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Properties

Label 1232.4
Level 1232
Weight 4
Dimension 72872
Nonzero newspaces 32
Sturm bound 368640
Trace bound 11

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Defining parameters

Level: \( N \) = \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(368640\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1232))\).

Total New Old
Modular forms 139920 73684 66236
Cusp forms 136560 72872 63688
Eisenstein series 3360 812 2548

Trace form

\( 72872 q - 64 q^{2} - 34 q^{3} - 24 q^{4} - 86 q^{5} - 184 q^{6} - 105 q^{7} - 328 q^{8} - 58 q^{9} + O(q^{10}) \) \( 72872 q - 64 q^{2} - 34 q^{3} - 24 q^{4} - 86 q^{5} - 184 q^{6} - 105 q^{7} - 328 q^{8} - 58 q^{9} - 328 q^{10} + 73 q^{11} + 264 q^{12} + 16 q^{13} + 300 q^{14} - 642 q^{15} + 1064 q^{16} + 58 q^{17} + 640 q^{18} + 218 q^{19} - 840 q^{20} + 182 q^{21} - 1352 q^{22} - 130 q^{23} - 3448 q^{24} - 1506 q^{25} - 1112 q^{26} - 1216 q^{27} + 484 q^{28} - 806 q^{29} + 4888 q^{30} + 1350 q^{31} + 3816 q^{32} + 2943 q^{33} + 1608 q^{34} + 2905 q^{35} - 2536 q^{36} + 714 q^{37} - 4984 q^{38} - 1352 q^{39} - 5400 q^{40} - 3760 q^{41} - 6620 q^{42} - 7476 q^{43} - 2028 q^{44} - 9344 q^{45} + 272 q^{46} - 8402 q^{47} + 6776 q^{48} + 7385 q^{49} + 6952 q^{50} - 1582 q^{51} + 8288 q^{52} + 4034 q^{53} + 12248 q^{54} + 6418 q^{55} + 8088 q^{56} + 14994 q^{57} + 8208 q^{58} + 11518 q^{59} + 10936 q^{60} + 8170 q^{61} + 2432 q^{62} + 5532 q^{63} - 960 q^{64} - 4870 q^{65} - 7524 q^{66} + 6410 q^{67} - 15696 q^{68} - 2674 q^{69} - 21496 q^{70} - 3690 q^{71} - 38576 q^{72} - 17782 q^{73} - 20864 q^{74} - 21252 q^{75} - 19368 q^{76} - 5242 q^{77} - 4880 q^{78} - 18874 q^{79} + 2992 q^{80} + 4128 q^{81} + 19928 q^{82} - 13504 q^{83} + 21844 q^{84} + 17506 q^{85} + 42200 q^{86} + 5686 q^{87} + 58668 q^{88} + 11334 q^{89} + 64552 q^{90} - 2507 q^{91} + 30272 q^{92} + 7090 q^{93} + 36632 q^{94} + 7322 q^{95} + 19176 q^{96} + 1984 q^{97} + 6048 q^{98} + 3218 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1232))\)

