# Properties

 Label 1407.1 Level 1407 Weight 1 Dimension 122 Nonzero newspaces 10 Newform subspaces 20 Sturm bound 143616 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$1407 = 3 \cdot 7 \cdot 67$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$10$$ Newform subspaces: $$20$$ Sturm bound: $$143616$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1407))$$.

Total New Old
Modular forms 1798 774 1024
Cusp forms 214 122 92
Eisenstein series 1584 652 932

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 122 0 0 0

## Trace form

 $$122q + 4q^{4} + 6q^{9} + O(q^{10})$$ $$122q + 4q^{4} + 6q^{9} - 6q^{15} + 4q^{16} + 2q^{21} - 8q^{22} + 10q^{36} - 12q^{37} - 6q^{39} + 12q^{49} - 22q^{52} - 22q^{57} + 6q^{60} - 11q^{63} - 4q^{64} - 4q^{67} - 22q^{73} - 22q^{79} + 6q^{81} - 21q^{84} - 16q^{88} + 4q^{91} - 2q^{93} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1407))$$

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
1407.1.b $$\chi_{1407}(736, \cdot)$$ None 0 1
1407.1.c $$\chi_{1407}(470, \cdot)$$ None 0 1
1407.1.f $$\chi_{1407}(202, \cdot)$$ None 0 1
1407.1.g $$\chi_{1407}(1406, \cdot)$$ 1407.1.g.a 1 1
1407.1.g.b 1
1407.1.g.c 1
1407.1.g.d 1
1407.1.g.e 1
1407.1.g.f 1
1407.1.g.g 2
1407.1.g.h 2
1407.1.g.i 2
1407.1.g.j 2
1407.1.o $$\chi_{1407}(431, \cdot)$$ 1407.1.o.a 2 2
1407.1.p $$\chi_{1407}(172, \cdot)$$ None 0 2
1407.1.q $$\chi_{1407}(440, \cdot)$$ None 0 2
1407.1.r $$\chi_{1407}(1042, \cdot)$$ None 0 2
1407.1.u $$\chi_{1407}(164, \cdot)$$ 1407.1.u.a 2 2
1407.1.v $$\chi_{1407}(565, \cdot)$$ None 0 2
1407.1.w $$\chi_{1407}(1006, \cdot)$$ None 0 2
1407.1.x $$\chi_{1407}(803, \cdot)$$ None 0 2
1407.1.z $$\chi_{1407}(29, \cdot)$$ None 0 2
1407.1.ba $$\chi_{1407}(1177, \cdot)$$ None 0 2
1407.1.bf $$\chi_{1407}(1138, \cdot)$$ None 0 2
1407.1.bg $$\chi_{1407}(872, \cdot)$$ None 0 2
1407.1.bh $$\chi_{1407}(305, \cdot)$$ 1407.1.bh.a 2 2
1407.1.bi $$\chi_{1407}(298, \cdot)$$ None 0 2
1407.1.bm $$\chi_{1407}(38, \cdot)$$ 1407.1.bm.a 2 2
1407.1.bn $$\chi_{1407}(439, \cdot)$$ None 0 2
1407.1.bq $$\chi_{1407}(125, \cdot)$$ 1407.1.bq.a 10 10
1407.1.bq.b 10
1407.1.br $$\chi_{1407}(76, \cdot)$$ None 0 10
1407.1.bu $$\chi_{1407}(92, \cdot)$$ None 0 10
1407.1.bv $$\chi_{1407}(43, \cdot)$$ None 0 10
1407.1.ca $$\chi_{1407}(19, \cdot)$$ None 0 20
1407.1.cb $$\chi_{1407}(101, \cdot)$$ 1407.1.cb.a 20 20
1407.1.cf $$\chi_{1407}(79, \cdot)$$ None 0 20
1407.1.cg $$\chi_{1407}(116, \cdot)$$ 1407.1.cg.a 20 20
1407.1.ch $$\chi_{1407}(107, \cdot)$$ None 0 20
1407.1.ci $$\chi_{1407}(58, \cdot)$$ None 0 20
1407.1.cn $$\chi_{1407}(85, \cdot)$$ None 0 20
1407.1.co $$\chi_{1407}(71, \cdot)$$ None 0 20
1407.1.cq $$\chi_{1407}(5, \cdot)$$ None 0 20
1407.1.cr $$\chi_{1407}(40, \cdot)$$ None 0 20
1407.1.cs $$\chi_{1407}(10, \cdot)$$ None 0 20
1407.1.ct $$\chi_{1407}(80, \cdot)$$ 1407.1.ct.a 20 20
1407.1.cw $$\chi_{1407}(55, \cdot)$$ None 0 20
1407.1.cx $$\chi_{1407}(20, \cdot)$$ None 0 20
1407.1.cy $$\chi_{1407}(46, \cdot)$$ None 0 20
1407.1.cz $$\chi_{1407}(23, \cdot)$$ 1407.1.cz.a 20 20

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1407))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1407)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(201))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(469))$$$$^{\oplus 2}$$