# Properties

 Label 1911.1 Level 1911 Weight 1 Dimension 229 Nonzero newspaces 20 Newform subspaces 39 Sturm bound 263424 Trace bound 37

## Defining parameters

 Level: $$N$$ = $$1911 = 3 \cdot 7^{2} \cdot 13$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$20$$ Newform subspaces: $$39$$ Sturm bound: $$263424$$ Trace bound: $$37$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1911))$$.

Total New Old
Modular forms 3180 1295 1885
Cusp forms 300 229 71
Eisenstein series 2880 1066 1814

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 213 16 0 0

## Trace form

 $$229 q + 3 q^{3} + 3 q^{4} + 4 q^{6} + 2 q^{7} + 7 q^{9} + O(q^{10})$$ $$229 q + 3 q^{3} + 3 q^{4} + 4 q^{6} + 2 q^{7} + 7 q^{9} + 2 q^{10} + 5 q^{12} + 11 q^{13} - 8 q^{15} + 7 q^{16} + 8 q^{19} + 2 q^{21} - 24 q^{22} - 2 q^{24} + 3 q^{25} + 3 q^{27} + 2 q^{28} + 4 q^{31} - 8 q^{34} + 33 q^{36} - 8 q^{37} - 2 q^{39} - 4 q^{40} - 34 q^{43} - 2 q^{46} - 11 q^{48} + 2 q^{49} - 4 q^{51} - 2 q^{52} + 2 q^{54} - 4 q^{57} - 2 q^{58} - 8 q^{61} - 12 q^{63} - 7 q^{64} + 8 q^{67} - 4 q^{69} - 12 q^{73} - 19 q^{75} - 16 q^{76} + 8 q^{78} + 10 q^{79} - 21 q^{81} + 2 q^{82} - 10 q^{84} - 8 q^{85} + 2 q^{87} - 8 q^{90} - 10 q^{91} - 16 q^{93} + 2 q^{94} + 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1911))$$

