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Properties

Label 1197.2
Level 1197
Weight 2
Dimension 38346
Nonzero newspaces 92
Sturm bound 207360
Trace bound 19

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Defining parameters

Level: \( N \) = \( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 92 \)
Sturm bound: \(207360\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1197))\).

Total New Old
Modular forms 53568 39878 13690
Cusp forms 50113 38346 11767
Eisenstein series 3455 1532 1923

Trace form

\( 38346 q - 90 q^{2} - 120 q^{3} - 82 q^{4} - 84 q^{5} - 120 q^{6} - 109 q^{7} - 216 q^{8} - 120 q^{9} + O(q^{10}) \) \( 38346 q - 90 q^{2} - 120 q^{3} - 82 q^{4} - 84 q^{5} - 120 q^{6} - 109 q^{7} - 216 q^{8} - 120 q^{9} - 240 q^{10} - 72 q^{11} - 144 q^{12} - 52 q^{13} - 111 q^{14} - 336 q^{15} - 42 q^{16} - 114 q^{17} - 168 q^{18} - 266 q^{19} - 216 q^{20} - 192 q^{21} - 216 q^{22} - 102 q^{23} - 192 q^{24} - 54 q^{25} - 120 q^{26} - 156 q^{27} - 300 q^{28} - 198 q^{29} - 204 q^{30} - 52 q^{31} - 96 q^{32} - 168 q^{33} - 42 q^{34} - 147 q^{35} - 504 q^{36} - 242 q^{37} - 36 q^{38} - 336 q^{39} - 42 q^{40} - 192 q^{41} - 288 q^{42} - 200 q^{43} - 312 q^{44} - 324 q^{45} - 498 q^{46} - 270 q^{47} - 348 q^{48} - 123 q^{49} - 630 q^{50} - 300 q^{51} - 520 q^{52} - 240 q^{53} - 276 q^{54} - 444 q^{55} - 312 q^{56} - 468 q^{57} - 360 q^{58} - 186 q^{59} - 348 q^{60} - 220 q^{61} - 30 q^{62} - 60 q^{63} - 808 q^{64} - 126 q^{65} - 324 q^{66} - 66 q^{67} - 120 q^{68} - 180 q^{69} - 183 q^{70} - 336 q^{71} - 120 q^{72} - 208 q^{73} - 96 q^{74} - 144 q^{75} + 34 q^{76} - 243 q^{77} - 384 q^{78} + 24 q^{79} - 144 q^{80} - 288 q^{81} - 18 q^{82} - 114 q^{83} - 444 q^{84} - 102 q^{85} - 162 q^{86} - 300 q^{87} + 60 q^{88} - 210 q^{89} - 624 q^{90} - 397 q^{91} - 300 q^{92} - 348 q^{93} - 198 q^{94} - 384 q^{95} - 912 q^{96} - 382 q^{97} - 606 q^{98} - 756 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1197))\)

