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Properties

Label 1232.2
Level 1232
Weight 2
Dimension 24020
Nonzero newspaces 32
Sturm bound 184320
Trace bound 11

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Defining parameters

Level: \( N \) = \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(184320\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1232))\).

Total New Old
Modular forms 47760 24832 22928
Cusp forms 44401 24020 20381
Eisenstein series 3359 812 2547

Trace form

\( 24020 q - 64 q^{2} - 50 q^{3} - 56 q^{4} - 78 q^{5} - 40 q^{6} - 57 q^{7} - 136 q^{8} - 14 q^{9} + O(q^{10}) \) \( 24020 q - 64 q^{2} - 50 q^{3} - 56 q^{4} - 78 q^{5} - 40 q^{6} - 57 q^{7} - 136 q^{8} - 14 q^{9} - 56 q^{10} - 47 q^{11} - 152 q^{12} - 72 q^{13} - 84 q^{14} - 98 q^{15} - 88 q^{16} - 142 q^{17} - 48 q^{18} - 6 q^{19} - 40 q^{20} - 58 q^{21} - 176 q^{22} - 66 q^{23} - 56 q^{24} + 34 q^{25} - 40 q^{26} - 32 q^{27} - 60 q^{28} - 142 q^{29} - 72 q^{30} - 58 q^{31} - 24 q^{32} - 97 q^{33} - 120 q^{34} + q^{35} - 168 q^{36} + 18 q^{37} - 104 q^{38} + 72 q^{39} - 88 q^{40} + 72 q^{41} - 220 q^{42} - 36 q^{43} - 124 q^{44} - 120 q^{45} - 128 q^{46} + 46 q^{47} - 264 q^{48} - 187 q^{49} - 344 q^{50} + 34 q^{51} - 288 q^{52} - 166 q^{53} - 392 q^{54} - 30 q^{55} - 360 q^{56} - 190 q^{57} - 272 q^{58} - 114 q^{59} - 392 q^{60} - 238 q^{61} - 208 q^{62} - 124 q^{63} - 320 q^{64} - 166 q^{65} - 180 q^{66} - 166 q^{67} - 176 q^{68} - 130 q^{69} - 296 q^{70} - 74 q^{71} - 432 q^{72} - 126 q^{73} - 256 q^{74} - 20 q^{75} - 328 q^{76} - 138 q^{77} - 848 q^{78} - 58 q^{79} - 464 q^{80} - 212 q^{81} - 456 q^{82} - 48 q^{83} - 332 q^{84} - 398 q^{85} - 376 q^{86} - 122 q^{87} - 692 q^{88} - 98 q^{89} - 568 q^{90} - 235 q^{91} - 544 q^{92} - 254 q^{93} - 456 q^{94} - 262 q^{95} - 280 q^{96} - 328 q^{97} - 168 q^{98} - 350 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1232))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1232.2.a \(\chi_{1232}(1, \cdot)\) 1232.2.a.a 1 1
1232.2.a.b 1
1232.2.a.c 1
1232.2.a.d 1
1232.2.a.e 1
1232.2.a.f 1
1232.2.a.g 1
1232.2.a.h 1
1232.2.a.i 1
1232.2.a.j 1
1232.2.a.k 1
1232.2.a.l 1
1232.2.a.m 2
1232.2.a.n 2
1232.2.a.o 2
1232.2.a.p 2
1232.2.a.q 3
1232.2.a.r 3
1232.2.a.s 4
1232.2.c \(\chi_{1232}(617, \cdot)\) None 0 1
1232.2.e \(\chi_{1232}(769, \cdot)\) 1232.2.e.a 2 1
1232.2.e.b 4
1232.2.e.c 4
1232.2.e.d 4
1232.2.e.e 8
1232.2.e.f 24
1232.2.f \(\chi_{1232}(351, \cdot)\) 1232.2.f.a 6 1
1232.2.f.b 6
1232.2.f.c 12
1232.2.f.d 12
1232.2.h \(\chi_{1232}(727, \cdot)\) None 0 1