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
1911.1.b $$\chi_{1911}(638, \cdot)$$ None 0 1
1911.1.d $$\chi_{1911}(1273, \cdot)$$ None 0 1
1911.1.f $$\chi_{1911}(391, \cdot)$$ None 0 1
1911.1.h $$\chi_{1911}(1520, \cdot)$$ 1911.1.h.a 1 1
1911.1.h.b 2
1911.1.h.c 2
1911.1.h.d 4
1911.1.h.e 4
1911.1.m $$\chi_{1911}(148, \cdot)$$ None 0 2
1911.1.o $$\chi_{1911}(1175, \cdot)$$ None 0 2
1911.1.q $$\chi_{1911}(166, \cdot)$$ None 0 2
1911.1.s $$\chi_{1911}(1439, \cdot)$$ 1911.1.s.a 2 2
1911.1.s.b 4
1911.1.v $$\chi_{1911}(685, \cdot)$$ None 0 2
1911.1.w $$\chi_{1911}(116, \cdot)$$ 1911.1.w.a 2 2
1911.1.w.b 2
1911.1.w.c 4
1911.1.w.d 4
1911.1.w.e 8
1911.1.w.f 8
1911.1.x $$\chi_{1911}(998, \cdot)$$ 1911.1.x.a 2 2
1911.1.z $$\chi_{1911}(607, \cdot)$$ None 0 2
1911.1.bb $$\chi_{1911}(313, \cdot)$$ None 0 2
1911.1.bc $$\chi_{1911}(491, \cdot)$$ 1911.1.bc.a 2 2
1911.1.bc.b 2
1911.1.be $$\chi_{1911}(932, \cdot)$$ 1911.1.be.a 2 2
1911.1.be.b 2
1911.1.be.c 4
1911.1.be.d 4
1911.1.bg $$\chi_{1911}(901, \cdot)$$ None 0 2
1911.1.bi $$\chi_{1911}(766, \cdot)$$ None 0 2
1911.1.bk $$\chi_{1911}(716, \cdot)$$ None 0 2
1911.1.bm $$\chi_{1911}(263, \cdot)$$ 1911.1.bm.a 2 2
1911.1.bm.b 4
1911.1.bo $$\chi_{1911}(244, \cdot)$$ None 0 2
1911.1.bp $$\chi_{1911}(569, \cdot)$$ 1911.1.bp.a 2 2
1911.1.bq $$\chi_{1911}(178, \cdot)$$ None 0 2
1911.1.bt $$\chi_{1911}(227, \cdot)$$ 1911.1.bt.a 4 4
1911.1.bv $$\chi_{1911}(214, \cdot)$$ None 0 4
1911.1.by $$\chi_{1911}(67, \cdot)$$ None 0 4
1911.1.cb $$\chi_{1911}(293, \cdot)$$ 1911.1.cb.a 4 4
1911.1.cb.b 4
1911.1.cc $$\chi_{1911}(668, \cdot)$$ 1911.1.cc.a 4 4
1911.1.cc.b 4
1911.1.cf $$\chi_{1911}(1177, \cdot)$$ None 0 4
1911.1.cg $$\chi_{1911}(226, \cdot)$$ None 0 4
1911.1.ci $$\chi_{1911}(80, \cdot)$$ 1911.1.ci.a 4 4
1911.1.cj $$\chi_{1911}(155, \cdot)$$ 1911.1.cj.a 6 6
1911.1.cj.b 6
1911.1.cl $$\chi_{1911}(118, \cdot)$$ None 0 6
1911.1.cn $$\chi_{1911}(181, \cdot)$$ None 0 6
1911.1.cp $$\chi_{1911}(92, \cdot)$$ None 0 6
1911.1.cv $$\chi_{1911}(83, \cdot)$$ 1911.1.cv.a 12 12
1911.1.cv.b 12
1911.1.cx $$\chi_{1911}(190, \cdot)$$ None 0 12
1911.1.cz $$\chi_{1911}(250, \cdot)$$ None 0 12
1911.1.da $$\chi_{1911}(23, \cdot)$$ 1911.1.da.a 12 12
1911.1.db $$\chi_{1911}(160, \cdot)$$ None 0 12
1911.1.dd $$\chi_{1911}(191, \cdot)$$ 1911.1.dd.a 12 12
1911.1.df $$\chi_{1911}(53, \cdot)$$ None 0 12
1911.1.dh $$\chi_{1911}(103, \cdot)$$ None 0 12
1911.1.dj $$\chi_{1911}(10, \cdot)$$ None 0 12
1911.1.dl $$\chi_{1911}(29, \cdot)$$ None 0 12
1911.1.dn $$\chi_{1911}(134, \cdot)$$ None 0 12
1911.1.do $$\chi_{1911}(40, \cdot)$$ None 0 12
1911.1.dq $$\chi_{1911}(61, \cdot)$$ None 0 12
1911.1.ds $$\chi_{1911}(179, \cdot)$$ 1911.1.ds.a 12 12
1911.1.dt $$\chi_{1911}(233, \cdot)$$ None 0 12
1911.1.du $$\chi_{1911}(55, \cdot)$$ None 0 12
1911.1.dx $$\chi_{1911}(74, \cdot)$$ 1911.1.dx.a 12 12
1911.1.dz $$\chi_{1911}(199, \cdot)$$ None 0 12
1911.1.ea $$\chi_{1911}(110, \cdot)$$ 1911.1.ea.a 24 24
1911.1.ec $$\chi_{1911}(109, \cdot)$$ None 0 24
1911.1.ed $$\chi_{1911}(85, \cdot)$$ None 0 24
1911.1.eg $$\chi_{1911}(5, \cdot)$$ None 0 24
1911.1.eh $$\chi_{1911}(20, \cdot)$$ None 0 24
1911.1.ek $$\chi_{1911}(58, \cdot)$$ None 0 24
1911.1.en $$\chi_{1911}(37, \cdot)$$ None 0 24
1911.1.ep $$\chi_{1911}(59, \cdot)$$ 1911.1.ep.a 24 24

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1911))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1911)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(273))$$$$^{\oplus 2}$$