# Properties

 Label 552.2.m Level $552$ Weight $2$ Character orbit 552.m Rep. character $\chi_{552}(137,\cdot)$ Character field $\Q$ Dimension $24$ Newform subspaces $2$ 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.m (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$69$$ Character field: $$\Q$$ Newform subspaces: $$2$$ 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 104 24 80
Cusp forms 88 24 64
Eisenstein series 16 0 16

## Trace form

 $$24 q + 4 q^{9} + O(q^{10})$$ $$24 q + 4 q^{9} + 16 q^{25} - 12 q^{27} + 8 q^{31} - 20 q^{39} + 8 q^{49} + 32 q^{55} - 16 q^{69} + 8 q^{75} + 12 q^{81} - 24 q^{85} - 28 q^{87} - 12 q^{93} + O(q^{100})$$

## 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.m.a $8$ $4.408$ 8.0.40960000.1 None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-1-\beta _{2})q^{3}+\beta _{3}q^{5}+\beta _{5}q^{7}+(1+\cdots)q^{9}+\cdots$$
552.2.m.b $16$ $4.408$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q-\beta _{7}q^{3}-\beta _{5}q^{5}-\beta _{1}q^{7}+(\beta _{2}+\beta _{4}+\cdots)q^{9}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(552, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(69, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(138, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(276, [\chi])$$$$^{\oplus 2}$$