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
1197.2.a \(\chi_{1197}(1, \cdot)\) 1197.2.a.a 1 1
1197.2.a.b 1
1197.2.a.c 1
1197.2.a.d 1
1197.2.a.e 1
1197.2.a.f 2
1197.2.a.g 2
1197.2.a.h 2
1197.2.a.i 2
1197.2.a.j 2
1197.2.a.k 3
1197.2.a.l 3
1197.2.a.m 3
1197.2.a.n 4
1197.2.a.o 5
1197.2.a.p 5
1197.2.a.q 6
1197.2.c \(\chi_{1197}(1063, \cdot)\) 1197.2.c.a 2 1
1197.2.c.b 2
1197.2.c.c 2
1197.2.c.d 4
1197.2.c.e 4
1197.2.c.f 4
1197.2.c.g 8
1197.2.c.h 12
1197.2.c.i 12
1197.2.c.j 16
1197.2.d \(\chi_{1197}(818, \cdot)\) 1197.2.d.a 8 1
1197.2.d.b 40
1197.2.f \(\chi_{1197}(512, \cdot)\) 1197.2.f.a 4 1
1197.2.f.b 16
1197.2.f.c 20
1197.2.i \(\chi_{1197}(163, \cdot)\) n/a 128 2
1197.2.j \(\chi_{1197}(172, \cdot)\) 1197.2.j.a 2 2
1197.2.j.b 2
1197.2.j.c 2
1197.2.j.d 4
1197.2.j.e 4
1197.2.j.f 4
1197.2.j.g 4
1197.2.j.h 4
1197.2.j.i 8
1197.2.j.j 8
1197.2.j.k 8
1197.2.j.l 14
1197.2.j.m 16
1197.2.j.n 16
1197.2.j.o 24
1197.2.k \(\chi_{1197}(64, \cdot)\) 1197.2.k.a 2 2
1197.2.k.b 2
1197.2.k.c 4
1197.2.k.d 6
1197.2.k.e 8
1197.2.k.f 8
1197.2.k.g 10
1197.2.k.h 12
1197.2.k.i 12
1197.2.k.j 16
1197.2.k.k 20
1197.2.l \(\chi_{1197}(121, \cdot)\) n/a 312 2
1197.2.m \(\chi_{1197}(400, \cdot)\) n/a 216 2
1197.2.n \(\chi_{1197}(520, \cdot)\) n/a 312 2
1197.2.o \(\chi_{1197}(106, \cdot)\) n/a 240 2
1197.2.p \(\chi_{1197}(562, \cdot)\) n/a 312 2
1197.2.q \(\chi_{1197}(457, \cdot)\) n/a 288 2
1197.2.r \(\chi_{1197}(58, \cdot)\) n/a 288 2
1197.2.s \(\chi_{1197}(862, \cdot)\) n/a 240 2
1197.2.t \(\chi_{1197}(634, \cdot)\) n/a 312 2
1197.2.u \(\chi_{1197}(676, \cdot)\) n/a 128 2
1197.2.v \(\chi_{1197}(145, \cdot)\) n/a 128 2
1197.2.x \(\chi_{1197}(311, \cdot)\) n/a 312 2
1197.2.ba \(\chi_{1197}(83, \cdot)\) n/a 312 2
1197.2.bb \(\chi_{1197}(761, \cdot)\) n/a 288 2
1197.2.be \(\chi_{1197}(493, \cdot)\) n/a 312 2
1197.2.bf \(\chi_{1197}(601, \cdot)\) n/a 312 2
1197.2.bi \(\chi_{1197}(31, \cdot)\) n/a 312 2
1197.2.bk \(\chi_{1197}(26, \cdot)\) n/a 104 2
1197.2.bl \(\chi_{1197}(284, \cdot)\) n/a 312 2
1197.2.bo \(\chi_{1197}(464, \cdot)\) n/a 312 2
1197.2.bp \(\chi_{1197}(50, \cdot)\) n/a 240 2
1197.2.bx \(\chi_{1197}(506, \cdot)\) n/a 312 2
1197.2.ca \(\chi_{1197}(113, \cdot)\) n/a 240 2
1197.2.cb \(\chi_{1197}(578, \cdot)\) n/a 312 2
1197.2.cd \(\chi_{1197}(8, \cdot)\) 1197.2.cd.a 8 2
1197.2.cd.b 32
1197.2.cd.c 40
1197.2.cg \(\chi_{1197}(170, \cdot)\) n/a 104 2
1197.2.ch \(\chi_{1197}(620, \cdot)\) n/a 104 2
1197.2.cn \(\chi_{1197}(160, \cdot)\) n/a 312 2
1197.2.co \(\chi_{1197}(103, \cdot)\) n/a 312 2
1197.2.cr \(\chi_{1197}(94, \cdot)\) n/a 312 2
1197.2.cs \(\chi_{1197}(425, \cdot)\) n/a 312 2
1197.2.cv \(\chi_{1197}(353, \cdot)\) n/a 312 2
