# Properties

 Label 440.2.y Level $440$ Weight $2$ Character orbit 440.y Rep. character $\chi_{440}(81,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $48$ Newform subspaces $4$ Sturm bound $144$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$440 = 2^{3} \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 440.y (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$4$$ Sturm bound: $$144$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(440, [\chi])$$.

Total New Old
Modular forms 320 48 272
Cusp forms 256 48 208
Eisenstein series 64 0 64

## Trace form

 $$48 q - 4 q^{3} + O(q^{10})$$ $$48 q - 4 q^{3} - 4 q^{11} - 4 q^{13} + 16 q^{17} + 14 q^{19} - 16 q^{21} + 16 q^{23} - 12 q^{25} + 14 q^{27} + 12 q^{29} - 12 q^{31} - 26 q^{33} + 8 q^{35} - 8 q^{37} - 44 q^{39} - 6 q^{41} - 60 q^{43} - 40 q^{47} - 46 q^{49} - 34 q^{51} + 48 q^{53} + 16 q^{55} - 14 q^{57} + 26 q^{59} + 48 q^{61} + 48 q^{63} + 44 q^{65} - 12 q^{67} + 64 q^{69} + 68 q^{71} + 52 q^{73} + 6 q^{75} - 36 q^{77} + 36 q^{79} - 62 q^{81} + 42 q^{83} - 4 q^{85} + 40 q^{87} - 48 q^{89} - 14 q^{91} + 16 q^{93} - 50 q^{97} + 12 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(440, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
440.2.y.a $8$ $3.513$ 8.0.13140625.1 None $$0$$ $$1$$ $$-2$$ $$1$$ $$q+(\beta _{1}-\beta _{5})q^{3}+\beta _{7}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$$
440.2.y.b $12$ $3.513$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$-1$$ $$3$$ $$-8$$ $$q+(\beta _{1}+\beta _{4})q^{3}+(1-\beta _{6}+\beta _{7}-\beta _{8}+\cdots)q^{5}+\cdots$$
440.2.y.c $12$ $3.513$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$-1$$ $$3$$ $$-1$$ $$q+(\beta _{3}+\beta _{8})q^{3}-\beta _{6}q^{5}+(1+\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots$$
440.2.y.d $16$ $3.513$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$-3$$ $$-4$$ $$8$$ $$q-\beta _{1}q^{3}+(-1+\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(440, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(440, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(22, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(44, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(88, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(110, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(220, [\chi])$$$$^{\oplus 2}$$