# Properties

 Label 252.2.i Level $252$ Weight $2$ Character orbit 252.i Rep. character $\chi_{252}(25,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $16$ Newform subspaces $2$ Sturm bound $96$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 252.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## 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

 $$16 q - 4 q^{5} + q^{7} - 2 q^{9} + O(q^{10})$$ $$16 q - 4 q^{5} + q^{7} - 2 q^{9} - 2 q^{11} - q^{13} + 7 q^{15} - 5 q^{17} + 2 q^{19} - 2 q^{21} + 7 q^{23} - 8 q^{25} + 9 q^{27} + 2 q^{29} - 4 q^{31} + 8 q^{33} - 11 q^{35} - q^{37} + 7 q^{39} - 24 q^{41} + 2 q^{43} - 4 q^{45} + 12 q^{47} + 7 q^{49} - 13 q^{51} - 18 q^{53} - 12 q^{55} - 3 q^{57} + 14 q^{59} + 26 q^{61} + 21 q^{63} - 18 q^{65} + 14 q^{67} - 43 q^{69} - 14 q^{71} + 14 q^{73} - 47 q^{75} - 43 q^{77} + 2 q^{79} - 38 q^{81} - 26 q^{83} - 6 q^{85} + 28 q^{87} - 21 q^{89} + 5 q^{91} + 31 q^{93} + 76 q^{95} - q^{97} - 17 q^{99} + O(q^{100})$$

## 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.i.a $$2$$ $$2.012$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$-2$$ $$-5$$ $$q+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots$$
252.2.i.b $$14$$ $$2.012$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$0$$ $$3$$ $$-2$$ $$6$$ $$q+(-\beta _{1}+\beta _{3})q^{3}-\beta _{9}q^{5}+\beta _{10}q^{7}+\cdots$$

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

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