# Properties

 Label 1911.2 Level 1911 Weight 2 Dimension 92596 Nonzero newspaces 60 Sturm bound 526848 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$1911 = 3 \cdot 7^{2} \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$60$$ Sturm bound: $$526848$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1911))$$.

Total New Old
Modular forms 134592 94732 39860
Cusp forms 128833 92596 36237
Eisenstein series 5759 2136 3623

## Trace form

 $$92596 q - 6 q^{2} - 154 q^{3} - 294 q^{4} + 12 q^{5} - 126 q^{6} - 344 q^{7} + 60 q^{8} - 128 q^{9} + O(q^{10})$$ $$92596 q - 6 q^{2} - 154 q^{3} - 294 q^{4} + 12 q^{5} - 126 q^{6} - 344 q^{7} + 60 q^{8} - 128 q^{9} - 198 q^{10} + 60 q^{11} - 92 q^{12} - 292 q^{13} + 48 q^{14} - 252 q^{15} - 190 q^{16} + 30 q^{17} - 126 q^{18} - 232 q^{19} + 126 q^{20} - 166 q^{21} - 420 q^{22} + 72 q^{23} - 66 q^{24} - 164 q^{25} + 102 q^{26} - 280 q^{27} - 216 q^{28} + 114 q^{29} - 60 q^{30} - 176 q^{31} + 198 q^{32} - 90 q^{33} - 108 q^{34} + 84 q^{35} - 304 q^{36} - 310 q^{37} - 72 q^{38} - 216 q^{39} - 960 q^{40} - 114 q^{41} - 318 q^{42} - 536 q^{43} - 276 q^{44} - 228 q^{45} - 528 q^{46} - 432 q^{48} - 588 q^{49} - 48 q^{50} - 246 q^{51} - 402 q^{52} + 12 q^{53} - 102 q^{54} - 432 q^{55} - 300 q^{56} - 126 q^{57} - 318 q^{58} + 132 q^{59} - 186 q^{60} - 246 q^{61} + 300 q^{62} - 144 q^{63} - 336 q^{64} + 186 q^{65} - 246 q^{66} - 96 q^{67} + 366 q^{68} - 90 q^{69} - 132 q^{70} + 120 q^{71} - 108 q^{72} - 268 q^{73} - 30 q^{74} - 308 q^{75} - 664 q^{76} - 72 q^{77} - 687 q^{78} - 1012 q^{79} - 918 q^{80} - 404 q^{81} - 1434 q^{82} - 564 q^{83} - 880 q^{84} - 1350 q^{85} - 828 q^{86} - 852 q^{87} - 2328 q^{88} - 732 q^{89} - 1260 q^{90} - 766 q^{91} - 1236 q^{92} - 930 q^{93} - 1932 q^{94} - 864 q^{95} - 1386 q^{96} - 1220 q^{97} - 1164 q^{98} - 696 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1911))$$

