# Properties

 Label 252.4.l Level $252$ Weight $4$ Character orbit 252.l Rep. character $\chi_{252}(193,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $48$ Newform subspaces $1$ Sturm bound $192$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 252.l (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$1$$ Sturm bound: $$192$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 300 48 252
Cusp forms 276 48 228
Eisenstein series 24 0 24

## Trace form

 $$48q - 40q^{5} - 6q^{7} - 2q^{9} + O(q^{10})$$ $$48q - 40q^{5} - 6q^{7} - 2q^{9} - 8q^{11} - 12q^{13} - 26q^{15} + 112q^{17} + 60q^{19} - 182q^{21} - 20q^{23} + 1200q^{25} + 194q^{29} - 30q^{31} + 380q^{33} + 394q^{35} - 84q^{37} + 10q^{39} + 210q^{41} + 42q^{43} + 386q^{45} + 66q^{47} + 516q^{49} - 640q^{51} - 468q^{53} + 612q^{55} + 1476q^{57} + 458q^{59} + 402q^{61} + 1518q^{63} - 828q^{65} + 294q^{67} - 28q^{69} - 2228q^{71} - 336q^{73} - 3338q^{75} - 1120q^{77} + 384q^{79} - 890q^{81} + 1024q^{83} + 360q^{85} - 1508q^{87} + 2922q^{89} - 120q^{91} + 1312q^{93} - 1214q^{95} - 264q^{97} - 2246q^{99} + O(q^{100})$$

## 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.l.a $$48$$ $$14.868$$ None $$0$$ $$0$$ $$-40$$ $$-6$$

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

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