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Properties

Label 1197.4
Level 1197
Weight 4
Dimension 116570
Nonzero newspaces 92
Sturm bound 414720
Trace bound 19

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Defining parameters

Level: \( N \) = \( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 92 \)
Sturm bound: \(414720\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1197))\).

Total New Old
Modular forms 157248 118102 39146
Cusp forms 153792 116570 37222
Eisenstein series 3456 1532 1924

Trace form

\( 116570 q - 102 q^{2} - 132 q^{3} - 142 q^{4} - 174 q^{5} - 84 q^{6} - 139 q^{7} + 84 q^{8} + 60 q^{9} + O(q^{10}) \) \( 116570 q - 102 q^{2} - 132 q^{3} - 142 q^{4} - 174 q^{5} - 84 q^{6} - 139 q^{7} + 84 q^{8} + 60 q^{9} - 168 q^{10} - 354 q^{11} - 840 q^{12} - 332 q^{13} - 1305 q^{14} - 444 q^{15} - 790 q^{16} + 834 q^{17} + 1416 q^{18} - 589 q^{19} + 1884 q^{20} + 606 q^{21} + 1314 q^{22} + 402 q^{23} + 60 q^{24} + 338 q^{25} - 1992 q^{26} - 2640 q^{27} - 976 q^{28} - 1290 q^{29} - 2148 q^{30} - 2618 q^{31} - 5808 q^{32} - 816 q^{33} - 5418 q^{34} - 1245 q^{35} - 180 q^{36} + 1396 q^{37} - 174 q^{38} + 5292 q^{39} + 3438 q^{40} + 4560 q^{41} + 4284 q^{42} - 1466 q^{43} - 8718 q^{44} - 8244 q^{45} - 6402 q^{46} - 3306 q^{47} + 828 q^{48} - 721 q^{49} + 11886 q^{50} + 7260 q^{51} + 6208 q^{52} + 3714 q^{53} + 9984 q^{54} + 10320 q^{55} + 8784 q^{56} + 5766 q^{57} + 16752 q^{58} + 5382 q^{59} + 1524 q^{60} + 20422 q^{61} + 11778 q^{62} - 8358 q^{63} + 3932 q^{64} - 10092 q^{65} - 26388 q^{66} - 16646 q^{67} - 56706 q^{68} - 18900 q^{69} - 36759 q^{70} - 28482 q^{71} - 16176 q^{72} - 22100 q^{73} - 11232 q^{74} + 11292 q^{75} - 12730 q^{76} + 12084 q^{77} + 21720 q^{78} + 10150 q^{79} + 37272 q^{80} + 10548 q^{81} + 34698 q^{82} + 19452 q^{83} + 16464 q^{84} + 21438 q^{85} + 24006 q^{86} + 2220 q^{87} - 9780 q^{88} + 4206 q^{89} - 8472 q^{90} - 1577 q^{91} - 4908 q^{92} - 4332 q^{93} - 47418 q^{94} - 57987 q^{95} - 58512 q^{96} - 55028 q^{97} - 67284 q^{98} - 31536 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1197))\)

