## Defining parameters

 Level: $$N$$ = $$287 = 7 \cdot 41$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$2$$ Sturm bound: $$6720$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(287))$$.

Total New Old
Modular forms 246 200 46
Cusp forms 6 6 0
Eisenstein series 240 194 46

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 0 0

## Trace form

 $$6q - 2q^{2} + 4q^{4} - 4q^{8} + 4q^{9} + O(q^{10})$$ $$6q - 2q^{2} + 4q^{4} - 4q^{8} + 4q^{9} + 2q^{16} - 6q^{18} - 2q^{21} - 2q^{23} + 6q^{25} - 6q^{32} - 2q^{36} - 2q^{37} - 4q^{39} - 4q^{42} - 2q^{43} - 4q^{46} + 6q^{49} - 2q^{50} - 4q^{51} - 4q^{57} + 2q^{72} + 10q^{74} + 6q^{78} + 2q^{81} + 8q^{84} - 4q^{86} - 2q^{91} + 8q^{92} - 2q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(287))$$

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
287.1.b $$\chi_{287}(83, \cdot)$$ None 0 1
287.1.d $$\chi_{287}(286, \cdot)$$ 287.1.d.a 3 1
287.1.d.b 3
287.1.g $$\chi_{287}(132, \cdot)$$ None 0 2
287.1.i $$\chi_{287}(40, \cdot)$$ None 0 2
287.1.k $$\chi_{287}(124, \cdot)$$ None 0 2
287.1.m $$\chi_{287}(85, \cdot)$$ None 0 4
287.1.o $$\chi_{287}(139, \cdot)$$ None 0 4
287.1.p $$\chi_{287}(146, \cdot)$$ None 0 4
287.1.q $$\chi_{287}(73, \cdot)$$ None 0 4
287.1.t $$\chi_{287}(20, \cdot)$$ None 0 8
287.1.v $$\chi_{287}(44, \cdot)$$ None 0 8
287.1.x $$\chi_{287}(31, \cdot)$$ None 0 8
287.1.y $$\chi_{287}(10, \cdot)$$ None 0 8
287.1.ba $$\chi_{287}(15, \cdot)$$ None 0 16
287.1.bd $$\chi_{287}(5, \cdot)$$ None 0 16
287.1.bf $$\chi_{287}(11, \cdot)$$ None 0 32