.3.d.a $2$ $0.572$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$0$$ $$2$$ $$q+q^{2}+\zeta_{6}q^{3}-3q^{4}-4\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(21, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(21, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 2}$$