# Properties

 Label 1287.2.b Level $1287$ Weight $2$ Character orbit 1287.b Rep. character $\chi_{1287}(298,\cdot)$ Character field $\Q$ Dimension $56$ Newform subspaces $4$ Sturm bound $336$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1287 = 3^{2} \cdot 11 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1287.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$336$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1287, [\chi])$$.

Total New Old
Modular forms 176 56 120
Cusp forms 160 56 104
Eisenstein series 16 0 16

## Trace form

 $$56q - 50q^{4} + O(q^{10})$$ $$56q - 50q^{4} + 4q^{13} + 16q^{14} + 30q^{16} - 12q^{17} - 2q^{22} + 4q^{23} - 36q^{25} - 2q^{26} + 8q^{29} - 8q^{35} + 14q^{38} - 40q^{40} + 12q^{43} - 76q^{49} + 48q^{52} + 4q^{53} - 8q^{55} - 6q^{56} + 12q^{61} - 24q^{62} + 50q^{64} - 20q^{65} - 36q^{68} - 44q^{74} - 8q^{77} + 32q^{79} - 132q^{82} - 18q^{88} + 16q^{91} + 38q^{92} - 16q^{94} - 4q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1287, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1287.2.b.a $$10$$ $$10.277$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{5}+\beta _{7}+\cdots)q^{5}+\cdots$$
1287.2.b.b $$12$$ $$10.277$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-1+\beta _{4}-\beta _{5})q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots$$
1287.2.b.c $$14$$ $$10.277$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-1-\beta _{5}+\beta _{6})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$$
1287.2.b.d $$20$$ $$10.277$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{12}q^{2}+(-1-\beta _{8})q^{4}+(\beta _{10}+\beta _{11}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1287, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1287, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(117, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(143, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(429, [\chi])$$$$^{\oplus 2}$$