We only show spaces with even 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
1911.2.a $$\chi_{1911}(1, \cdot)$$ 1911.2.a.a 1 1
1911.2.a.b 1
1911.2.a.c 1
1911.2.a.d 1
1911.2.a.e 1
1911.2.a.f 1
1911.2.a.g 1
1911.2.a.h 2
1911.2.a.i 2
1911.2.a.j 2
1911.2.a.k 2
1911.2.a.l 3
1911.2.a.m 3
1911.2.a.n 3
1911.2.a.o 3
1911.2.a.p 3
1911.2.a.q 4
1911.2.a.r 4
1911.2.a.s 4
1911.2.a.t 5
1911.2.a.u 5
1911.2.a.v 5
1911.2.a.w 5
1911.2.a.x 10
1911.2.a.y 10
1911.2.c $$\chi_{1911}(883, \cdot)$$ 1911.2.c.a 2 1
1911.2.c.b 2
1911.2.c.c 2
1911.2.c.d 2
1911.2.c.e 2
1911.2.c.f 2
1911.2.c.g 6
1911.2.c.h 6
1911.2.c.i 6
1911.2.c.j 8
1911.2.c.k 8
1911.2.c.l 8
1911.2.c.m 8
1911.2.c.n 8
1911.2.c.o 12
1911.2.c.p 12
1911.2.e $$\chi_{1911}(1028, \cdot)$$ n/a 160 1
1911.2.g $$\chi_{1911}(1910, \cdot)$$ n/a 180 1
1911.2.i $$\chi_{1911}(79, \cdot)$$ n/a 160 2
1911.2.j $$\chi_{1911}(373, \cdot)$$ n/a 186 2
1911.2.k $$\chi_{1911}(295, \cdot)$$ n/a 194 2
1911.2.l $$\chi_{1911}(802, \cdot)$$ n/a 186 2
1911.2.n $$\chi_{1911}(785, \cdot)$$ n/a 364 2
1911.2.p $$\chi_{1911}(538, \cdot)$$ n/a 184 2
1911.2.r $$\chi_{1911}(68, \cdot)$$ n/a 358 2
1911.2.t $$\chi_{1911}(1096, \cdot)$$ n/a 186 2
1911.2.u $$\chi_{1911}(881, \cdot)$$ n/a 356 2
1911.2.y $$\chi_{1911}(374, \cdot)$$ n/a 358 2
1911.2.ba $$\chi_{1911}(1403, \cdot)$$ n/a 356 2
1911.2.bd $$\chi_{1911}(589, \cdot)$$ n/a 190 2
1911.2.bf $$\chi_{1911}(1244, \cdot)$$ n/a 358 2
1911.2.bh $$\chi_{1911}(521, \cdot)$$ n/a 320 2
1911.2.bj $$\chi_{1911}(961, \cdot)$$ n/a 188 2
1911.2.bl $$\chi_{1911}(361, \cdot)$$ n/a 186 2
1911.2.bn $$\chi_{1911}(146, \cdot)$$ n/a 356 2
1911.2.br $$\chi_{1911}(803, \cdot)$$ n/a 358 2
1911.2.bs $$\chi_{1911}(274, \cdot)$$ n/a 672 6
1911.2.bu $$\chi_{1911}(1060, \cdot)$$ n/a 372 4
1911.2.bw $$\chi_{1911}(128, \cdot)$$ n/a 716 4
1911.2.bx $$\chi_{1911}(422, \cdot)$$ n/a 716 4
1911.2.bz $$\chi_{1911}(97, \cdot)$$ n/a 376 4
1911.2.ca $$\chi_{1911}(31, \cdot)$$ n/a 376 4
1911.2.cd $$\chi_{1911}(50, \cdot)$$ n/a 724 4
1911.2.ce $$\chi_{1911}(863, \cdot)$$ n/a 712 4
1911.2.ch $$\chi_{1911}(19, \cdot)$$ n/a 372 4
1911.2.ck $$\chi_{1911}(272, \cdot)$$ n/a 1536 6
1911.2.cm $$\chi_{1911}(209, \cdot)$$ n/a 1344 6
1911.2.co $$\chi_{1911}(64, \cdot)$$ n/a 792 6
1911.2.cq $$\chi_{1911}(16, \cdot)$$ n/a 1572 12
1911.2.cr $$\chi_{1911}(22, \cdot)$$ n/a 1560 12
1911.2.cs $$\chi_{1911}(100, \cdot)$$ n/a 1572 12
1911.2.ct $$\chi_{1911}(235, \cdot)$$ n/a 1344 12
1911.2.cu $$\chi_{1911}(34, \cdot)$$ n/a 1584 12
1911.2.cw $$\chi_{1911}(8, \cdot)$$ n/a 3072 12
1911.2.cy $$\chi_{1911}(17, \cdot)$$ n/a 3084 12
1911.2.dc $$\chi_{1911}(230, \cdot)$$ n/a 3096 12
1911.2.de $$\chi_{1911}(88, \cdot)$$ n/a 1572 12
1911.2.dg $$\chi_{1911}(25, \cdot)$$ n/a 1560 12
1911.2.di $$\chi_{1911}(131, \cdot)$$ n/a 2688 12
1911.2.dk $$\chi_{1911}(152, \cdot)$$ n/a 3084 12
1911.2.dm $$\chi_{1911}(43, \cdot)$$ n/a 1560 12
1911.2.dp $$\chi_{1911}(38, \cdot)$$ n/a 3096 12
1911.2.dr $$\chi_{1911}(101, \cdot)$$ n/a 3084 12
1911.2.dv $$\chi_{1911}(62, \cdot)$$ n/a 3096 12
1911.2.dw $$\chi_{1911}(4, \cdot)$$ n/a 1572 12
1911.2.dy $$\chi_{1911}(269, \cdot)$$ n/a 3084 12
1911.2.eb $$\chi_{1911}(115, \cdot)$$ n/a 3144 24
1911.2.ee $$\chi_{1911}(44, \cdot)$$ n/a 6192 24
1911.2.ef $$\chi_{1911}(71, \cdot)$$ n/a 6192 24
1911.2.ei $$\chi_{1911}(73, \cdot)$$ n/a 3120 24
1911.2.ej $$\chi_{1911}(76, \cdot)$$ n/a 3120 24
1911.2.el $$\chi_{1911}(11, \cdot)$$ n/a 6168 24
1911.2.em $$\chi_{1911}(2, \cdot)$$ n/a 6168 24
1911.2.eo $$\chi_{1911}(136, \cdot)$$ n/a 3144 24

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1911))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1911)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(273))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(637))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1911))$$$$^{\oplus 1}$$