# Properties

 Label 3920.1 Level 3920 Weight 1 Dimension 119 Nonzero newspaces 9 Newform subspaces 21 Sturm bound 903168 Trace bound 15

## Defining parameters

 Level: $$N$$ = $$3920 = 2^{4} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$9$$ Newform subspaces: $$21$$ Sturm bound: $$903168$$ Trace bound: $$15$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(3920))$$.

Total New Old
Modular forms 7496 1429 6067
Cusp forms 776 119 657
Eisenstein series 6720 1310 5410

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 95 0 24 0

## Trace form

 $$119 q - q^{5} + 11 q^{9} + O(q^{10})$$ $$119 q - q^{5} + 11 q^{9} - 2 q^{11} - 8 q^{15} + 6 q^{21} - q^{25} - 2 q^{29} + 2 q^{39} - 2 q^{41} + 24 q^{43} - 11 q^{45} + 2 q^{51} - 24 q^{57} + 10 q^{61} + 2 q^{65} - 24 q^{69} - 8 q^{71} - 2 q^{79} + 3 q^{81} - 16 q^{85} - 10 q^{89} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(3920))$$

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
3920.1.c $$\chi_{3920}(489, \cdot)$$ None 0 1
3920.1.d $$\chi_{3920}(1471, \cdot)$$ None 0 1
3920.1.f $$\chi_{3920}(881, \cdot)$$ None 0 1
3920.1.i $$\chi_{3920}(1079, \cdot)$$ None 0 1
3920.1.j $$\chi_{3920}(3039, \cdot)$$ 3920.1.j.a 1 1
3920.1.j.b 2
3920.1.j.c 2
3920.1.j.d 2
3920.1.j.e 4
3920.1.m $$\chi_{3920}(2841, \cdot)$$ None 0 1
3920.1.o $$\chi_{3920}(3431, \cdot)$$ None 0 1
3920.1.p $$\chi_{3920}(2449, \cdot)$$ None 0 1
3920.1.s $$\chi_{3920}(197, \cdot)$$ None 0 2
3920.1.u $$\chi_{3920}(587, \cdot)$$ None 0 2
3920.1.v $$\chi_{3920}(783, \cdot)$$ 3920.1.v.a 8 2
3920.1.y $$\chi_{3920}(393, \cdot)$$ None 0 2
3920.1.z $$\chi_{3920}(1861, \cdot)$$ None 0 2
3920.1.ba $$\chi_{3920}(99, \cdot)$$ None 0 2
3920.1.bf $$\chi_{3920}(1469, \cdot)$$ None 0 2
3920.1.bg $$\chi_{3920}(491, \cdot)$$ None 0 2
3920.1.bh $$\chi_{3920}(2353, \cdot)$$ 3920.1.bh.a 4 2
3920.1.bh.b 4
3920.1.bk $$\chi_{3920}(2743, \cdot)$$ None 0 2
3920.1.bm $$\chi_{3920}(2547, \cdot)$$ None 0 2
3920.1.bo $$\chi_{3920}(2157, \cdot)$$ None 0 2
3920.1.bp $$\chi_{3920}(471, \cdot)$$ None 0 2
3920.1.br $$\chi_{3920}(129, \cdot)$$ 3920.1.br.a 2 2
3920.1.br.b 2
3920.1.bt $$\chi_{3920}(79, \cdot)$$ 3920.1.bt.a 2 2
3920.1.bt.b 2
3920.1.bt.c 4
3920.1.bt.d 4
3920.1.bt.e 4
3920.1.bt.f 4
3920.1.bu $$\chi_{3920}(521, \cdot)$$ None 0 2
3920.1.bx $$\chi_{3920}(2481, \cdot)$$ None 0 2
3920.1.by $$\chi_{3920}(2039, \cdot)$$ None 0 2
3920.1.ca $$\chi_{3920}(2089, \cdot)$$ None 0 2
3920.1.cd $$\chi_{3920}(2431, \cdot)$$ None 0 2
3920.1.cf $$\chi_{3920}(227, \cdot)$$ None 0 4
3920.1.ch $$\chi_{3920}(373, \cdot)$$ None 0 4
3920.1.ck $$\chi_{3920}(423, \cdot)$$ None 0 4
3920.1.cl $$\chi_{3920}(177, \cdot)$$ 3920.1.cl.a 8 4
3920.1.cl.b 8
3920.1.cn $$\chi_{3920}(851, \cdot)$$ None 0 4
