# Properties

 Label 252.2.w Level $252$ Weight $2$ Character orbit 252.w Rep. character $\chi_{252}(5,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $1$ Sturm bound $96$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 252.w (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$96$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(252, [\chi])$$.

Total New Old
Modular forms 108 16 92
Cusp forms 84 16 68
Eisenstein series 24 0 24

## Trace form

 $$16 q - q^{7} + 6 q^{9} + O(q^{10})$$ $$16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47} - 5 q^{49} - 33 q^{51} + 15 q^{57} - 30 q^{59} - 15 q^{63} + 14 q^{67} + 21 q^{69} - 57 q^{75} + 3 q^{77} + 2 q^{79} + 18 q^{81} + 6 q^{85} + 48 q^{87} + 21 q^{89} + 9 q^{91} + 21 q^{93} - 3 q^{97} - 9 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(252, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
252.2.w.a $$16$$ $$2.012$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-1$$ $$q-\beta _{10}q^{3}+\beta _{7}q^{5}+(\beta _{3}-\beta _{8})q^{7}-\beta _{4}q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(252, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(252, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 2}$$