# Properties

 Label 2112.4 Level 2112 Weight 4 Dimension 152532 Nonzero newspaces 32 Sturm bound 983040 Trace bound 33

## Defining parameters

 Level: $$N$$ = $$2112 = 2^{6} \cdot 3 \cdot 11$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$32$$ Sturm bound: $$983040$$ Trace bound: $$33$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(2112))$$.

Total New Old
Modular forms 371520 153324 218196
Cusp forms 365760 152532 213228
Eisenstein series 5760 792 4968

## Trace form

 $$152532 q - 48 q^{3} - 128 q^{4} - 64 q^{6} - 104 q^{7} - 80 q^{9} + O(q^{10})$$ $$152532 q - 48 q^{3} - 128 q^{4} - 64 q^{6} - 104 q^{7} - 80 q^{9} - 128 q^{10} - 40 q^{11} - 144 q^{12} + 160 q^{13} + 196 q^{15} - 128 q^{16} + 416 q^{17} - 64 q^{18} - 88 q^{21} + 800 q^{22} + 1936 q^{24} + 44 q^{25} - 160 q^{26} - 312 q^{27} - 3168 q^{28} - 1600 q^{29} - 4704 q^{30} - 1544 q^{31} - 4960 q^{32} - 928 q^{33} - 4288 q^{34} - 912 q^{35} - 1824 q^{36} - 192 q^{37} + 1760 q^{38} + 1148 q^{39} + 6432 q^{40} + 3776 q^{41} + 6256 q^{42} + 1520 q^{43} + 2000 q^{44} - 1112 q^{45} - 128 q^{46} - 64 q^{48} + 1148 q^{49} - 11424 q^{50} + 6100 q^{51} - 13376 q^{52} - 928 q^{54} + 1328 q^{55} + 1568 q^{56} + 516 q^{57} + 9376 q^{58} - 13760 q^{59} + 9728 q^{60} - 128 q^{61} + 11712 q^{62} - 5100 q^{63} + 24064 q^{64} - 8096 q^{65} + 5464 q^{66} - 24312 q^{67} + 8256 q^{68} - 1768 q^{69} + 7936 q^{70} - 1792 q^{71} - 64 q^{72} + 3936 q^{73} - 10528 q^{74} + 13904 q^{75} - 23936 q^{76} + 3504 q^{77} - 24384 q^{78} + 34552 q^{79} - 20064 q^{80} - 2544 q^{81} - 128 q^{82} + 5360 q^{83} - 8352 q^{84} + 4576 q^{85} + 2544 q^{87} - 144 q^{88} - 704 q^{89} + 18656 q^{90} - 6232 q^{91} + 272 q^{93} - 128 q^{94} - 15456 q^{95} + 25776 q^{96} - 13696 q^{97} + 784 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(2112))$$

