Defining parameters

 Level: $$N$$ = $$639 = 3^{2} \cdot 71$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$3$$ Sturm bound: $$30240$$ Trace bound: $$1$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(639))$$.

Total New Old
Modular forms 586 328 258
Cusp forms 26 17 9
Eisenstein series 560 311 249

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 17 0 0 0

Trace form

 $$17 q + q^{2} - 5 q^{4} + q^{5} + 2 q^{8} + O(q^{10})$$ $$17 q + q^{2} - 5 q^{4} + q^{5} + 2 q^{8} - 2 q^{10} - 6 q^{16} + 14 q^{18} - q^{19} + 3 q^{20} - 7 q^{24} - 5 q^{25} + q^{29} - 7 q^{30} + 3 q^{32} - q^{37} - 19 q^{38} - 4 q^{40} - q^{43} - 7 q^{48} - 4 q^{49} + 3 q^{50} - 2 q^{58} - 7 q^{60} + 14 q^{64} + 11 q^{71} - 7 q^{72} - q^{73} + 2 q^{74} + 14 q^{75} - 3 q^{76} - q^{79} - 16 q^{80} + q^{83} + 2 q^{86} - 7 q^{87} + q^{89} + 14 q^{90} + 2 q^{95} - 7 q^{96} + q^{98} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(639))$$

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
639.1.c $$\chi_{639}(143, \cdot)$$ None 0 1
639.1.d $$\chi_{639}(496, \cdot)$$ 639.1.d.a 3 1
639.1.g $$\chi_{639}(70, \cdot)$$ 639.1.g.a 2 2
639.1.g.b 12
639.1.h $$\chi_{639}(356, \cdot)$$ None 0 2
639.1.k $$\chi_{639}(46, \cdot)$$ None 0 4
639.1.l $$\chi_{639}(125, \cdot)$$ None 0 4
639.1.n $$\chi_{639}(181, \cdot)$$ None 0 6
639.1.o $$\chi_{639}(116, \cdot)$$ None 0 6
639.1.t $$\chi_{639}(5, \cdot)$$ None 0 8
639.1.u $$\chi_{639}(85, \cdot)$$ None 0 8
639.1.x $$\chi_{639}(20, \cdot)$$ None 0 12
639.1.y $$\chi_{639}(34, \cdot)$$ None 0 12
639.1.ba $$\chi_{639}(8, \cdot)$$ None 0 24
639.1.bb $$\chi_{639}(28, \cdot)$$ None 0 24
639.1.bd $$\chi_{639}(7, \cdot)$$ None 0 48
639.1.be $$\chi_{639}(2, \cdot)$$ None 0 48

Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(639))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(639)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(71))$$$$^{\oplus 3}$$