# Properties

 Label 552.2.f Level $552$ Weight $2$ Character orbit 552.f Rep. character $\chi_{552}(277,\cdot)$ Character field $\Q$ Dimension $44$ Newform subspaces $4$ Sturm bound $192$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$552 = 2^{3} \cdot 3 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 552.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$192$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(552, [\chi])$$.

Total New Old
Modular forms 100 44 56
Cusp forms 92 44 48
Eisenstein series 8 0 8

## Trace form

 $$44q - 12q^{8} - 44q^{9} + O(q^{10})$$ $$44q - 12q^{8} - 44q^{9} - 4q^{10} - 8q^{12} - 4q^{14} + 24q^{16} + 8q^{17} - 4q^{20} - 20q^{22} + 12q^{24} - 52q^{25} + 16q^{26} - 8q^{30} - 24q^{31} - 20q^{32} + 8q^{34} + 4q^{38} + 16q^{39} + 36q^{40} - 8q^{41} + 12q^{42} - 24q^{44} + 48q^{47} + 60q^{49} + 16q^{50} - 12q^{56} - 16q^{57} + 24q^{58} - 24q^{60} + 48q^{62} - 32q^{65} - 16q^{66} + 44q^{68} + 16q^{70} - 64q^{71} + 12q^{72} + 24q^{73} - 64q^{74} + 60q^{76} - 16q^{78} - 28q^{80} + 44q^{81} + 24q^{84} + 12q^{86} + 24q^{87} - 68q^{88} + 40q^{89} + 4q^{90} - 8q^{94} - 48q^{95} - 20q^{96} + 8q^{97} - 56q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(552, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
552.2.f.a $$2$$ $$4.408$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$8$$ $$q+(1+i)q^{2}+iq^{3}+2iq^{4}+2iq^{5}+\cdots$$
552.2.f.b $$4$$ $$4.408$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\zeta_{8}^{3}q^{2}+\zeta_{8}q^{3}+2q^{4}+(2\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{5}+\cdots$$
552.2.f.c $$18$$ $$4.408$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\beta _{3}q^{2}-\beta _{4}q^{3}-\beta _{2}q^{4}+\beta _{9}q^{5}+\cdots$$
552.2.f.d $$20$$ $$4.408$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-2$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{1}q^{2}+\beta _{5}q^{3}+\beta _{2}q^{4}+\beta _{11}q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(552, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(552, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(184, [\chi])$$$$^{\oplus 2}$$