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
2112.4.a $$\chi_{2112}(1, \cdot)$$ 2112.4.a.a 1 1
2112.4.a.b 1
2112.4.a.c 1
2112.4.a.d 1
2112.4.a.e 1
2112.4.a.f 1
2112.4.a.g 1
2112.4.a.h 1
2112.4.a.i 1
2112.4.a.j 1
2112.4.a.k 1
2112.4.a.l 1
2112.4.a.m 1
2112.4.a.n 1
2112.4.a.o 1
2112.4.a.p 1
2112.4.a.q 1
2112.4.a.r 1
2112.4.a.s 1
2112.4.a.t 1
2112.4.a.u 1
2112.4.a.v 1
2112.4.a.w 1
2112.4.a.x 1
2112.4.a.y 1
2112.4.a.z 1
2112.4.a.ba 2
2112.4.a.bb 2
2112.4.a.bc 2
2112.4.a.bd 2
2112.4.a.be 2
2112.4.a.bf 2
2112.4.a.bg 2
2112.4.a.bh 2
2112.4.a.bi 2
2112.4.a.bj 2
2112.4.a.bk 2
2112.4.a.bl 2
2112.4.a.bm 2
2112.4.a.bn 2
2112.4.a.bo 3
2112.4.a.bp 3
2112.4.a.bq 3
2112.4.a.br 3
2112.4.a.bs 3
2112.4.a.bt 3
2112.4.a.bu 3
2112.4.a.bv 3
2112.4.a.bw 3
2112.4.a.bx 3
2112.4.a.by 4
2112.4.a.bz 4
2112.4.a.ca 4
2112.4.a.cb 4
2112.4.a.cc 5
2112.4.a.cd 5
2112.4.a.ce 5
2112.4.a.cf 5
2112.4.b $$\chi_{2112}(65, \cdot)$$ n/a 284 1
2112.4.d $$\chi_{2112}(1343, \cdot)$$ n/a 240 1
2112.4.f $$\chi_{2112}(1057, \cdot)$$ n/a 120 1
2112.4.h $$\chi_{2112}(1759, \cdot)$$ n/a 144 1
2112.4.k $$\chi_{2112}(287, \cdot)$$ n/a 240 1
2112.4.m $$\chi_{2112}(1121, \cdot)$$ n/a 288 1
2112.4.o $$\chi_{2112}(703, \cdot)$$ n/a 144 1
2112.4.q $$\chi_{2112}(175, \cdot)$$ n/a 288 2
2112.4.t $$\chi_{2112}(529, \cdot)$$ n/a 240 2
2112.4.u $$\chi_{2112}(815, \cdot)$$ n/a 480 2
2112.4.x $$\chi_{2112}(593, \cdot)$$ n/a 568 2
2112.4.y $$\chi_{2112}(577, \cdot)$$ n/a 576 4
2112.4.bb $$\chi_{2112}(265, \cdot)$$ None 0 4
2112.4.bc $$\chi_{2112}(329, \cdot)$$ None 0 4
2112.4.bd $$\chi_{2112}(23, \cdot)$$ None 0 4
2112.4.be $$\chi_{2112}(439, \cdot)$$ None 0 4
2112.4.bi $$\chi_{2112}(127, \cdot)$$ n/a 576 4
2112.4.bk $$\chi_{2112}(161, \cdot)$$ n/a 1152 4
2112.4.bm $$\chi_{2112}(863, \cdot)$$ n/a 1152 4
2112.4.bp $$\chi_{2112}(415, \cdot)$$ n/a 576 4
2112.4.br $$\chi_{2112}(97, \cdot)$$ n/a 576 4
2112.4.bt $$\chi_{2112}(191, \cdot)$$ n/a 1136 4
2112.4.bv $$\chi_{2112}(833, \cdot)$$ n/a 1136 4
2112.4.by $$\chi_{2112}(197, \cdot)$$ n/a 9184 8
2112.4.bz $$\chi_{2112}(133, \cdot)$$ n/a 3840 8
2112.4.ca $$\chi_{2112}(155, \cdot)$$ n/a 7680 8
2112.4.cb $$\chi_{2112}(43, \cdot)$$ n/a 4608 8
2112.4.ce $$\chi_{2112}(17, \cdot)$$ n/a 2272 8
2112.4.ch $$\chi_{2112}(47, \cdot)$$ n/a 2272 8
2112.4.ci $$\chi_{2112}(49, \cdot)$$ n/a 1152 8
2112.4.cl $$\chi_{2112}(79, \cdot)$$ n/a 1152 8
2112.4.co $$\chi_{2112}(7, \cdot)$$ None 0 16
2112.4.cp $$\chi_{2112}(71, \cdot)$$ None 0 16
2112.4.cq $$\chi_{2112}(41, \cdot)$$ None 0 16
2112.4.cr $$\chi_{2112}(25, \cdot)$$ None 0 16
2112.4.cu $$\chi_{2112}(19, \cdot)$$ n/a 18432 32
2112.4.cv $$\chi_{2112}(59, \cdot)$$ n/a 36736 32
2112.4.da $$\chi_{2112}(37, \cdot)$$ n/a 18432 32
2112.4.db $$\chi_{2112}(29, \cdot)$$ n/a 36736 32

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(2112))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(2112)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 28}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 14}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 20}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 16}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 14}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 10}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 7}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 10}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(132))$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(264))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(352))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(528))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(704))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(1056))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2112))$$$$^{\oplus 1}$$