# Properties

 Label 441.2.p Level $441$ Weight $2$ Character orbit 441.p Rep. character $\chi_{441}(80,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $28$ Newform subspaces $3$ 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.p (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ 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 144 28 116
Cusp forms 80 28 52
Eisenstein series 64 0 64

## Trace form

 $$28 q + 16 q^{4} + O(q^{10})$$ $$28 q + 16 q^{4} + 12 q^{10} - 28 q^{16} - 6 q^{19} - 22 q^{25} - 6 q^{31} + 34 q^{37} - 24 q^{40} - 68 q^{43} - 12 q^{46} - 4 q^{58} + 12 q^{61} + 32 q^{64} - 6 q^{67} - 6 q^{73} - 10 q^{79} + 36 q^{82} - 80 q^{85} - 4 q^{88} - 60 q^{94} + O(q^{100})$$

## 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.p.a $4$ $3.521$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}-2\beta _{3})q^{5}-2\beta _{3}q^{8}+\cdots$$
441.2.p.b $8$ $3.521$ 8.0.$$\cdots$$.5 $$\Q(\sqrt{-7})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(2+\beta _{3}-2\beta _{4}+\beta _{6})q^{4}+\cdots$$
441.2.p.c $16$ $3.521$ $$\Q(\zeta_{48})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{48}-\zeta_{48}^{3}+\zeta_{48}^{5})q^{2}+(1-\zeta_{48}^{2}+\cdots)q^{4}+\cdots$$

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

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