# Properties

 Label 288.2.v Level $288$ Weight $2$ Character orbit 288.v Rep. character $\chi_{288}(37,\cdot)$ Character field $\Q(\zeta_{8})$ Dimension $76$ Newform subspaces $4$ Sturm bound $96$ Trace bound $14$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$288 = 2^{5} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 288.v (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$32$$ Character field: $$\Q(\zeta_{8})$$ Newform subspaces: $$4$$ Sturm bound: $$96$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(288, [\chi])$$.

Total New Old
Modular forms 208 84 124
Cusp forms 176 76 100
Eisenstein series 32 8 24

## Trace form

 $$76q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10})$$ $$76q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 12q^{10} + 4q^{11} - 4q^{13} + 20q^{14} - 4q^{19} + 20q^{20} - 24q^{22} + 12q^{23} - 4q^{25} - 16q^{26} - 24q^{28} + 4q^{29} + 16q^{31} - 16q^{32} - 16q^{34} + 28q^{35} - 4q^{37} - 44q^{38} - 56q^{40} + 4q^{41} + 4q^{43} - 44q^{44} - 36q^{46} - 60q^{50} - 12q^{52} + 20q^{53} + 28q^{55} - 64q^{56} - 72q^{58} - 28q^{59} - 36q^{61} - 24q^{62} + 56q^{64} + 8q^{65} - 12q^{67} - 8q^{68} + 80q^{70} - 28q^{71} - 4q^{73} + 20q^{74} + 12q^{76} + 20q^{77} + 64q^{80} + 76q^{82} - 36q^{83} + 16q^{85} + 88q^{86} + 80q^{88} + 4q^{89} - 52q^{91} + 120q^{92} + 56q^{94} - 56q^{95} - 8q^{97} + 104q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(288, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
288.2.v.a $$4$$ $$2.300$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$4$$ $$4$$ $$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(1+\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots$$
288.2.v.b $$8$$ $$2.300$$ 8.0.18939904.2 None $$4$$ $$0$$ $$0$$ $$-8$$ $$q+\beta _{2}q^{2}+(\beta _{2}-\beta _{3}+\beta _{6})q^{4}+(\beta _{6}+\beta _{7})q^{5}+\cdots$$
288.2.v.c $$32$$ $$2.300$$ None $$0$$ $$0$$ $$0$$ $$0$$
288.2.v.d $$32$$ $$2.300$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(288, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(288, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 2}$$