3920.1.co $$\chi_{3920}(509, \cdot)$$ None 0 4
3920.1.ct $$\chi_{3920}(459, \cdot)$$ None 0 4
3920.1.cu $$\chi_{3920}(901, \cdot)$$ None 0 4
3920.1.cw $$\chi_{3920}(1353, \cdot)$$ None 0 4
3920.1.cx $$\chi_{3920}(607, \cdot)$$ 3920.1.cx.a 16 4
3920.1.cz $$\chi_{3920}(1157, \cdot)$$ None 0 4
3920.1.db $$\chi_{3920}(803, \cdot)$$ None 0 4
3920.1.dd $$\chi_{3920}(209, \cdot)$$ None 0 6
3920.1.df $$\chi_{3920}(71, \cdot)$$ None 0 6
3920.1.dh $$\chi_{3920}(41, \cdot)$$ None 0 6
3920.1.di $$\chi_{3920}(239, \cdot)$$ 3920.1.di.a 12 6
3920.1.dl $$\chi_{3920}(519, \cdot)$$ None 0 6
3920.1.dm $$\chi_{3920}(321, \cdot)$$ None 0 6
3920.1.do $$\chi_{3920}(351, \cdot)$$ None 0 6
3920.1.dr $$\chi_{3920}(1049, \cdot)$$ None 0 6
3920.1.du $$\chi_{3920}(477, \cdot)$$ None 0 12
3920.1.dw $$\chi_{3920}(307, \cdot)$$ None 0 12
3920.1.dy $$\chi_{3920}(113, \cdot)$$ None 0 12
3920.1.dz $$\chi_{3920}(167, \cdot)$$ None 0 12
3920.1.eb $$\chi_{3920}(211, \cdot)$$ None 0 12
3920.1.ec $$\chi_{3920}(69, \cdot)$$ None 0 12
3920.1.eh $$\chi_{3920}(379, \cdot)$$ None 0 12
3920.1.ei $$\chi_{3920}(181, \cdot)$$ None 0 12
3920.1.ek $$\chi_{3920}(223, \cdot)$$ None 0 12
3920.1.el $$\chi_{3920}(57, \cdot)$$ None 0 12
3920.1.eo $$\chi_{3920}(27, \cdot)$$ None 0 12
3920.1.eq $$\chi_{3920}(253, \cdot)$$ None 0 12
3920.1.es $$\chi_{3920}(191, \cdot)$$ None 0 12
3920.1.et $$\chi_{3920}(89, \cdot)$$ None 0 12
3920.1.ev $$\chi_{3920}(39, \cdot)$$ None 0 12
3920.1.ey $$\chi_{3920}(241, \cdot)$$ None 0 12
3920.1.ez $$\chi_{3920}(201, \cdot)$$ None 0 12
3920.1.fc $$\chi_{3920}(319, \cdot)$$ 3920.1.fc.a 24 12
3920.1.fd $$\chi_{3920}(369, \cdot)$$ None 0 12
3920.1.fe $$\chi_{3920}(151, \cdot)$$ None 0 12
3920.1.fg $$\chi_{3920}(3, \cdot)$$ None 0 24
3920.1.fi $$\chi_{3920}(37, \cdot)$$ None 0 24
3920.1.fk $$\chi_{3920}(137, \cdot)$$ None 0 24
3920.1.fn $$\chi_{3920}(47, \cdot)$$ None 0 24
3920.1.fo $$\chi_{3920}(61, \cdot)$$ None 0 24
3920.1.fp $$\chi_{3920}(179, \cdot)$$ None 0 24
3920.1.fu $$\chi_{3920}(229, \cdot)$$ None 0 24
3920.1.fv $$\chi_{3920}(11, \cdot)$$ None 0 24
3920.1.fw $$\chi_{3920}(87, \cdot)$$ None 0 24
3920.1.fz $$\chi_{3920}(193, \cdot)$$ None 0 24
3920.1.ga $$\chi_{3920}(53, \cdot)$$ None 0 24
3920.1.gc $$\chi_{3920}(283, \cdot)$$ None 0 24

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(3920))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(3920)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(280))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(392))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(560))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(784))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(980))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1960))$$$$^{\oplus 2}$$