# Properties

 Label 287.2.c Level 287 Weight 2 Character orbit c Rep. character $$\chi_{287}(204,\cdot)$$ Character field $$\Q$$ Dimension 22 Newforms 2 Sturm bound 56 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$287 = 7 \cdot 41$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 287.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$41$$ Character field: $$\Q$$ Newforms: $$2$$ Sturm bound: $$56$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(287, [\chi])$$.

Total New Old
Modular forms 30 22 8
Cusp forms 26 22 4
Eisenstein series 4 0 4

## Trace form

 $$22q + 24q^{4} - 8q^{5} - 12q^{8} - 14q^{9} + O(q^{10})$$ $$22q + 24q^{4} - 8q^{5} - 12q^{8} - 14q^{9} + 4q^{10} + 12q^{16} - 20q^{18} - 20q^{20} - 4q^{21} + 12q^{23} + 30q^{25} + 8q^{31} - 24q^{32} + 16q^{33} - 16q^{36} - 32q^{37} - 36q^{39} - 20q^{40} - 6q^{41} + 24q^{42} - 32q^{43} + 56q^{45} - 22q^{49} - 4q^{50} + 12q^{51} + 12q^{57} - 36q^{59} + 24q^{61} + 24q^{62} + 16q^{64} + 56q^{66} - 18q^{72} - 64q^{73} + 30q^{74} - 8q^{77} + 66q^{78} - 36q^{80} + 6q^{81} + 18q^{82} + 40q^{83} - 26q^{84} + 60q^{86} - 28q^{87} - 96q^{90} + 26q^{92} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(287, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
287.2.c.a $$10$$ $$2.292$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$4$$ $$0$$ $$-10$$ $$0$$ $$q+\beta _{2}q^{2}+(\beta _{1}-\beta _{7})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$$
287.2.c.b $$12$$ $$2.292$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$-4$$ $$0$$ $$2$$ $$0$$ $$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{8})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(287, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(287, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(41, [\chi])$$$$^{\oplus 2}$$