# Properties

 Label 1984.1 Level 1984 Weight 1 Dimension 52 Nonzero newspaces 6 Newform subspaces 10 Sturm bound 245760 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$1984 = 2^{6} \cdot 31$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$6$$ Newform subspaces: $$10$$ Sturm bound: $$245760$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1984))$$.

Total New Old
Modular forms 2330 690 1640
Cusp forms 170 52 118
Eisenstein series 2160 638 1522

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 32 12 0 8

## Trace form

 $$52 q + 2 q^{9} + O(q^{10})$$ $$52 q + 2 q^{9} + 2 q^{13} + 4 q^{17} + 4 q^{21} + 4 q^{25} + 6 q^{29} - 6 q^{31} + 4 q^{33} - 6 q^{35} + 10 q^{37} - 8 q^{41} + 2 q^{45} - 6 q^{49} + 24 q^{50} + 14 q^{57} + 4 q^{65} + 6 q^{67} - 2 q^{69} - 4 q^{73} - 4 q^{77} + 24 q^{80} + 4 q^{81} - 10 q^{89} - 10 q^{93} + 12 q^{95} - 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1984))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1984.1.d $$\chi_{1984}(63, \cdot)$$ None 0 1
1984.1.e $$\chi_{1984}(1921, \cdot)$$ 1984.1.e.a 1 1
1984.1.e.b 1
1984.1.f $$\chi_{1984}(1055, \cdot)$$ None 0 1
1984.1.g $$\chi_{1984}(929, \cdot)$$ None 0 1
1984.1.j $$\chi_{1984}(433, \cdot)$$ 1984.1.j.a 2 2
1984.1.j.b 4
1984.1.l $$\chi_{1984}(559, \cdot)$$ None 0 2
1984.1.p $$\chi_{1984}(161, \cdot)$$ None 0 2
1984.1.q $$\chi_{1984}(1183, \cdot)$$ 1984.1.q.a 4 2
1984.1.q.b 4
1984.1.r $$\chi_{1984}(1153, \cdot)$$ None 0 2
1984.1.s $$\chi_{1984}(191, \cdot)$$ 1984.1.s.a 4 2
1984.1.x $$\chi_{1984}(311, \cdot)$$ None 0 4
1984.1.y $$\chi_{1984}(185, \cdot)$$ None 0 4
1984.1.z $$\chi_{1984}(1441, \cdot)$$ None 0 4
1984.1.ba $$\chi_{1984}(95, \cdot)$$ None 0 4
1984.1.be $$\chi_{1984}(449, \cdot)$$ None 0 4
1984.1.bf $$\chi_{1984}(1087, \cdot)$$ 1984.1.bf.a 8 4
1984.1.bg $$\chi_{1984}(335, \cdot)$$ None 0 4
1984.1.bi $$\chi_{1984}(305, \cdot)$$ None 0 4
1984.1.bm $$\chi_{1984}(187, \cdot)$$ None 0 8
1984.1.bn $$\chi_{1984}(61, \cdot)$$ 1984.1.bn.a 8 8
1984.1.bn.b 16
1984.1.bq $$\chi_{1984}(47, \cdot)$$ None 0 8
1984.1.bs $$\chi_{1984}(209, \cdot)$$ None 0 8
1984.1.bv $$\chi_{1984}(57, \cdot)$$ None 0 8
1984.1.bw $$\chi_{1984}(87, \cdot)$$ None 0 8
1984.1.bx $$\chi_{1984}(255, \cdot)$$ None 0 8
1984.1.by $$\chi_{1984}(65, \cdot)$$ None 0 8
1984.1.cc $$\chi_{1984}(351, \cdot)$$ None 0 8
1984.1.cd $$\chi_{1984}(353, \cdot)$$ None 0 8
1984.1.ce $$\chi_{1984}(89, \cdot)$$ None 0 16
1984.1.cf $$\chi_{1984}(39, \cdot)$$ None 0 16
1984.1.ci $$\chi_{1984}(67, \cdot)$$ None 0 16
1984.1.cl $$\chi_{1984}(37, \cdot)$$ None 0 16
1984.1.cn $$\chi_{1984}(17, \cdot)$$ None 0 16
1984.1.cp $$\chi_{1984}(111, \cdot)$$ None 0 16
1984.1.cq $$\chi_{1984}(35, \cdot)$$ None 0 32
1984.1.ct $$\chi_{1984}(29, \cdot)$$ None 0 32
1984.1.cu $$\chi_{1984}(7, \cdot)$$ None 0 32
1984.1.cv $$\chi_{1984}(73, \cdot)$$ None 0 32
1984.1.cz $$\chi_{1984}(19, \cdot)$$ None 0 64
1984.1.da $$\chi_{1984}(13, \cdot)$$ None 0 64

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1984))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1984)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 14}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 10}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 7}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(62))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(124))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(248))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(496))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(992))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1984))$$$$^{\oplus 1}$$