Defining parameters

 Level: $$N$$ = $$495 = 3^{2} \cdot 5 \cdot 11$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$7$$ Sturm bound: $$17280$$ Trace bound: $$1$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(495))$$.

Total New Old
Modular forms 672 259 413
Cusp forms 32 17 15
Eisenstein series 640 242 398

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

 $$17 q + 2 q^{3} + 5 q^{4} - 2 q^{9} + O(q^{10})$$ $$17 q + 2 q^{3} + 5 q^{4} - 2 q^{9} + 3 q^{11} - 2 q^{12} - q^{15} - q^{16} - 6 q^{20} + 4 q^{25} - 4 q^{27} - 4 q^{31} + 4 q^{33} - 8 q^{34} - 4 q^{36} - 4 q^{37} + 3 q^{44} + 2 q^{45} - 6 q^{47} + 4 q^{48} + 5 q^{49} - 9 q^{55} - 2 q^{60} - 9 q^{64} - 2 q^{67} - 8 q^{70} - 6 q^{71} - 2 q^{75} + 3 q^{80} - 6 q^{81} - 6 q^{89} - 8 q^{91} - 6 q^{93} - 2 q^{97} + 2 q^{99} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(495))$$

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
495.1.b $$\chi_{495}(406, \cdot)$$ None 0 1
495.1.e $$\chi_{495}(386, \cdot)$$ None 0 1
495.1.g $$\chi_{495}(89, \cdot)$$ None 0 1
495.1.h $$\chi_{495}(109, \cdot)$$ 495.1.h.a 1 1
495.1.h.b 2
495.1.h.c 2
495.1.j $$\chi_{495}(298, \cdot)$$ None 0 2
495.1.m $$\chi_{495}(98, \cdot)$$ None 0 2
495.1.o $$\chi_{495}(274, \cdot)$$ 495.1.o.a 2 2
495.1.o.b 2
495.1.q $$\chi_{495}(254, \cdot)$$ None 0 2
495.1.s $$\chi_{495}(56, \cdot)$$ None 0 2
495.1.t $$\chi_{495}(76, \cdot)$$ None 0 2
495.1.v $$\chi_{495}(19, \cdot)$$ None 0 4
495.1.w $$\chi_{495}(179, \cdot)$$ None 0 4
495.1.y $$\chi_{495}(26, \cdot)$$ None 0 4
495.1.bb $$\chi_{495}(46, \cdot)$$ None 0 4
495.1.bd $$\chi_{495}(32, \cdot)$$ 495.1.bd.a 4 4
495.1.bd.b 4
495.1.be $$\chi_{495}(67, \cdot)$$ None 0 4
495.1.bh $$\chi_{495}(8, \cdot)$$ None 0 8
495.1.bk $$\chi_{495}(37, \cdot)$$ None 0 8
495.1.bm $$\chi_{495}(61, \cdot)$$ None 0 8
495.1.bn $$\chi_{495}(86, \cdot)$$ None 0 8
495.1.bp $$\chi_{495}(14, \cdot)$$ None 0 8
495.1.br $$\chi_{495}(79, \cdot)$$ None 0 8
495.1.bt $$\chi_{495}(58, \cdot)$$ None 0 16
495.1.bu $$\chi_{495}(2, \cdot)$$ None 0 16

Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(495))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(495)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 2}$$