# Properties

 Label 252.4.j Level $252$ Weight $4$ Character orbit 252.j Rep. character $\chi_{252}(85,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $36$ Newform subspaces $2$ Sturm bound $192$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 252.j (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$192$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(252, [\chi])$$.

Total New Old
Modular forms 300 36 264
Cusp forms 276 36 240
Eisenstein series 24 0 24

## Trace form

 $$36q + 6q^{3} + 8q^{5} - 74q^{9} + O(q^{10})$$ $$36q + 6q^{3} + 8q^{5} - 74q^{9} - 98q^{11} + 208q^{15} + 76q^{17} - 180q^{19} - 56q^{21} - 284q^{23} - 594q^{25} - 900q^{27} - 676q^{29} - 36q^{31} + 446q^{33} + 280q^{35} - 144q^{37} + 508q^{39} - 246q^{41} - 342q^{43} - 1588q^{45} - 1176q^{47} - 882q^{49} + 1850q^{51} + 1488q^{53} - 792q^{55} - 258q^{57} + 302q^{59} + 588q^{63} - 1872q^{65} - 162q^{67} + 128q^{69} + 1984q^{71} - 828q^{73} - 2234q^{75} - 616q^{77} - 468q^{79} - 890q^{81} + 2164q^{83} - 2016q^{85} + 3856q^{87} + 720q^{89} + 504q^{91} + 700q^{93} + 3364q^{95} + 342q^{97} + 5956q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(252, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
252.4.j.a $$18$$ $$14.868$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$-5$$ $$14$$ $$63$$ $$q+\beta _{4}q^{3}+(2-2\beta _{2}+\beta _{12})q^{5}+7\beta _{2}q^{7}+\cdots$$
252.4.j.b $$18$$ $$14.868$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$11$$ $$-6$$ $$-63$$ $$q+(1-\beta _{1})q^{3}+(-1+\beta _{2}+\beta _{3})q^{5}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(252, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(252, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 2}$$