# Properties

 Label 441.2.g Level $441$ Weight $2$ Character orbit 441.g Rep. character $\chi_{441}(67,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $72$ Newform subspaces $8$ Sturm bound $112$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 441.g (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$8$$ Sturm bound: $$112$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$, $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(441, [\chi])$$.

Total New Old
Modular forms 128 88 40
Cusp forms 96 72 24
Eisenstein series 32 16 16

## Trace form

 $$72q - q^{2} + q^{3} - 33q^{4} + 10q^{5} + 2q^{6} - 12q^{8} - q^{9} + O(q^{10})$$ $$72q - q^{2} + q^{3} - 33q^{4} + 10q^{5} + 2q^{6} - 12q^{8} - q^{9} + 6q^{10} - 6q^{11} - 19q^{12} + 3q^{13} + 10q^{15} - 27q^{16} - 9q^{17} + 19q^{18} - 4q^{20} - 8q^{23} - 12q^{24} + 42q^{25} - 16q^{26} + 7q^{27} - 18q^{29} + 72q^{30} + 3q^{31} + 41q^{32} + 16q^{33} - 70q^{36} + 3q^{37} + 38q^{38} - 28q^{39} - 12q^{40} - 10q^{41} - 11q^{44} + 4q^{45} - 12q^{46} - 27q^{47} + 5q^{48} - 45q^{50} - 14q^{51} - 30q^{52} + 16q^{53} + 62q^{54} + 6q^{55} - 15q^{57} - 18q^{58} - 30q^{59} - 16q^{60} + 12q^{62} + 12q^{64} + 30q^{65} + 41q^{66} + 6q^{67} + 60q^{68} - 6q^{69} + 6q^{71} - 51q^{72} - 12q^{73} - 82q^{74} - 43q^{75} - 6q^{76} + 69q^{78} + 18q^{79} - 19q^{80} - q^{81} - 18q^{83} + 3q^{85} - 50q^{86} - 29q^{87} + 18q^{88} - 41q^{89} - 25q^{90} - 52q^{92} + 58q^{93} + 3q^{94} - 17q^{95} - 14q^{96} + 3q^{97} - 34q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(441, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
441.2.g.a $$2$$ $$3.521$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$3$$ $$2$$ $$0$$ $$q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
441.2.g.b $$6$$ $$3.521$$ $$\Q(\zeta_{18})$$ None $$-3$$ $$0$$ $$-6$$ $$0$$ $$q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{3}+\cdots$$
441.2.g.c $$6$$ $$3.521$$ $$\Q(\zeta_{18})$$ None $$-3$$ $$0$$ $$6$$ $$0$$ $$q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-\zeta_{18}^{2}+\cdots)q^{3}+\cdots$$
441.2.g.d $$6$$ $$3.521$$ 6.0.309123.1 None $$1$$ $$-2$$ $$10$$ $$0$$ $$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(-1+\cdots)q^{3}+\cdots$$
441.2.g.e $$6$$ $$3.521$$ 6.0.309123.1 None $$1$$ $$2$$ $$-10$$ $$0$$ $$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(1-\beta _{1}+\cdots)q^{3}+\cdots$$
441.2.g.f $$10$$ $$3.521$$ 10.0.$$\cdots$$.1 None $$2$$ $$-2$$ $$8$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$$
441.2.g.g $$12$$ $$3.521$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{2}+\beta _{5})q^{2}+(-\beta _{8}-\beta _{10})q^{3}+\cdots$$
441.2.g.h $$24$$ $$3.521$$ None $$4$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(441, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(441, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 2}$$