Properties

Label 1968.2
Level 1968
Weight 2
Dimension 44954
Nonzero newspaces 40
Sturm bound 430080
Trace bound 21

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1968 = 2^{4} \cdot 3 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(430080\)
Trace bound: \(21\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1968))\).

Total New Old
Modular forms 109760 45658 64102
Cusp forms 105281 44954 60327
Eisenstein series 4479 704 3775

Trace form

\( 44954 q - 58 q^{3} - 144 q^{4} + 4 q^{5} - 64 q^{6} - 104 q^{7} + 24 q^{8} - 10 q^{9} + O(q^{10}) \) \( 44954 q - 58 q^{3} - 144 q^{4} + 4 q^{5} - 64 q^{6} - 104 q^{7} + 24 q^{8} - 10 q^{9} - 144 q^{10} + 24 q^{11} - 80 q^{12} - 180 q^{13} - 24 q^{14} - 40 q^{15} - 192 q^{16} - 4 q^{17} - 96 q^{18} - 88 q^{19} - 32 q^{20} - 108 q^{21} - 192 q^{22} - 16 q^{23} - 136 q^{24} - 58 q^{25} - 40 q^{26} - 82 q^{27} - 160 q^{28} + 20 q^{29} - 120 q^{30} - 152 q^{31} - 164 q^{33} - 144 q^{34} - 48 q^{35} - 112 q^{36} - 132 q^{37} + 16 q^{38} - 96 q^{39} - 112 q^{40} + 6 q^{41} - 72 q^{42} - 120 q^{43} + 80 q^{44} - 72 q^{45} - 64 q^{46} + 48 q^{48} - 270 q^{49} + 72 q^{50} - 128 q^{51} - 96 q^{52} - 28 q^{53} + 16 q^{54} - 184 q^{55} - 4 q^{57} - 192 q^{58} - 56 q^{59} - 96 q^{60} - 308 q^{61} + 24 q^{62} - 76 q^{63} - 288 q^{64} + 24 q^{65} - 184 q^{66} - 152 q^{67} - 64 q^{68} - 156 q^{69} - 304 q^{70} + 16 q^{71} - 152 q^{72} - 100 q^{73} - 104 q^{74} - 22 q^{75} - 288 q^{76} - 32 q^{77} - 176 q^{78} - 88 q^{79} - 16 q^{80} - 174 q^{81} - 184 q^{82} + 72 q^{83} - 64 q^{84} - 224 q^{85} + 32 q^{86} + 48 q^{87} - 96 q^{88} + 12 q^{89} - 32 q^{90} + 8 q^{91} + 32 q^{92} - 68 q^{93} - 80 q^{94} + 112 q^{95} + 32 q^{96} - 292 q^{97} + 80 q^{98} + 68 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1968))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1968.2.a \(\chi_{1968}(1, \cdot)\) 1968.2.a.a 1 1
1968.2.a.b 1
1968.2.a.c 1
1968.2.a.d 1
1968.2.a.e 1
1968.2.a.f 1
1968.2.a.g 1
1968.2.a.h 1
1968.2.a.i 1
1968.2.a.j 1
1968.2.a.k 1
1968.2.a.l 1
1968.2.a.m 1
1968.2.a.n 1
1968.2.a.o 1
1968.2.a.p 2
1968.2.a.q 2
1968.2.a.r 2
1968.2.a.s 2
1968.2.a.t 3
1968.2.a.u 3
1968.2.a.v 3
1968.2.a.w 3
1968.2.a.x 5
1968.2.d \(\chi_{1968}(575, \cdot)\) 1968.2.d.a 4 1
1968.2.d.b 28
1968.2.d.c 48
1968.2.e \(\chi_{1968}(409, \cdot)\) None 0 1
1968.2.f \(\chi_{1968}(985, \cdot)\) None 0 1
1968.2.g \(\chi_{1968}(1967, \cdot)\) 1968.2.g.a 4 1
1968.2.g.b 4
1968.2.g.c 4
1968.2.g.d 8
1968.2.g.e 16
1968.2.g.f 16
1968.2.g.g 32
1968.2.j \(\chi_{1968}(1393, \cdot)\) 1968.2.j.a 2 1
1968.2.j.b 2
1968.2.j.c 4
1968.2.j.d 6
1968.2.j.e 8
1968.2.j.f 8
1968.2.j.g 12
1968.2.k \(\chi_{1968}(1559, \cdot)\) None 0 1
1968.2.p \(\chi_{1968}(983, \cdot)\) None 0 1
