# Properties

 Label 441.3.q Level $441$ Weight $3$ Character orbit 441.q Rep. character $\chi_{441}(116,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $52$ Newform subspaces $5$ Sturm bound $168$ Trace bound $10$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 441.q (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$168$$ Trace bound: $$10$$ Distinguishing $$T_p$$: $$2$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(441, [\chi])$$.

Total New Old
Modular forms 256 52 204
Cusp forms 192 52 140
Eisenstein series 64 0 64

## Trace form

 $$52 q + 48 q^{4} + O(q^{10})$$ $$52 q + 48 q^{4} + 16 q^{10} + 52 q^{13} - 88 q^{16} - 26 q^{19} - 104 q^{22} + 22 q^{25} - 22 q^{31} + 528 q^{34} + 238 q^{37} - 300 q^{40} + 140 q^{43} - 236 q^{46} - 252 q^{52} - 16 q^{55} - 104 q^{58} + 136 q^{61} - 1096 q^{64} - 422 q^{67} + 482 q^{73} + 504 q^{76} + 386 q^{79} + 212 q^{82} + 448 q^{85} + 336 q^{88} - 612 q^{94} - 568 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(441, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
441.3.q.a $$8$$ $$12.016$$ 8.0.$$\cdots$$.5 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{3}+\beta _{6})q^{4}-2\beta _{1}q^{5}+(-2\beta _{1}+\cdots)q^{8}+\cdots$$
441.3.q.b $$8$$ $$12.016$$ 8.0.$$\cdots$$.5 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{3}+\beta _{6})q^{4}+2\beta _{1}q^{5}+(-2\beta _{1}+\cdots)q^{8}+\cdots$$
441.3.q.c $$8$$ $$12.016$$ 8.0.$$\cdots$$.5 $$\Q(\sqrt{-7})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(4-4\beta _{3}+\beta _{5}+\beta _{7})q^{4}+\cdots$$
441.3.q.d $$12$$ $$12.016$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-3\beta _{6}+\beta _{9})q^{4}+\beta _{4}q^{5}+\cdots$$
441.3.q.e $$16$$ $$12.016$$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{8}q^{2}+(2\beta _{1}+\beta _{10})q^{4}+\beta _{4}q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(441, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(441, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 2}$$