# Properties

 Label 441.2.i Level $441$ Weight $2$ Character orbit 441.i Rep. character $\chi_{441}(68,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $72$ Newform subspaces $4$ Sturm bound $112$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 441.i (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$112$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## 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

 $$72q + 3q^{3} - 62q^{4} + 3q^{5} - 6q^{6} + q^{9} + O(q^{10})$$ $$72q + 3q^{3} - 62q^{4} + 3q^{5} - 6q^{6} + q^{9} + 6q^{10} + 15q^{11} + 12q^{12} + 3q^{13} - 28q^{15} + 46q^{16} - 9q^{17} - 4q^{18} + 6q^{19} - 6q^{20} - 8q^{22} + 18q^{23} + 6q^{24} - 21q^{25} + 6q^{26} + 27q^{27} + 6q^{29} - 39q^{30} + 3q^{33} - 6q^{34} - 2q^{36} + q^{37} - 27q^{38} - 29q^{39} - 24q^{40} - 6q^{41} - 8q^{43} - 69q^{44} - 39q^{45} + 16q^{46} - 30q^{47} - 15q^{48} + 3q^{50} - 18q^{51} + 15q^{52} - 36q^{53} - 27q^{54} + 35q^{57} + q^{58} + 36q^{59} + 153q^{60} + 24q^{62} - 28q^{64} + 48q^{66} - 12q^{67} + 24q^{68} - 12q^{69} - 40q^{72} + 6q^{73} + 129q^{74} + 6q^{75} - 85q^{78} + 36q^{79} - 45q^{80} - 39q^{81} - 30q^{83} - 21q^{85} - 63q^{86} + 3q^{87} + 23q^{88} + 27q^{89} + 51q^{90} - 84q^{92} + 16q^{93} - 51q^{96} + 3q^{97} - 84q^{99} + O(q^{100})$$

## 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.i.a $$2$$ $$3.521$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$0$$ $$q+(1-2\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-q^{4}+\cdots$$
441.2.i.b $$10$$ $$3.521$$ 10.0.$$\cdots$$.1 None $$0$$ $$3$$ $$0$$ $$0$$ $$q+(-\beta _{3}-\beta _{5})q^{2}+(-\beta _{1}+\beta _{7})q^{3}+\cdots$$
441.2.i.c $$12$$ $$3.521$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}+\beta _{5})q^{2}+(\beta _{2}-\beta _{9})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$$
441.2.i.d $$48$$ $$3.521$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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