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
1197.4.a \(\chi_{1197}(1, \cdot)\) 1197.4.a.a 1 1
1197.4.a.b 1
1197.4.a.c 1
1197.4.a.d 1
1197.4.a.e 1
1197.4.a.f 2
1197.4.a.g 4
1197.4.a.h 5
1197.4.a.i 6
1197.4.a.j 6
1197.4.a.k 6
1197.4.a.l 7
1197.4.a.m 7
1197.4.a.n 8
1197.4.a.o 8
1197.4.a.p 9
1197.4.a.q 9
1197.4.a.r 12
1197.4.a.s 12
1197.4.a.t 14
1197.4.a.u 16
1197.4.c \(\chi_{1197}(1063, \cdot)\) n/a 198 1
1197.4.d \(\chi_{1197}(818, \cdot)\) n/a 144 1
1197.4.f \(\chi_{1197}(512, \cdot)\) n/a 120 1
1197.4.i \(\chi_{1197}(163, \cdot)\) n/a 396 2
1197.4.j \(\chi_{1197}(172, \cdot)\) n/a 360 2
1197.4.k \(\chi_{1197}(64, \cdot)\) n/a 300 2
1197.4.l \(\chi_{1197}(121, \cdot)\) n/a 952 2
1197.4.m \(\chi_{1197}(400, \cdot)\) n/a 648 2
1197.4.n \(\chi_{1197}(520, \cdot)\) n/a 952 2
1197.4.o \(\chi_{1197}(106, \cdot)\) n/a 720 2
1197.4.p \(\chi_{1197}(562, \cdot)\) n/a 952 2
1197.4.q \(\chi_{1197}(457, \cdot)\) n/a 864 2
1197.4.r \(\chi_{1197}(58, \cdot)\) n/a 864 2
1197.4.s \(\chi_{1197}(862, \cdot)\) n/a 720 2
1197.4.t \(\chi_{1197}(634, \cdot)\) n/a 952 2
1197.4.u \(\chi_{1197}(676, \cdot)\) n/a 396 2
1197.4.v \(\chi_{1197}(145, \cdot)\) n/a 396 2
1197.4.x \(\chi_{1197}(311, \cdot)\) n/a 952 2
1197.4.ba \(\chi_{1197}(83, \cdot)\) n/a 952 2
1197.4.bb \(\chi_{1197}(761, \cdot)\) n/a 864 2
1197.4.be \(\chi_{1197}(493, \cdot)\) n/a 952 2
1197.4.bf \(\chi_{1197}(601, \cdot)\) n/a 952 2
1197.4.bi \(\chi_{1197}(31, \cdot)\) n/a 952 2
1197.4.bk \(\chi_{1197}(26, \cdot)\) n/a 320 2
1197.4.bl \(\chi_{1197}(284, \cdot)\) n/a 952 2
1197.4.bo \(\chi_{1197}(464, \cdot)\) n/a 952 2
1197.4.bp \(\chi_{1197}(50, \cdot)\) n/a 720 2
1197.4.bx \(\chi_{1197}(506, \cdot)\) n/a 952 2
1197.4.ca \(\chi_{1197}(113, \cdot)\) n/a 720 2
1197.4.cb \(\chi_{1197}(578, \cdot)\) n/a 952 2
1197.4.cd \(\chi_{1197}(8, \cdot)\) n/a 240 2
1197.4.cg \(\chi_{1197}(170, \cdot)\) n/a 320 2
1197.4.ch \(\chi_{1197}(620, \cdot)\) n/a 320 2
1197.4.cn \(\chi_{1197}(160, \cdot)\) n/a 952 2
1197.4.co \(\chi_{1197}(103, \cdot)\) n/a 952 2
1197.4.cr \(\chi_{1197}(94, \cdot)\) n/a 952 2
1197.4.cs \(\chi_{1197}(425, \cdot)\) n/a 952 2
1197.4.cv \(\chi_{1197}(353, \cdot)\) n/a 952 2
1197.4.cw \(\chi_{1197}(20, \cdot)\) n/a 864 2
1197.4.cy \(\chi_{1197}(125, \cdot)\) n/a 320 2
1197.4.db \(\chi_{1197}(647, \cdot)\) n/a 288 2
1197.4.dc \(\chi_{1197}(467, \cdot)\) n/a 320 2
1197.4.df \(\chi_{1197}(829, \cdot)\) n/a 396 2
1197.4.dg \(\chi_{1197}(208, \cdot)\) n/a 396 2
