# Properties

 Label 441.2.c Level $441$ Weight $2$ Character orbit 441.c Rep. character $\chi_{441}(440,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $2$ Sturm bound $112$ Trace bound $1$

# Learn more

## Defining parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 441.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q$$ Newform subspaces: $$2$$ 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 72 12 60
Cusp forms 40 12 28
Eisenstein series 32 0 32

## Trace form

 $$12 q - 8 q^{4} + O(q^{10})$$ $$12 q - 8 q^{4} + 8 q^{16} - 24 q^{22} + 44 q^{25} - 36 q^{37} - 36 q^{43} - 48 q^{46} + 64 q^{58} + 24 q^{64} + 44 q^{67} - 12 q^{79} - 16 q^{85} - 32 q^{88} + O(q^{100})$$

## 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.c.a $4$ $3.521$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{3}q^{5}-2\beta _{1}q^{8}-2\beta _{2}q^{10}+\cdots$$
441.2.c.b $8$ $3.521$ $$\Q(\zeta_{16})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{16}-\zeta_{16}^{2})q^{2}+(-1+2\zeta_{16}^{3}+\cdots)q^{4}+\cdots$$

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

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