# Properties

 Label 800.2.y Level $800$ Weight $2$ Character orbit 800.y Rep. character $\chi_{800}(101,\cdot)$ Character field $\Q(\zeta_{8})$ Dimension $292$ Newform subspaces $6$ Sturm bound $240$ Trace bound $18$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$800 = 2^{5} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 800.y (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$32$$ Character field: $$\Q(\zeta_{8})$$ Newform subspaces: $$6$$ Sturm bound: $$240$$ Trace bound: $$18$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(800, [\chi])$$.

Total New Old
Modular forms 504 316 188
Cusp forms 456 292 164
Eisenstein series 48 24 24

## Trace form

 $$292 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 12 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} + O(q^{10})$$ $$292 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 12 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} - 12 q^{11} - 12 q^{12} + 4 q^{13} - 12 q^{14} + 8 q^{16} + 24 q^{18} + 4 q^{19} - 12 q^{21} - 16 q^{22} + 12 q^{23} - 24 q^{24} + 8 q^{26} + 28 q^{27} - 16 q^{28} + 4 q^{29} - 48 q^{31} - 16 q^{32} + 8 q^{33} + 8 q^{34} + 40 q^{36} + 4 q^{37} - 44 q^{38} + 28 q^{39} - 12 q^{41} + 24 q^{42} + 12 q^{43} + 44 q^{44} + 20 q^{46} - 48 q^{48} - 8 q^{51} + 12 q^{52} + 20 q^{53} + 80 q^{54} - 24 q^{56} + 4 q^{57} - 64 q^{58} + 36 q^{59} - 44 q^{61} - 32 q^{63} + 40 q^{64} + 12 q^{66} - 36 q^{67} - 64 q^{68} - 28 q^{69} + 20 q^{71} - 92 q^{72} + 4 q^{73} - 92 q^{74} - 12 q^{76} + 20 q^{77} - 108 q^{78} + 4 q^{82} + 44 q^{83} - 16 q^{84} - 96 q^{86} - 52 q^{87} - 80 q^{88} + 4 q^{89} + 36 q^{91} + 48 q^{92} + 16 q^{93} - 88 q^{94} - 152 q^{96} + 8 q^{97} - 56 q^{98} - 96 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(800, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
800.2.y.a $4$ $6.388$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+\cdots$$
800.2.y.b $8$ $6.388$ 8.0.18939904.2 None $$4$$ $$4$$ $$0$$ $$8$$ $$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{3}-\beta _{5}-\beta _{7})q^{3}+\cdots$$
800.2.y.c $64$ $6.388$ None $$0$$ $$0$$ $$0$$ $$0$$
800.2.y.d $64$ $6.388$ None $$0$$ $$0$$ $$0$$ $$0$$
800.2.y.e $64$ $6.388$ None $$0$$ $$0$$ $$0$$ $$0$$
800.2.y.f $88$ $6.388$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(800, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(800, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 2}$$