# Properties

 Label 2112.2 Level 2112 Weight 2 Dimension 50580 Nonzero newspaces 32 Sturm bound 491520 Trace bound 33

## Defining parameters

 Level: $$N$$ = $$2112 = 2^{6} \cdot 3 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$491520$$ Trace bound: $$33$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2112))$$.

Total New Old
Modular forms 125760 51372 74388
Cusp forms 120001 50580 69421
Eisenstein series 5759 792 4967

## Trace form

 $$50580 q - 48 q^{3} - 128 q^{4} - 64 q^{6} - 104 q^{7} - 80 q^{9} + O(q^{10})$$ $$50580 q - 48 q^{3} - 128 q^{4} - 64 q^{6} - 104 q^{7} - 80 q^{9} - 128 q^{10} - 8 q^{11} - 144 q^{12} - 160 q^{13} - 60 q^{15} - 128 q^{16} - 32 q^{17} - 64 q^{18} - 128 q^{19} - 56 q^{21} - 128 q^{22} + 16 q^{24} - 116 q^{25} + 160 q^{26} - 24 q^{27} + 32 q^{28} + 64 q^{29} + 96 q^{30} - 8 q^{31} + 160 q^{32} - 16 q^{33} - 128 q^{34} + 48 q^{35} + 96 q^{36} - 64 q^{37} + 160 q^{38} - 4 q^{39} + 32 q^{40} + 64 q^{41} + 16 q^{42} - 80 q^{43} + 16 q^{44} - 56 q^{45} - 128 q^{46} - 64 q^{48} - 196 q^{49} - 96 q^{50} + 84 q^{51} - 320 q^{52} - 96 q^{54} + 48 q^{55} - 224 q^{56} - 28 q^{57} - 416 q^{58} + 320 q^{59} - 256 q^{60} - 128 q^{61} - 192 q^{62} + 20 q^{63} - 512 q^{64} + 32 q^{65} - 152 q^{66} + 136 q^{67} - 192 q^{68} - 136 q^{69} - 512 q^{70} + 256 q^{71} - 64 q^{72} - 160 q^{73} - 224 q^{74} + 48 q^{75} - 384 q^{76} - 48 q^{77} - 288 q^{78} - 8 q^{79} - 96 q^{80} - 240 q^{81} - 128 q^{82} - 80 q^{83} - 288 q^{84} - 224 q^{85} - 144 q^{87} - 144 q^{88} - 64 q^{89} - 352 q^{90} - 216 q^{91} - 176 q^{93} - 128 q^{94} - 96 q^{95} - 336 q^{96} - 192 q^{97} - 112 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2112))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
2112.2.a $$\chi_{2112}(1, \cdot)$$ 2112.2.a.a 1 1
2112.2.a.b 1
2112.2.a.c 1
2112.2.a.d 1
2112.2.a.e 1
2112.2.a.f 1
2112.2.a.g 1
2112.2.a.h 1
2112.2.a.i 1
2112.2.a.j 1
2112.2.a.k 1
2112.2.a.l 1
2112.2.a.m 1
2112.2.a.n 1
2112.2.a.o 1
2112.2.a.p 1
2112.2.a.q 1
2112.2.a.r 1
2112.2.a.s 1
2112.2.a.t 1
2112.2.a.u 1
2112.2.a.v 1
2112.2.a.w 1
2112.2.a.x 1
2112.2.a.y 1
2112.2.a.z 1
2112.2.a.ba 1
2112.2.a.bb 1
2112.2.a.bc 1
2112.2.a.bd 1
2112.2.a.be 2
2112.2.a.bf 2
2112.2.a.bg 3
2112.2.a.bh 3
2112.2.b $$\chi_{2112}(65, \cdot)$$ 2112.2.b.a 2 1
2112.2.b.b 2
2112.2.b.c 2
2112.2.b.d 2
2112.2.b.e 2
2112.2.b.f 2
2112.2.b.g 2
2112.2.b.h 2
2112.2.b.i 2
2112.2.b.j 2
2112.2.b.k 4
2112.2.b.l 4
2112.2.b.m 4
2112.2.b.n 4
2112.2.b.o 6
2112.2.b.p 6
2112.2.b.q 6
2112.2.b.r 6
2112.2.b.s 8
2112.2.b.t 8
2112.2.b.u 8
2112.2.b.v 8
2112.2.d $$\chi_{2112}(1343, \cdot)$$ 2112.2.d.a 2 1
2112.2.d.b 2
2112.2.d.c 2