1197.4.dj \(\chi_{1197}(559, \cdot)\) n/a 396 2
1197.4.dl \(\chi_{1197}(265, \cdot)\) n/a 952 2
1197.4.dm \(\chi_{1197}(544, \cdot)\) n/a 952 2
1197.4.dp \(\chi_{1197}(787, \cdot)\) n/a 952 2
1197.4.dq \(\chi_{1197}(248, \cdot)\) n/a 864 2
1197.4.dt \(\chi_{1197}(68, \cdot)\) n/a 952 2
1197.4.du \(\chi_{1197}(482, \cdot)\) n/a 952 2
1197.4.dx \(\chi_{1197}(107, \cdot)\) n/a 320 2
1197.4.eb \(\chi_{1197}(65, \cdot)\) n/a 952 2
1197.4.ee \(\chi_{1197}(806, \cdot)\) n/a 720 2
1197.4.ef \(\chi_{1197}(968, \cdot)\) n/a 952 2
1197.4.ei \(\chi_{1197}(130, \cdot)\) n/a 2856 6
1197.4.ej \(\chi_{1197}(43, \cdot)\) n/a 2160 6
1197.4.ek \(\chi_{1197}(25, \cdot)\) n/a 2856 6
1197.4.el \(\chi_{1197}(4, \cdot)\) n/a 2856 6
1197.4.em \(\chi_{1197}(253, \cdot)\) n/a 900 6
1197.4.en \(\chi_{1197}(289, \cdot)\) n/a 1188 6
1197.4.eo \(\chi_{1197}(214, \cdot)\) n/a 2856 6
1197.4.ep \(\chi_{1197}(232, \cdot)\) n/a 2160 6
1197.4.eq \(\chi_{1197}(100, \cdot)\) n/a 1188 6
1197.4.er \(\chi_{1197}(53, \cdot)\) n/a 960 6
1197.4.eu \(\chi_{1197}(29, \cdot)\) n/a 2160 6
1197.4.ev \(\chi_{1197}(86, \cdot)\) n/a 2856 6
1197.4.fd \(\chi_{1197}(116, \cdot)\) n/a 960 6
1197.4.fe \(\chi_{1197}(71, \cdot)\) n/a 720 6
1197.4.fj \(\chi_{1197}(2, \cdot)\) n/a 2856 6
1197.4.fk \(\chi_{1197}(200, \cdot)\) n/a 2856 6
1197.4.fl \(\chi_{1197}(155, \cdot)\) n/a 2160 6
1197.4.fm \(\chi_{1197}(317, \cdot)\) n/a 2856 6
1197.4.ft \(\chi_{1197}(272, \cdot)\) n/a 2856 6
1197.4.fu \(\chi_{1197}(194, \cdot)\) n/a 2856 6
1197.4.fx \(\chi_{1197}(80, \cdot)\) n/a 960 6
1197.4.fy \(\chi_{1197}(181, \cdot)\) n/a 1188 6
1197.4.fz \(\chi_{1197}(136, \cdot)\) n/a 1188 6
1197.4.ge \(\chi_{1197}(40, \cdot)\) n/a 2856 6
1197.4.gf \(\chi_{1197}(250, \cdot)\) n/a 2856 6
1197.4.gg \(\chi_{1197}(13, \cdot)\) n/a 2856 6
1197.4.gh \(\chi_{1197}(124, \cdot)\) n/a 2856 6
1197.4.gm \(\chi_{1197}(47, \cdot)\) n/a 2856 6
1197.4.gn \(\chi_{1197}(104, \cdot)\) n/a 2856 6
1197.4.go \(\chi_{1197}(500, \cdot)\) n/a 2856 6
1197.4.gp \(\chi_{1197}(5, \cdot)\) n/a 2856 6
1197.4.gu \(\chi_{1197}(17, \cdot)\) n/a 960 6
1197.4.gv \(\chi_{1197}(62, \cdot)\) n/a 960 6
1197.4.gw \(\chi_{1197}(10, \cdot)\) n/a 1188 6
1197.4.gz \(\chi_{1197}(52, \cdot)\) n/a 2856 6
1197.4.ha \(\chi_{1197}(34, \cdot)\) n/a 2856 6

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1197))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1197)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(399))\)\(^{\oplus 2}\)