# Properties

 Label 920.2.f Level $920$ Weight $2$ Character orbit 920.f Rep. character $\chi_{920}(461,\cdot)$ Character field $\Q$ Dimension $88$ Newform subspaces $4$ Sturm bound $288$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$920 = 2^{3} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 920.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$288$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(920, [\chi])$$.

Total New Old
Modular forms 148 88 60
Cusp forms 140 88 52
Eisenstein series 8 0 8

## Trace form

 $$88q - 6q^{6} + 6q^{8} - 88q^{9} + O(q^{10})$$ $$88q - 6q^{6} + 6q^{8} - 88q^{9} + 14q^{12} + 12q^{14} + 8q^{16} - 14q^{18} - 8q^{20} - 24q^{22} + 12q^{23} - 12q^{24} - 88q^{25} - 2q^{26} - 24q^{28} + 16q^{30} - 40q^{32} - 16q^{33} + 12q^{34} + 10q^{36} + 20q^{38} - 24q^{39} + 16q^{41} + 48q^{42} - 16q^{44} - 40q^{47} + 50q^{48} + 120q^{49} + 14q^{52} - 18q^{54} + 16q^{55} + 8q^{56} - 16q^{57} - 46q^{58} - 28q^{60} - 2q^{62} + 80q^{63} - 18q^{64} - 12q^{66} + 48q^{68} + 16q^{70} - 32q^{71} + 26q^{72} - 32q^{73} + 8q^{74} + 92q^{76} + 10q^{78} - 16q^{80} + 72q^{81} - 58q^{82} + 8q^{84} + 56q^{86} + 72q^{87} - 60q^{88} - 36q^{90} + 18q^{94} - 32q^{95} - 58q^{96} + 32q^{97} + 16q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(920, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
920.2.f.a $$2$$ $$7.346$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(1+i)q^{2}+2iq^{4}+iq^{5}+(-2+2i)q^{8}+\cdots$$
920.2.f.b $$8$$ $$7.346$$ 8.0.1871773696.1 None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{6}q^{2}+(\beta _{1}+\beta _{3})q^{3}-2q^{4}-\beta _{1}q^{5}+\cdots$$
920.2.f.c $$30$$ $$7.346$$ None $$0$$ $$0$$ $$0$$ $$-4$$
920.2.f.d $$48$$ $$7.346$$ None $$-2$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(920, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(920, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(184, [\chi])$$$$^{\oplus 2}$$