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Properties

Label 1911.4
Level 1911
Weight 4
Dimension 279930
Nonzero newspaces 60
Sturm bound 1053696
Trace bound 12

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Defining parameters

Level: \( N \) = \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(1053696\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1911))\).

Total New Old
Modular forms 398016 282066 115950
Cusp forms 392256 279930 112326
Eisenstein series 5760 2136 3624

Trace form

\( 279930 q - 132 q^{3} - 312 q^{4} - 96 q^{5} - 288 q^{6} - 456 q^{7} + 360 q^{8} + 12 q^{9} + O(q^{10}) \) \( 279930 q - 132 q^{3} - 312 q^{4} - 96 q^{5} - 288 q^{6} - 456 q^{7} + 360 q^{8} + 12 q^{9} - 276 q^{10} - 120 q^{11} - 762 q^{12} - 786 q^{13} - 624 q^{14} - 1116 q^{15} - 792 q^{16} + 330 q^{17} + 1602 q^{18} + 2832 q^{19} + 5208 q^{20} + 996 q^{21} + 444 q^{22} - 1128 q^{23} - 720 q^{24} - 2730 q^{25} - 2088 q^{26} - 1590 q^{27} - 2568 q^{28} - 2982 q^{29} - 7320 q^{30} - 3168 q^{31} - 3852 q^{32} - 2460 q^{33} + 864 q^{34} + 168 q^{35} + 3846 q^{36} - 3366 q^{37} - 3576 q^{38} + 1953 q^{39} - 3204 q^{40} + 1902 q^{41} + 5478 q^{42} + 8472 q^{43} + 23148 q^{44} + 11202 q^{45} + 21192 q^{46} + 9408 q^{47} + 7014 q^{48} + 11088 q^{49} - 1992 q^{50} - 7806 q^{51} - 246 q^{52} - 5592 q^{53} - 15072 q^{54} - 4656 q^{55} - 2652 q^{56} - 4032 q^{57} - 2340 q^{58} - 12744 q^{59} - 11730 q^{60} - 6642 q^{61} - 15900 q^{62} + 2124 q^{63} - 12 q^{64} + 3438 q^{65} + 738 q^{66} + 3624 q^{67} - 10824 q^{68} - 8436 q^{69} - 7356 q^{70} - 2496 q^{71} - 13254 q^{72} - 26808 q^{73} - 57564 q^{74} - 26658 q^{75} - 102144 q^{76} - 20232 q^{77} - 7569 q^{78} - 21372 q^{79} - 54012 q^{80} - 7980 q^{81} - 9936 q^{82} - 7704 q^{83} - 7404 q^{84} + 50166 q^{85} + 46788 q^{86} + 38460 q^{87} + 140208 q^{88} + 55560 q^{89} + 51948 q^{90} + 37734 q^{91} + 115596 q^{92} + 54792 q^{93} + 167700 q^{94} + 99768 q^{95} + 91824 q^{96} + 63876 q^{97} + 111900 q^{98} + 2286 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1911))\)

