# Properties

 Label 441.2.e Level $441$ Weight $2$ Character orbit 441.e Rep. character $\chi_{441}(226,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $30$ Newform subspaces $10$ Sturm bound $112$ Trace bound $10$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 441.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$10$$ Sturm bound: $$112$$ Trace bound: $$10$$ Distinguishing $$T_p$$: $$2$$, $$5$$, $$13$$

## Dimensions

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

Total New Old
Modular forms 144 38 106
Cusp forms 80 30 50
Eisenstein series 64 8 56

## Trace form

 $$30 q - 3 q^{2} - 15 q^{4} + 2 q^{5} + 18 q^{8} + O(q^{10})$$ $$30 q - 3 q^{2} - 15 q^{4} + 2 q^{5} + 18 q^{8} - 4 q^{10} + 2 q^{11} + 12 q^{13} - 11 q^{16} - 6 q^{19} - 8 q^{20} - 8 q^{22} - 9 q^{25} - 2 q^{26} + 28 q^{29} + 2 q^{31} - q^{32} - 12 q^{37} - 2 q^{38} - 20 q^{41} - 4 q^{43} - 24 q^{44} + 12 q^{46} + 6 q^{47} - 46 q^{50} + 16 q^{52} + 6 q^{53} - 8 q^{55} + 42 q^{58} + 12 q^{59} + 24 q^{61} + 36 q^{62} + 14 q^{64} + 30 q^{65} - 10 q^{67} - 4 q^{71} - 10 q^{73} + 4 q^{74} - 32 q^{76} - 42 q^{79} - 8 q^{80} - 20 q^{82} + 12 q^{83} - 64 q^{85} + 38 q^{86} + 72 q^{88} - 16 q^{89} - 96 q^{92} - 12 q^{94} - 34 q^{95} - 16 q^{97} + O(q^{100})$$

## 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.e.a $2$ $3.521$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-2$$ $$0$$ $$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-2\zeta_{6}q^{5}-3q^{8}+\cdots$$
441.2.e.b $2$ $3.521$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$2$$ $$0$$ $$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+2\zeta_{6}q^{5}-3q^{8}+\cdots$$
441.2.e.c $2$ $3.521$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(2-2\zeta_{6})q^{4}+7q^{13}-4\zeta_{6}q^{16}+\cdots$$
441.2.e.d $2$ $3.521$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-7})$$ $$1$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+3q^{8}+(4-4\zeta_{6})q^{11}+\cdots$$
441.2.e.e $2$ $3.521$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$2$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots$$
441.2.e.f $4$ $3.521$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-2$$ $$0$$ $$-4$$ $$0$$ $$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
441.2.e.g $4$ $3.521$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-2$$ $$0$$ $$4$$ $$0$$ $$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
441.2.e.h $4$ $3.521$ $$\Q(\sqrt{-3}, \sqrt{7})$$ $$\Q(\sqrt{-7})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+5\beta _{2}q^{4}+3\beta _{3}q^{8}+(2\beta _{1}+\cdots)q^{11}+\cdots$$
441.2.e.i $4$ $3.521$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}-2\zeta_{12}^{2}q^{5}+\cdots$$
441.2.e.j $4$ $3.521$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+2\zeta_{12}^{2}q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(441, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 2}$$