## Defining parameters

 Level: $$N$$ = $$936 = 2^{3} \cdot 3^{2} \cdot 13$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$7$$ Sturm bound: $$48384$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(936))$$.

Total New Old
Modular forms 1320 224 1096
Cusp forms 168 26 142
Eisenstein series 1152 198 954

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 18 0 8 0

## Trace form

 $$26q - 4q^{4} + 2q^{5} - 2q^{7} - 4q^{9} + O(q^{10})$$ $$26q - 4q^{4} + 2q^{5} - 2q^{7} - 4q^{9} - 6q^{10} - 2q^{11} - 2q^{13} + 2q^{14} - 2q^{15} - 8q^{16} + 2q^{17} - 4q^{19} + 4q^{21} - 4q^{22} - 2q^{25} + 10q^{26} - 6q^{27} + 12q^{30} - 2q^{31} + 4q^{33} - 14q^{35} + 2q^{39} + 2q^{40} - 6q^{42} + 6q^{43} - 4q^{45} + 4q^{47} - 10q^{49} - 6q^{51} - 4q^{52} + 2q^{56} + 2q^{57} + 2q^{59} - 4q^{61} - 16q^{62} - 2q^{63} + 14q^{64} + 4q^{65} + 2q^{68} + 4q^{73} + 2q^{74} + 12q^{75} - 4q^{81} + 4q^{82} - 2q^{85} - 4q^{88} - 4q^{89} - 6q^{90} + 2q^{91} + 2q^{93} + 2q^{94} - 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(936))$$

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
936.1.b $$\chi_{936}(701, \cdot)$$ None 0 1
936.1.e $$\chi_{936}(235, \cdot)$$ None 0 1
936.1.f $$\chi_{936}(521, \cdot)$$ None 0 1
936.1.i $$\chi_{936}(415, \cdot)$$ None 0 1
936.1.k $$\chi_{936}(703, \cdot)$$ None 0 1
936.1.l $$\chi_{936}(233, \cdot)$$ None 0 1
936.1.o $$\chi_{936}(883, \cdot)$$ 936.1.o.a 1 1
936.1.o.b 1
936.1.o.c 4
936.1.p $$\chi_{936}(53, \cdot)$$ None 0 1
936.1.u $$\chi_{936}(109, \cdot)$$ None 0 2
936.1.v $$\chi_{936}(73, \cdot)$$ None 0 2
936.1.y $$\chi_{936}(359, \cdot)$$ None 0 2
936.1.z $$\chi_{936}(395, \cdot)$$ None 0 2
936.1.bc $$\chi_{936}(127, \cdot)$$ None 0 2
936.1.bf $$\chi_{936}(737, \cdot)$$ None 0 2
936.1.bg $$\chi_{936}(451, \cdot)$$ None 0 2
936.1.bj $$\chi_{936}(413, \cdot)$$ None 0 2
936.1.bl $$\chi_{936}(257, \cdot)$$ None 0 2
936.1.bm $$\chi_{936}(295, \cdot)$$ None 0 2
936.1.bo $$\chi_{936}(355, \cdot)$$ None 0 2
936.1.bq $$\chi_{936}(365, \cdot)$$ None 0 2
936.1.bs $$\chi_{936}(259, \cdot)$$ 936.1.bs.a 6 2
936.1.bs.b 6
936.1.bt $$\chi_{936}(29, \cdot)$$ None 0 2
936.1.bu $$\chi_{936}(367, \cdot)$$ None 0 2
936.1.bw $$\chi_{936}(545, \cdot)$$ None 0 2
936.1.bz $$\chi_{936}(79, \cdot)$$ None 0 2
936.1.cb $$\chi_{936}(329, \cdot)$$ None 0 2
936.1.cc $$\chi_{936}(653, \cdot)$$ None 0 2
936.1.cd $$\chi_{936}(43, \cdot)$$ None 0 2
936.1.cf $$\chi_{936}(211, \cdot)$$ None 0 2
936.1.ci $$\chi_{936}(173, \cdot)$$ None 0 2
936.1.ck $$\chi_{936}(113, \cdot)$$ None 0 2
936.1.cm $$\chi_{936}(103, \cdot)$$ None 0 2
936.1.cn $$\chi_{936}(209, \cdot)$$ None 0 2
936.1.cp $$\chi_{936}(439, \cdot)$$ None 0 2
936.1.cs $$\chi_{936}(101, \cdot)$$ None 0 2
936.1.cu $$\chi_{936}(547, \cdot)$$ None 0 2
936.1.cv $$\chi_{936}(77, \cdot)$$ None 0 2
936.1.cx $$\chi_{936}(139, \cdot)$$ None 0 2
936.1.cz $$\chi_{936}(511, \cdot)$$ None 0 2
936.1.dc $$\chi_{936}(185, \cdot)$$ None 0 2
936.1.dd $$\chi_{936}(269, \cdot)$$ None 0 2
936.1.de $$\chi_{936}(595, \cdot)$$ None 0 2
936.1.dh $$\chi_{936}(17, \cdot)$$ None 0 2
936.1.di $$\chi_{936}(55, \cdot)$$ None 0 2
936.1.dm $$\chi_{936}(265, \cdot)$$ 936.1.dm.a 4 4
936.1.dm.b 4
936.1.dn $$\chi_{936}(229, \cdot)$$ None 0 4
936.1.do $$\chi_{936}(227, \cdot)$$ None 0 4
936.1.dp $$\chi_{936}(167, \cdot)$$ None 0 4
936.1.du $$\chi_{936}(323, \cdot)$$ None 0 4
936.1.dv $$\chi_{936}(71, \cdot)$$ None 0 4
936.1.dw $$\chi_{936}(119, \cdot)$$ None 0 4
936.1.dx $$\chi_{936}(11, \cdot)$$ None 0 4
936.1.ea $$\chi_{936}(97, \cdot)$$ None 0 4
936.1.eb $$\chi_{936}(301, \cdot)$$ None 0 4
936.1.eg $$\chi_{936}(145, \cdot)$$ None 0 4
936.1.eh $$\chi_{936}(37, \cdot)$$ None 0 4
936.1.ei $$\chi_{936}(85, \cdot)$$ None 0 4
936.1.ej $$\chi_{936}(409, \cdot)$$ None 0 4
936.1.eo $$\chi_{936}(83, \cdot)$$ None 0 4
936.1.ep $$\chi_{936}(47, \cdot)$$ None 0 4

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(936))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(936)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(468))$$$$^{\oplus 2}$$