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
1911.4.a \(\chi_{1911}(1, \cdot)\) 1911.4.a.a 1 1
1911.4.a.b 1
1911.4.a.c 1
1911.4.a.d 1
1911.4.a.e 1
1911.4.a.f 1
1911.4.a.g 2
1911.4.a.h 2
1911.4.a.i 3
1911.4.a.j 3
1911.4.a.k 3
1911.4.a.l 4
1911.4.a.m 4
1911.4.a.n 5
1911.4.a.o 6
1911.4.a.p 6
1911.4.a.q 6
1911.4.a.r 7
1911.4.a.s 7
1911.4.a.t 7
1911.4.a.u 7
1911.4.a.v 11
1911.4.a.w 11
1911.4.a.x 11
1911.4.a.y 11
1911.4.a.z 13
1911.4.a.ba 13
1911.4.a.bb 13
1911.4.a.bc 13
1911.4.a.bd 14
1911.4.a.be 14
1911.4.a.bf 22
1911.4.a.bg 22
1911.4.c \(\chi_{1911}(883, \cdot)\) n/a 288 1
1911.4.e \(\chi_{1911}(1028, \cdot)\) n/a 480 1
1911.4.g \(\chi_{1911}(1910, \cdot)\) n/a 552 1
1911.4.i \(\chi_{1911}(79, \cdot)\) n/a 480 2
1911.4.j \(\chi_{1911}(373, \cdot)\) n/a 560 2
1911.4.k \(\chi_{1911}(295, \cdot)\) n/a 572 2
1911.4.l \(\chi_{1911}(802, \cdot)\) n/a 560 2
1911.4.n \(\chi_{1911}(785, \cdot)\) n/a 1128 2
1911.4.p \(\chi_{1911}(538, \cdot)\) n/a 560 2
1911.4.r \(\chi_{1911}(68, \cdot)\) n/a 1104 2
1911.4.t \(\chi_{1911}(1096, \cdot)\) n/a 560 2
1911.4.u \(\chi_{1911}(881, \cdot)\) n/a 1104 2
1911.4.y \(\chi_{1911}(374, \cdot)\) n/a 1104 2
1911.4.ba \(\chi_{1911}(1403, \cdot)\) n/a 1104 2
1911.4.bd \(\chi_{1911}(589, \cdot)\) n/a 576 2
1911.4.bf \(\chi_{1911}(1244, \cdot)\) n/a 1104 2
1911.4.bh \(\chi_{1911}(521, \cdot)\) n/a 960 2
1911.4.bj \(\chi_{1911}(961, \cdot)\) n/a 560 2
1911.4.bl \(\chi_{1911}(361, \cdot)\) n/a 560 2
1911.4.bn \(\chi_{1911}(146, \cdot)\) n/a 1104 2
1911.4.br \(\chi_{1911}(803, \cdot)\) n/a 1104 2
1911.4.bs \(\chi_{1911}(274, \cdot)\) n/a 2016 6
1911.4.bu \(\chi_{1911}(1060, \cdot)\) n/a 1120 4
1911.4.bw \(\chi_{1911}(128, \cdot)\) n/a 2208 4
1911.4.bx \(\chi_{1911}(422, \cdot)\) n/a 2208 4
1911.4.bz \(\chi_{1911}(97, \cdot)\) n/a 1120 4
1911.4.ca \(\chi_{1911}(31, \cdot)\) n/a 1120 4
1911.4.cd \(\chi_{1911}(50, \cdot)\) n/a 2256 4
1911.4.ce \(\chi_{1911}(863, \cdot)\) n/a 2208 4
1911.4.ch \(\chi_{1911}(19, \cdot)\) n/a 1120 4
1911.4.ck \(\chi_{1911}(272, \cdot)\) n/a 4680 6
1911.4.cm \(\chi_{1911}(209, \cdot)\) n/a 4032 6
1911.4.co \(\chi_{1911}(64, \cdot)\) n/a 2352 6
1911.4.cq \(\chi_{1911}(16, \cdot)\) n/a 4704 12
1911.4.cr \(\chi_{1911}(22, \cdot)\) n/a 4704 12
1911.4.cs \(\chi_{1911}(100, \cdot)\) n/a 4704 12
1911.4.ct \(\chi_{1911}(235, \cdot)\) n/a 4032 12
1911.4.cu \(\chi_{1911}(34, \cdot)\) n/a 4704 12
1911.4.cw \(\chi_{1911}(8, \cdot)\) n/a 9360 12
1911.4.cy \(\chi_{1911}(17, \cdot)\) n/a 9360 12
1911.4.dc \(\chi_{1911}(230, \cdot)\) n/a 9360 12
1911.4.de \(\chi_{1911}(88, \cdot)\) n/a 4704 12
1911.4.dg \(\chi_{1911}(25, \cdot)\) n/a 4704 12
1911.4.di \(\chi_{1911}(131, \cdot)\) n/a 8064 12
1911.4.dk \(\chi_{1911}(152, \cdot)\) n/a 9360 12
1911.4.dm \(\chi_{1911}(43, \cdot)\) n/a 4704 12
1911.4.dp \(\chi_{1911}(38, \cdot)\) n/a 9360 12
1911.4.dr \(\chi_{1911}(101, \cdot)\) n/a 9360 12
1911.4.dv \(\chi_{1911}(62, \cdot)\) n/a 9360 12
1911.4.dw \(\chi_{1911}(4, \cdot)\) n/a 4704 12
1911.4.dy \(\chi_{1911}(269, \cdot)\) n/a 9360 12
1911.4.eb \(\chi_{1911}(115, \cdot)\) n/a 9408 24
1911.4.ee \(\chi_{1911}(44, \cdot)\) n/a 18720 24
1911.4.ef \(\chi_{1911}(71, \cdot)\) n/a 18720 24
1911.4.ei \(\chi_{1911}(73, \cdot)\) n/a 9408 24
1911.4.ej \(\chi_{1911}(76, \cdot)\) n/a 9408 24
1911.4.el \(\chi_{1911}(11, \cdot)\) n/a 18720 24
1911.4.em \(\chi_{1911}(2, \cdot)\) n/a 18720 24
1911.4.eo \(\chi_{1911}(136, \cdot)\) n/a 9408 24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1911))\) into lower level spaces

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