1232.2.j \(\chi_{1232}(111, \cdot)\) 1232.2.j.a 16 1
1232.2.j.b 24
1232.2.l \(\chi_{1232}(967, \cdot)\) None 0 1
1232.2.o \(\chi_{1232}(153, \cdot)\) None 0 1
1232.2.q \(\chi_{1232}(177, \cdot)\) 1232.2.q.a 2 2
1232.2.q.b 2
1232.2.q.c 2
1232.2.q.d 2
1232.2.q.e 2
1232.2.q.f 4
1232.2.q.g 4
1232.2.q.h 4
1232.2.q.i 6
1232.2.q.j 6
1232.2.q.k 6
1232.2.q.l 6
1232.2.q.m 6
1232.2.q.n 8
1232.2.q.o 10
1232.2.q.p 10
1232.2.r \(\chi_{1232}(43, \cdot)\) n/a 288 2
1232.2.s \(\chi_{1232}(419, \cdot)\) n/a 320 2
1232.2.x \(\chi_{1232}(461, \cdot)\) n/a 376 2
1232.2.y \(\chi_{1232}(309, \cdot)\) n/a 240 2
1232.2.z \(\chi_{1232}(113, \cdot)\) n/a 144 4
1232.2.ba \(\chi_{1232}(857, \cdot)\) None 0 2
1232.2.be \(\chi_{1232}(815, \cdot)\) 1232.2.be.a 24 2
1232.2.be.b 28
1232.2.be.c 28
1232.2.bg \(\chi_{1232}(263, \cdot)\) None 0 2
1232.2.bi \(\chi_{1232}(527, \cdot)\) 1232.2.bi.a 32 2
1232.2.bi.b 32
1232.2.bi.c 32
1232.2.bk \(\chi_{1232}(199, \cdot)\) None 0 2
1232.2.bl \(\chi_{1232}(793, \cdot)\) None 0 2
1232.2.bn \(\chi_{1232}(241, \cdot)\) 1232.2.bn.a 12 2
1232.2.bn.b 16
1232.2.bn.c 16
1232.2.bn.d 48
1232.2.bq \(\chi_{1232}(41, \cdot)\) None 0 4
1232.2.bt \(\chi_{1232}(183, \cdot)\) None 0 4
1232.2.bv \(\chi_{1232}(223, \cdot)\) n/a 192 4
1232.2.bx \(\chi_{1232}(279, \cdot)\) None 0 4
1232.2.bz \(\chi_{1232}(127, \cdot)\) n/a 144 4
1232.2.ca \(\chi_{1232}(321, \cdot)\) n/a 184 4
1232.2.cc \(\chi_{1232}(169, \cdot)\) None 0 4
1232.2.cg \(\chi_{1232}(243, \cdot)\) n/a 640 4
1232.2.ch \(\chi_{1232}(219, \cdot)\) n/a 752 4
1232.2.ci \(\chi_{1232}(221, \cdot)\) n/a 640 4
1232.2.cj \(\chi_{1232}(285, \cdot)\) n/a 752 4
1232.2.cm \(\chi_{1232}(81, \cdot)\) n/a 368 8
1232.2.cn \(\chi_{1232}(141, \cdot)\) n/a 1152 8
1232.2.co \(\chi_{1232}(13, \cdot)\) n/a 1504 8
1232.2.ct \(\chi_{1232}(27, \cdot)\) n/a 1504 8
1232.2.cu \(\chi_{1232}(211, \cdot)\) n/a 1152 8
1232.2.cw \(\chi_{1232}(17, \cdot)\) n/a 368 8
1232.2.cy \(\chi_{1232}(9, \cdot)\) None 0 8
1232.2.cz \(\chi_{1232}(103, \cdot)\) None 0 8
1232.2.db \(\chi_{1232}(79, \cdot)\) n/a 384 8
1232.2.dd \(\chi_{1232}(39, \cdot)\) None 0 8
1232.2.df \(\chi_{1232}(31, \cdot)\) n/a 384 8
1232.2.dj \(\chi_{1232}(73, \cdot)\) None 0 8
1232.2.dm \(\chi_{1232}(61, \cdot)\) n/a 3008 16
1232.2.dn \(\chi_{1232}(37, \cdot)\) n/a 3008 16
1232.2.do \(\chi_{1232}(51, \cdot)\) n/a 3008 16
1232.2.dp \(\chi_{1232}(3, \cdot)\) n/a 3008 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1232))\) into lower level spaces

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