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
1232.4.a \(\chi_{1232}(1, \cdot)\) 1232.4.a.a 1 1
1232.4.a.b 1
1232.4.a.c 1
1232.4.a.d 1
1232.4.a.e 1
1232.4.a.f 1
1232.4.a.g 1
1232.4.a.h 1
1232.4.a.i 1
1232.4.a.j 2
1232.4.a.k 2
1232.4.a.l 2
1232.4.a.m 2
1232.4.a.n 2
1232.4.a.o 2
1232.4.a.p 2
1232.4.a.q 3
1232.4.a.r 3
1232.4.a.s 4
1232.4.a.t 4
1232.4.a.u 4
1232.4.a.v 4
1232.4.a.w 4
1232.4.a.x 5
1232.4.a.y 5
1232.4.a.z 5
1232.4.a.ba 6
1232.4.a.bb 6
1232.4.a.bc 7
1232.4.a.bd 7
1232.4.c \(\chi_{1232}(617, \cdot)\) None 0 1
1232.4.e \(\chi_{1232}(769, \cdot)\) n/a 142 1
1232.4.f \(\chi_{1232}(351, \cdot)\) n/a 108 1
1232.4.h \(\chi_{1232}(727, \cdot)\) None 0 1
1232.4.j \(\chi_{1232}(111, \cdot)\) n/a 120 1
1232.4.l \(\chi_{1232}(967, \cdot)\) None 0 1
1232.4.o \(\chi_{1232}(153, \cdot)\) None 0 1
1232.4.q \(\chi_{1232}(177, \cdot)\) n/a 240 2
1232.4.r \(\chi_{1232}(43, \cdot)\) n/a 864 2
1232.4.s \(\chi_{1232}(419, \cdot)\) n/a 960 2
1232.4.x \(\chi_{1232}(461, \cdot)\) n/a 1144 2
1232.4.y \(\chi_{1232}(309, \cdot)\) n/a 720 2
1232.4.z \(\chi_{1232}(113, \cdot)\) n/a 432 4
1232.4.ba \(\chi_{1232}(857, \cdot)\) None 0 2
1232.4.be \(\chi_{1232}(815, \cdot)\) n/a 240 2
1232.4.bg \(\chi_{1232}(263, \cdot)\) None 0 2
1232.4.bi \(\chi_{1232}(527, \cdot)\) n/a 288 2
1232.4.bk \(\chi_{1232}(199, \cdot)\) None 0 2
1232.4.bl \(\chi_{1232}(793, \cdot)\) None 0 2
1232.4.bn \(\chi_{1232}(241, \cdot)\) n/a 284 2
1232.4.bq \(\chi_{1232}(41, \cdot)\) None 0 4
1232.4.bt \(\chi_{1232}(183, \cdot)\) None 0 4
1232.4.bv \(\chi_{1232}(223, \cdot)\) n/a 576 4
1232.4.bx \(\chi_{1232}(279, \cdot)\) None 0 4
1232.4.bz \(\chi_{1232}(127, \cdot)\) n/a 432 4
1232.4.ca \(\chi_{1232}(321, \cdot)\) n/a 568 4
1232.4.cc \(\chi_{1232}(169, \cdot)\) None 0 4
1232.4.cg \(\chi_{1232}(243, \cdot)\) n/a 1920 4
1232.4.ch \(\chi_{1232}(219, \cdot)\) n/a 2288 4
1232.4.ci \(\chi_{1232}(221, \cdot)\) n/a 1920 4
1232.4.cj \(\chi_{1232}(285, \cdot)\) n/a 2288 4
1232.4.cm \(\chi_{1232}(81, \cdot)\) n/a 1136 8
1232.4.cn \(\chi_{1232}(141, \cdot)\) n/a 3456 8
1232.4.co \(\chi_{1232}(13, \cdot)\) n/a 4576 8
1232.4.ct \(\chi_{1232}(27, \cdot)\) n/a 4576 8
1232.4.cu \(\chi_{1232}(211, \cdot)\) n/a 3456 8
1232.4.cw \(\chi_{1232}(17, \cdot)\) n/a 1136 8
1232.4.cy \(\chi_{1232}(9, \cdot)\) None 0 8
1232.4.cz \(\chi_{1232}(103, \cdot)\) None 0 8
1232.4.db \(\chi_{1232}(79, \cdot)\) n/a 1152 8
1232.4.dd \(\chi_{1232}(39, \cdot)\) None 0 8
1232.4.df \(\chi_{1232}(31, \cdot)\) n/a 1152 8
1232.4.dj \(\chi_{1232}(73, \cdot)\) None 0 8
1232.4.dm \(\chi_{1232}(61, \cdot)\) n/a 9152 16
1232.4.dn \(\chi_{1232}(37, \cdot)\) n/a 9152 16
1232.4.do \(\chi_{1232}(51, \cdot)\) n/a 9152 16
1232.4.dp \(\chi_{1232}(3, \cdot)\) n/a 9152 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1232))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1232)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(616))\)\(^{\oplus 2}\)