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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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

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