# Properties

 Label 441.2.bb Level $441$ Weight $2$ Character orbit 441.bb Rep. character $\chi_{441}(37,\cdot)$ Character field $\Q(\zeta_{21})$ Dimension $264$ Newform subspaces $6$ Sturm bound $112$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 441.bb (of order $$21$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$49$$ Character field: $$\Q(\zeta_{21})$$ Newform subspaces: $$6$$ Sturm bound: $$112$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(441, [\chi])$$.

Total New Old
Modular forms 720 288 432
Cusp forms 624 264 360
Eisenstein series 96 24 72

## Trace form

 $$264q + 13q^{2} + 7q^{4} + 16q^{5} - 8q^{7} + 8q^{8} + O(q^{10})$$ $$264q + 13q^{2} + 7q^{4} + 16q^{5} - 8q^{7} + 8q^{8} - 18q^{10} + 23q^{11} - 2q^{13} - 19q^{14} + 9q^{16} + 21q^{17} + 15q^{19} + 34q^{20} - 16q^{22} - 7q^{23} - 2q^{25} + 26q^{26} - 72q^{28} - 28q^{29} + 37q^{31} + 61q^{32} - 42q^{34} + 26q^{35} - 61q^{37} - 30q^{38} + 14q^{40} - 34q^{41} - 34q^{43} - 34q^{44} - 98q^{46} - 29q^{47} + 44q^{49} + 148q^{50} + 114q^{52} - 51q^{53} + 13q^{55} - 140q^{56} + 72q^{58} + 12q^{59} + 45q^{61} + 8q^{62} + 32q^{64} + 16q^{65} + q^{67} - 77q^{68} - 82q^{70} + 41q^{71} - 3q^{73} + 28q^{74} + 3q^{76} + 27q^{77} - 7q^{79} - 120q^{80} - 174q^{82} - 58q^{83} - 74q^{85} - 51q^{86} - 137q^{88} - 72q^{89} - 142q^{91} - 46q^{92} - 222q^{94} - 125q^{95} - 16q^{97} - 185q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(441, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
441.2.bb.a $$12$$ $$3.521$$ $$\Q(\zeta_{21})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$1$$ $$q+(2-2\zeta_{21}^{2}+2\zeta_{21}^{3}-2\zeta_{21}^{5}+2\zeta_{21}^{6}+\cdots)q^{4}+\cdots$$
441.2.bb.b $$24$$ $$3.521$$ None $$0$$ $$0$$ $$0$$ $$28$$
441.2.bb.c $$48$$ $$3.521$$ None $$1$$ $$0$$ $$0$$ $$0$$
441.2.bb.d $$48$$ $$3.521$$ None $$13$$ $$0$$ $$14$$ $$-14$$
441.2.bb.e $$60$$ $$3.521$$ None $$-1$$ $$0$$ $$2$$ $$5$$
441.2.bb.f $$72$$ $$3.521$$ None $$0$$ $$0$$ $$0$$ $$-28$$

## Decomposition of $$S_{2}^{\mathrm{old}}(441, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(441, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 2}$$