1968.2.s \(\chi_{1968}(647, \cdot)\) None 0 2
1968.2.t \(\chi_{1968}(337, \cdot)\) 1968.2.t.a 4 2
1968.2.t.b 8
1968.2.t.c 8
1968.2.t.d 12
1968.2.t.e 16
1968.2.t.f 16
1968.2.t.g 20
1968.2.w \(\chi_{1968}(491, \cdot)\) n/a 664 2
1968.2.x \(\chi_{1968}(493, \cdot)\) n/a 320 2
1968.2.ba \(\chi_{1968}(1549, \cdot)\) n/a 336 2
1968.2.bb \(\chi_{1968}(1139, \cdot)\) n/a 664 2
1968.2.bc \(\chi_{1968}(155, \cdot)\) n/a 664 2
1968.2.bd \(\chi_{1968}(565, \cdot)\) n/a 336 2
1968.2.bg \(\chi_{1968}(83, \cdot)\) n/a 640 2
1968.2.bh \(\chi_{1968}(901, \cdot)\) n/a 336 2
1968.2.bm \(\chi_{1968}(911, \cdot)\) n/a 168 2
1968.2.bn \(\chi_{1968}(73, \cdot)\) None 0 2
1968.2.bo \(\chi_{1968}(385, \cdot)\) n/a 168 4
1968.2.bp \(\chi_{1968}(413, \cdot)\) n/a 1328 4
1968.2.bq \(\chi_{1968}(331, \cdot)\) n/a 672 4
1968.2.bx \(\chi_{1968}(137, \cdot)\) None 0 4
1968.2.by \(\chi_{1968}(161, \cdot)\) n/a 328 4
1968.2.bz \(\chi_{1968}(55, \cdot)\) None 0 4
1968.2.ca \(\chi_{1968}(79, \cdot)\) n/a 168 4
1968.2.cb \(\chi_{1968}(1397, \cdot)\) n/a 1328 4
1968.2.cc \(\chi_{1968}(1315, \cdot)\) n/a 672 4
1968.2.cf \(\chi_{1968}(23, \cdot)\) None 0 4
1968.2.ck \(\chi_{1968}(119, \cdot)\) None 0 4
1968.2.cl \(\chi_{1968}(433, \cdot)\) n/a 168 4
1968.2.co \(\chi_{1968}(1007, \cdot)\) n/a 336 4
1968.2.cp \(\chi_{1968}(1369, \cdot)\) None 0 4
1968.2.cq \(\chi_{1968}(25, \cdot)\) None 0 4
1968.2.cr \(\chi_{1968}(959, \cdot)\) n/a 336 4
1968.2.cu \(\chi_{1968}(121, \cdot)\) None 0 8
1968.2.cv \(\chi_{1968}(143, \cdot)\) n/a 672 8
1968.2.da \(\chi_{1968}(277, \cdot)\) n/a 1344 8
1968.2.db \(\chi_{1968}(59, \cdot)\) n/a 2656 8
1968.2.de \(\chi_{1968}(349, \cdot)\) n/a 1344 8
1968.2.df \(\chi_{1968}(131, \cdot)\) n/a 2656 8
1968.2.dg \(\chi_{1968}(203, \cdot)\) n/a 2656 8
1968.2.dh \(\chi_{1968}(61, \cdot)\) n/a 1344 8
1968.2.dk \(\chi_{1968}(37, \cdot)\) n/a 1344 8
1968.2.dl \(\chi_{1968}(107, \cdot)\) n/a 2656 8
1968.2.do \(\chi_{1968}(49, \cdot)\) n/a 336 8
1968.2.dp \(\chi_{1968}(695, \cdot)\) None 0 8
1968.2.du \(\chi_{1968}(259, \cdot)\) n/a 2688 16
1968.2.dv \(\chi_{1968}(53, \cdot)\) n/a 5312 16
1968.2.dw \(\chi_{1968}(175, \cdot)\) n/a 672 16
1968.2.dx \(\chi_{1968}(7, \cdot)\) None 0 16
1968.2.dy \(\chi_{1968}(17, \cdot)\) n/a 1312 16
1968.2.dz \(\chi_{1968}(89, \cdot)\) None 0 16
1968.2.eg \(\chi_{1968}(19, \cdot)\) n/a 2688 16
1968.2.eh \(\chi_{1968}(29, \cdot)\) n/a 5312 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1968))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1968)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(246))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(492))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(656))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(984))\)\(^{\oplus 2}\)