2112.2.d.d 2
2112.2.d.e 2
2112.2.d.f 2
2112.2.d.g 2
2112.2.d.h 2
2112.2.d.i 4
2112.2.d.j 4
2112.2.d.k 8
2112.2.d.l 8
2112.2.d.m 20
2112.2.d.n 20
2112.2.f $$\chi_{2112}(1057, \cdot)$$ 2112.2.f.a 4 1
2112.2.f.b 4
2112.2.f.c 4
2112.2.f.d 4
2112.2.f.e 4
2112.2.f.f 4
2112.2.f.g 8
2112.2.f.h 8
2112.2.h $$\chi_{2112}(1759, \cdot)$$ 2112.2.h.a 8 1
2112.2.h.b 8
2112.2.h.c 16
2112.2.h.d 16
2112.2.k $$\chi_{2112}(287, \cdot)$$ 2112.2.k.a 4 1
2112.2.k.b 4
2112.2.k.c 4
2112.2.k.d 4
2112.2.k.e 4
2112.2.k.f 4
2112.2.k.g 4
2112.2.k.h 4
2112.2.k.i 8
2112.2.k.j 8
2112.2.k.k 16
2112.2.k.l 16
2112.2.m $$\chi_{2112}(1121, \cdot)$$ 2112.2.m.a 4 1
2112.2.m.b 4
2112.2.m.c 4
2112.2.m.d 4
2112.2.m.e 8
2112.2.m.f 8
2112.2.m.g 8
2112.2.m.h 8
2112.2.m.i 8
2112.2.m.j 8
2112.2.m.k 8
2112.2.m.l 8
2112.2.m.m 16
2112.2.o $$\chi_{2112}(703, \cdot)$$ 2112.2.o.a 4 1
2112.2.o.b 4
2112.2.o.c 4
2112.2.o.d 4
2112.2.o.e 8
2112.2.o.f 12
2112.2.o.g 12
2112.2.q $$\chi_{2112}(175, \cdot)$$ 2112.2.q.a 96 2
2112.2.t $$\chi_{2112}(529, \cdot)$$ 2112.2.t.a 40 2
2112.2.t.b 40
2112.2.u $$\chi_{2112}(815, \cdot)$$ n/a 160 2
2112.2.x $$\chi_{2112}(593, \cdot)$$ n/a 184 2
2112.2.y $$\chi_{2112}(577, \cdot)$$ n/a 192 4
2112.2.bb $$\chi_{2112}(265, \cdot)$$ None 0 4
2112.2.bc $$\chi_{2112}(329, \cdot)$$ None 0 4
2112.2.bd $$\chi_{2112}(23, \cdot)$$ None 0 4
2112.2.be $$\chi_{2112}(439, \cdot)$$ None 0 4
2112.2.bi $$\chi_{2112}(127, \cdot)$$ n/a 192 4
2112.2.bk $$\chi_{2112}(161, \cdot)$$ n/a 384 4
2112.2.bm $$\chi_{2112}(863, \cdot)$$ n/a 384 4
2112.2.bp $$\chi_{2112}(415, \cdot)$$ n/a 192 4
2112.2.br $$\chi_{2112}(97, \cdot)$$ n/a 192 4
2112.2.bt $$\chi_{2112}(191, \cdot)$$ n/a 368 4
2112.2.bv $$\chi_{2112}(833, \cdot)$$ n/a 368 4
2112.2.by $$\chi_{2112}(197, \cdot)$$ n/a 3040 8
2112.2.bz $$\chi_{2112}(133, \cdot)$$ n/a 1280 8
2112.2.ca $$\chi_{2112}(155, \cdot)$$ n/a 2560 8
2112.2.cb $$\chi_{2112}(43, \cdot)$$ n/a 1536 8
2112.2.ce $$\chi_{2112}(17, \cdot)$$ n/a 736 8
2112.2.ch $$\chi_{2112}(47, \cdot)$$ n/a 736 8
2112.2.ci $$\chi_{2112}(49, \cdot)$$ n/a 384 8
2112.2.cl $$\chi_{2112}(79, \cdot)$$ n/a 384 8
2112.2.co $$\chi_{2112}(7, \cdot)$$ None 0 16
2112.2.cp $$\chi_{2112}(71, \cdot)$$ None 0 16
2112.2.cq $$\chi_{2112}(41, \cdot)$$ None 0 16
2112.2.cr $$\chi_{2112}(25, \cdot)$$ None 0 16
2112.2.cu $$\chi_{2112}(19, \cdot)$$ n/a 6144 32
2112.2.cv $$\chi_{2112}(59, \cdot)$$ n/a 12160 32
2112.2.da $$\chi_{2112}(37, \cdot)$$ n/a 6144 32
2112.2.db $$\chi_{2112}(29, \cdot)$$ n/a 12160 32

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2112))$$ into lower level spaces

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