Properties

Label 1224.4
Level 1224
Weight 4
Dimension 54748
Nonzero newspaces 30
Sturm bound 331776
Trace bound 10

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Defining parameters

Level: \( N \) = \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(331776\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1224))\).

Total New Old
Modular forms 125952 55288 70664
Cusp forms 122880 54748 68132
Eisenstein series 3072 540 2532

Trace form

\( 54748 q - 40 q^{2} - 58 q^{3} - 20 q^{4} + 44 q^{5} - 24 q^{6} + 36 q^{7} - 100 q^{8} - 170 q^{9} + O(q^{10}) \) \( 54748 q - 40 q^{2} - 58 q^{3} - 20 q^{4} + 44 q^{5} - 24 q^{6} + 36 q^{7} - 100 q^{8} - 170 q^{9} - 304 q^{10} - 262 q^{11} - 276 q^{12} - 128 q^{13} - 340 q^{14} - 112 q^{15} - 316 q^{16} + 46 q^{17} + 112 q^{18} + 228 q^{19} + 860 q^{20} - 456 q^{21} + 1196 q^{22} - 540 q^{23} + 464 q^{24} - 894 q^{25} - 112 q^{26} - 640 q^{27} + 160 q^{28} + 644 q^{29} - 300 q^{30} + 880 q^{31} - 380 q^{32} + 810 q^{33} - 1430 q^{34} + 1784 q^{35} + 1468 q^{36} + 1008 q^{37} - 836 q^{38} + 488 q^{39} - 1668 q^{40} + 838 q^{41} + 172 q^{42} + 1598 q^{43} + 2028 q^{44} - 892 q^{45} + 5248 q^{46} + 2604 q^{47} + 1528 q^{48} - 1502 q^{49} + 6188 q^{50} - 409 q^{51} + 3028 q^{52} - 2164 q^{53} - 1312 q^{54} + 528 q^{55} - 96 q^{56} - 3202 q^{57} - 7068 q^{58} - 8506 q^{59} - 1660 q^{60} + 4 q^{61} - 12792 q^{62} - 2432 q^{63} - 9224 q^{64} - 536 q^{65} - 5064 q^{66} - 1622 q^{67} - 9980 q^{68} + 7420 q^{69} + 2020 q^{70} + 9376 q^{71} - 1972 q^{72} + 2088 q^{73} + 548 q^{74} + 11694 q^{75} + 2996 q^{76} + 3624 q^{77} - 7956 q^{78} - 4520 q^{79} - 6400 q^{80} - 4002 q^{81} - 6512 q^{82} - 704 q^{83} - 368 q^{84} + 18040 q^{85} - 388 q^{86} - 3700 q^{87} - 8908 q^{88} - 1408 q^{89} - 3804 q^{90} + 5760 q^{91} + 1860 q^{92} - 11204 q^{93} + 10056 q^{94} - 4192 q^{95} + 8000 q^{96} - 6750 q^{97} + 20604 q^{98} + 1172 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1224))\)

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
1224.4.a \(\chi_{1224}(1, \cdot)\) 1224.4.a.a 1 1
1224.4.a.b 1
1224.4.a.c 2
1224.4.a.d 2
1224.4.a.e 3
1224.4.a.f 3
1224.4.a.g 3
1224.4.a.h 3
1224.4.a.i 3
1224.4.a.j 3
1224.4.a.k 4
1224.4.a.l 4
1224.4.a.m 4
1224.4.a.n 5
1224.4.a.o 5
1224.4.a.p 7
1224.4.a.q 7
1224.4.c \(\chi_{1224}(577, \cdot)\) 1224.4.c.a 2 1
1224.4.c.b 6
1224.4.c.c 6
1224.4.c.d 6
1224.4.c.e 8
1224.4.c.f 12
1224.4.c.g 14
1224.4.c.h 14
1224.4.e \(\chi_{1224}(647, \cdot)\) None 0 1
1224.4.f \(\chi_{1224}(613, \cdot)\) n/a 240 1
1224.4.h \(\chi_{1224}(611, \cdot)\) n/a 216 1
1224.4.j \(\chi_{1224}(35, \cdot)\) n/a 192 1
1224.4.l \(\chi_{1224}(1189, \cdot)\) n/a 268 1
1224.4.o \(\chi_{1224}(1223, \cdot)\) None 0 1
1224.4.q \(\chi_{1224}(409, \cdot)\) n/a 288 2
1224.4.r \(\chi_{1224}(251, \cdot)\) n/a 432 2
1224.4.t \(\chi_{1224}(829, \cdot)\) n/a 536 2
1224.4.w \(\chi_{1224}(217, \cdot)\) n/a 136 2
1224.4.y \(\chi_{1224}(863, \cdot)\) None 0 2
1224.4.ba \(\chi_{1224}(407, \cdot)\) None 0 2
1224.4.bd \(\chi_{1224}(373, \cdot)\) n/a 1288 2
1224.4.bf \(\chi_{1224}(443, \cdot)\) n/a 1152 2
1224.4.bh \(\chi_{1224}(203, \cdot)\) n/a 1288 2
1224.4.bj \(\chi_{1224}(205, \cdot)\) n/a 1152 2
1224.4.bk \(\chi_{1224}(239, \cdot)\) None 0 2
1224.4.bm \(\chi_{1224}(169, \cdot)\) n/a 324 2
1224.4.bq \(\chi_{1224}(145, \cdot)\) n/a 268 4
1224.4.br \(\chi_{1224}(287, \cdot)\) None 0 4
1224.4.bs \(\chi_{1224}(253, \cdot)\) n/a 1072 4
1224.4.bt \(\chi_{1224}(179, \cdot)\) n/a 864 4
1224.4.bx \(\chi_{1224}(625, \cdot)\) n/a 648 4
1224.4.bz \(\chi_{1224}(47, \cdot)\) None 0 4
1224.4.ca \(\chi_{1224}(659, \cdot)\) n/a 2576 4
1224.4.cc \(\chi_{1224}(13, \cdot)\) n/a 2576 4
1224.4.cf \(\chi_{1224}(233, \cdot)\) n/a 432 8
1224.4.cg \(\chi_{1224}(199, \cdot)\) None 0 8
1224.4.cj \(\chi_{1224}(91, \cdot)\) n/a 2144 8
1224.4.ck \(\chi_{1224}(125, \cdot)\) n/a 1728 8
1224.4.cm \(\chi_{1224}(229, \cdot)\) n/a 5152 8
1224.4.cn \(\chi_{1224}(59, \cdot)\) n/a 5152 8
1224.4.cs \(\chi_{1224}(25, \cdot)\) n/a 1296 8
1224.4.ct \(\chi_{1224}(263, \cdot)\) None 0 8
1224.4.cv \(\chi_{1224}(7, \cdot)\) None 0 16
1224.4.cw \(\chi_{1224}(41, \cdot)\) n/a 2592 16
1224.4.cz \(\chi_{1224}(5, \cdot)\) n/a 10304 16
1224.4.da \(\chi_{1224}(139, \cdot)\) n/a 10304 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1224))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1224)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(408))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(612))\)\(^{\oplus 2}\)