1197.2.cw \(\chi_{1197}(20, \cdot)\) n/a 288 2
1197.2.cy \(\chi_{1197}(125, \cdot)\) n/a 112 2
1197.2.db \(\chi_{1197}(647, \cdot)\) 1197.2.db.a 96 2
1197.2.dc \(\chi_{1197}(467, \cdot)\) n/a 104 2
1197.2.df \(\chi_{1197}(829, \cdot)\) n/a 128 2
1197.2.dg \(\chi_{1197}(208, \cdot)\) n/a 128 2
1197.2.dj \(\chi_{1197}(559, \cdot)\) n/a 132 2
1197.2.dl \(\chi_{1197}(265, \cdot)\) n/a 312 2
1197.2.dm \(\chi_{1197}(544, \cdot)\) n/a 312 2
1197.2.dp \(\chi_{1197}(787, \cdot)\) n/a 312 2
1197.2.dq \(\chi_{1197}(248, \cdot)\) n/a 288 2
1197.2.dt \(\chi_{1197}(68, \cdot)\) n/a 312 2
1197.2.du \(\chi_{1197}(482, \cdot)\) n/a 312 2
1197.2.dx \(\chi_{1197}(107, \cdot)\) n/a 104 2
1197.2.eb \(\chi_{1197}(65, \cdot)\) n/a 312 2
1197.2.ee \(\chi_{1197}(806, \cdot)\) n/a 240 2
1197.2.ef \(\chi_{1197}(968, \cdot)\) n/a 312 2
1197.2.ei \(\chi_{1197}(130, \cdot)\) n/a 936 6
1197.2.ej \(\chi_{1197}(43, \cdot)\) n/a 720 6
1197.2.ek \(\chi_{1197}(25, \cdot)\) n/a 936 6
1197.2.el \(\chi_{1197}(4, \cdot)\) n/a 936 6
1197.2.em \(\chi_{1197}(253, \cdot)\) n/a 300 6
1197.2.en \(\chi_{1197}(289, \cdot)\) n/a 390 6
1197.2.eo \(\chi_{1197}(214, \cdot)\) n/a 936 6
1197.2.ep \(\chi_{1197}(232, \cdot)\) n/a 720 6
1197.2.eq \(\chi_{1197}(100, \cdot)\) n/a 390 6
1197.2.er \(\chi_{1197}(53, \cdot)\) n/a 324 6
1197.2.eu \(\chi_{1197}(29, \cdot)\) n/a 720 6
1197.2.ev \(\chi_{1197}(86, \cdot)\) n/a 936 6
1197.2.fd \(\chi_{1197}(116, \cdot)\) n/a 324 6
1197.2.fe \(\chi_{1197}(71, \cdot)\) n/a 240 6
1197.2.fj \(\chi_{1197}(2, \cdot)\) n/a 936 6
1197.2.fk \(\chi_{1197}(200, \cdot)\) n/a 936 6
1197.2.fl \(\chi_{1197}(155, \cdot)\) n/a 720 6
1197.2.fm \(\chi_{1197}(317, \cdot)\) n/a 936 6
1197.2.ft \(\chi_{1197}(272, \cdot)\) n/a 936 6
1197.2.fu \(\chi_{1197}(194, \cdot)\) n/a 936 6
1197.2.fx \(\chi_{1197}(80, \cdot)\) n/a 324 6
1197.2.fy \(\chi_{1197}(181, \cdot)\) n/a 384 6
1197.2.fz \(\chi_{1197}(136, \cdot)\) n/a 390 6
1197.2.ge \(\chi_{1197}(40, \cdot)\) n/a 936 6
1197.2.gf \(\chi_{1197}(250, \cdot)\) n/a 936 6
1197.2.gg \(\chi_{1197}(13, \cdot)\) n/a 936 6
1197.2.gh \(\chi_{1197}(124, \cdot)\) n/a 936 6
1197.2.gm \(\chi_{1197}(47, \cdot)\) n/a 936 6
1197.2.gn \(\chi_{1197}(104, \cdot)\) n/a 936 6
1197.2.go \(\chi_{1197}(500, \cdot)\) n/a 936 6
1197.2.gp \(\chi_{1197}(5, \cdot)\) n/a 936 6
1197.2.gu \(\chi_{1197}(17, \cdot)\) n/a 324 6
1197.2.gv \(\chi_{1197}(62, \cdot)\) n/a 312 6
1197.2.gw \(\chi_{1197}(10, \cdot)\) n/a 390 6
1197.2.gz \(\chi_{1197}(52, \cdot)\) n/a 936 6
1197.2.ha \(\chi_{1197}(34, \cdot)\) n/a 936 6

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1197))\) into lower level spaces

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