# Properties

 Label 252.4.bm Level $252$ Weight $4$ Character orbit 252.bm Rep. character $\chi_{252}(173,\cdot)$ Character field $\Q(\zeta_{6})$ 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.bm (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{6})$$ 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

 $$48q + 6q^{7} - 30q^{9} + O(q^{10})$$ $$48q + 6q^{7} - 30q^{9} + 36q^{13} + 66q^{15} + 72q^{17} + 126q^{21} + 1200q^{25} + 396q^{27} + 42q^{29} - 90q^{31} + 108q^{33} - 390q^{35} + 84q^{37} + 1014q^{39} + 618q^{41} - 42q^{43} - 1014q^{45} + 198q^{47} - 276q^{49} + 408q^{51} + 1620q^{53} + 492q^{57} + 750q^{59} - 1314q^{61} + 1542q^{63} + 564q^{65} + 294q^{67} + 924q^{69} - 1410q^{75} - 2448q^{77} - 804q^{79} - 666q^{81} - 360q^{85} + 1788q^{87} - 1722q^{89} + 540q^{91} + 1128q^{93} - 2946q^{95} + 792q^{97} - 54q^{99} + O(q^{100})$$

## 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.bm.a $$48$$ $$14.868$$ None $$0$$ $$0$$ $$0$$ $$6$$

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

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