# Properties

 Label 663.1 Level 663 Weight 1 Dimension 14 Nonzero newspaces 3 Newform subspaces 8 Sturm bound 32256 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$663 = 3 \cdot 13 \cdot 17$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$8$$ Sturm bound: $$32256$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(663))$$.

Total New Old
Modular forms 784 346 438
Cusp forms 16 14 2
Eisenstein series 768 332 436

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 14 0 0 0

## Trace form

 $$14q + 2q^{4} + 2q^{9} + O(q^{10})$$ $$14q + 2q^{4} + 2q^{9} + 6q^{13} + 8q^{15} - 6q^{16} - 4q^{19} - 2q^{25} - 4q^{33} + 2q^{36} - 8q^{42} - 4q^{43} + 2q^{49} + 6q^{51} - 6q^{52} + 4q^{55} - 4q^{60} - 6q^{64} - 4q^{67} - 4q^{69} - 4q^{76} + 2q^{81} - 4q^{85} - 4q^{87} - 8q^{94} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(663))$$

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
663.1.c $$\chi_{663}(443, \cdot)$$ None 0 1
663.1.d $$\chi_{663}(560, \cdot)$$ None 0 1
663.1.g $$\chi_{663}(662, \cdot)$$ 663.1.g.a 1 1
663.1.g.b 1
663.1.g.c 2
663.1.g.d 2
663.1.h $$\chi_{663}(545, \cdot)$$ None 0 1
663.1.k $$\chi_{663}(38, \cdot)$$ None 0 2
663.1.l $$\chi_{663}(268, \cdot)$$ None 0 2
663.1.o $$\chi_{663}(307, \cdot)$$ None 0 2
663.1.p $$\chi_{663}(424, \cdot)$$ None 0 2
663.1.s $$\chi_{663}(421, \cdot)$$ None 0 2
663.1.t $$\chi_{663}(404, \cdot)$$ None 0 2
663.1.v $$\chi_{663}(101, \cdot)$$ 663.1.v.a 2 2
663.1.v.b 2
663.1.x $$\chi_{663}(290, \cdot)$$ None 0 2
663.1.y $$\chi_{663}(35, \cdot)$$ None 0 2
663.1.bb $$\chi_{663}(152, \cdot)$$ 663.1.bb.a 2 2
663.1.bb.b 2
663.1.bc $$\chi_{663}(151, \cdot)$$ None 0 4
663.1.be $$\chi_{663}(77, \cdot)$$ None 0 4
663.1.bf $$\chi_{663}(53, \cdot)$$ None 0 4
663.1.bj $$\chi_{663}(70, \cdot)$$ None 0 4
663.1.bl $$\chi_{663}(191, \cdot)$$ None 0 4
663.1.bn $$\chi_{663}(106, \cdot)$$ None 0 4
663.1.bo $$\chi_{663}(67, \cdot)$$ None 0 4
663.1.br $$\chi_{663}(154, \cdot)$$ None 0 4
663.1.bs $$\chi_{663}(310, \cdot)$$ None 0 4
663.1.bu $$\chi_{663}(140, \cdot)$$ None 0 4
663.1.bw $$\chi_{663}(44, \cdot)$$ None 0 8
663.1.bz $$\chi_{663}(5, \cdot)$$ None 0 8
663.1.cb $$\chi_{663}(40, \cdot)$$ None 0 8
663.1.cc $$\chi_{663}(142, \cdot)$$ None 0 8
663.1.ce $$\chi_{663}(19, \cdot)$$ None 0 8
663.1.ci $$\chi_{663}(134, \cdot)$$ None 0 8
663.1.cj $$\chi_{663}(185, \cdot)$$ None 0 8
663.1.cl $$\chi_{663}(145, \cdot)$$ None 0 8
663.1.cn $$\chi_{663}(10, \cdot)$$ None 0 16
663.1.co $$\chi_{663}(22, \cdot)$$ None 0 16
663.1.cq $$\chi_{663}(20, \cdot)$$ None 0 16
663.1.ct $$\chi_{663}(11, \cdot)$$ None 0 16

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(663))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(663)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 2}$$