## Defining parameters

 Level: $$N$$ = $$1100 = 2^{2} \cdot 5^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$42$$ Sturm bound: $$144000$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1100))$$.

Total New Old
Modular forms 37400 19403 17997
Cusp forms 34601 18663 15938
Eisenstein series 2799 740 2059

## Trace form

 $$18663 q - 53 q^{2} - 8 q^{3} - 45 q^{4} - 130 q^{5} - 69 q^{6} + 3 q^{7} - 29 q^{8} - 96 q^{9} + O(q^{10})$$ $$18663 q - 53 q^{2} - 8 q^{3} - 45 q^{4} - 130 q^{5} - 69 q^{6} + 3 q^{7} - 29 q^{8} - 96 q^{9} - 48 q^{10} - 5 q^{11} - 110 q^{12} - 95 q^{13} - 40 q^{14} + 4 q^{15} - 81 q^{16} - 65 q^{17} - 44 q^{18} + 39 q^{19} - 68 q^{20} - 84 q^{21} - 25 q^{22} + 69 q^{23} - 35 q^{24} - 46 q^{25} - 108 q^{26} + 76 q^{27} - 20 q^{28} - 31 q^{29} - 60 q^{30} + 24 q^{31} - 8 q^{32} - 100 q^{33} - 130 q^{34} + 16 q^{35} - 110 q^{36} - 118 q^{37} - 130 q^{38} - 91 q^{39} - 168 q^{40} - 203 q^{41} - 290 q^{42} - 50 q^{43} - 160 q^{44} - 370 q^{45} - 214 q^{46} + 11 q^{47} - 360 q^{48} - 27 q^{49} - 268 q^{50} + 93 q^{51} - 246 q^{52} + 33 q^{53} - 340 q^{54} + 40 q^{55} - 264 q^{56} - 23 q^{57} - 118 q^{58} + 128 q^{59} - 260 q^{60} + 121 q^{61} - 70 q^{62} + 228 q^{63} - 45 q^{64} + 30 q^{65} - 70 q^{66} + 223 q^{67} - 28 q^{68} + 117 q^{69} - 60 q^{70} + 52 q^{71} + 17 q^{72} - 95 q^{73} - 20 q^{74} + 156 q^{75} - 80 q^{76} - 15 q^{77} - 180 q^{78} + 117 q^{79} - 28 q^{80} - 363 q^{81} + 69 q^{82} + 99 q^{83} - 50 q^{84} - 214 q^{85} + q^{86} - 78 q^{87} - 15 q^{88} - 459 q^{89} + 72 q^{90} - 139 q^{91} - 40 q^{92} - 548 q^{93} - 30 q^{94} - 152 q^{95} - 424 q^{96} - 668 q^{97} - 184 q^{98} - 450 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1100))$$

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
1100.2.a $$\chi_{1100}(1, \cdot)$$ 1100.2.a.a 1 1
1100.2.a.b 1
1100.2.a.c 1
1100.2.a.d 1
1100.2.a.e 1
1100.2.a.f 2
1100.2.a.g 2
1100.2.a.h 2
1100.2.a.i 2
1100.2.a.j 4
1100.2.b $$\chi_{1100}(749, \cdot)$$ 1100.2.b.a 2 1
1100.2.b.b 2
1100.2.b.c 2
1100.2.b.d 4
1100.2.b.e 4
1100.2.d $$\chi_{1100}(351, \cdot)$$ n/a 108 1
1100.2.g $$\chi_{1100}(1099, \cdot)$$ n/a 104 1
1100.2.k $$\chi_{1100}(593, \cdot)$$ 1100.2.k.a 4 2
1100.2.k.b 8
1100.2.k.c 8
1100.2.k.d 8
1100.2.k.e 8
1100.2.l $$\chi_{1100}(243, \cdot)$$ n/a 180 2
1100.2.m $$\chi_{1100}(361, \cdot)$$ n/a 120 4
1100.2.n $$\chi_{1100}(201, \cdot)$$ 1100.2.n.a 4 4
1100.2.n.b 8
1100.2.n.c 8
1100.2.n.d 16
1100.2.n.e 16
1100.2.n.f 24
1100.2.o $$\chi_{1100}(581, \cdot)$$ n/a 120 4
1100.2.p $$\chi_{1100}(81, \cdot)$$ n/a 120 4
1100.2.q $$\chi_{1100}(221, \cdot)$$ 1100.2.q.a 44 4
1100.2.q.b 52
1100.2.r $$\chi_{1100}(181, \cdot)$$ n/a 120 4
1100.2.s $$\chi_{1100}(491, \cdot)$$ n/a 704 4
1100.2.u $$\chi_{1100}(229, \cdot)$$ n/a 120 4
1100.2.w $$\chi_{1100}(219, \cdot)$$ n/a 704 4
1100.2.bc $$\chi_{1100}(299, \cdot)$$ n/a 416 4
1100.2.bd $$\chi_{1100}(19, \cdot)$$ n/a 704 4
1100.2.be $$\chi_{1100}(139, \cdot)$$ n/a 704 4
1100.2.bf $$\chi_{1100}(39, \cdot)$$ n/a 704 4
1100.2.bm $$\chi_{1100}(89, \cdot)$$ n/a 104 4
1100.2.br $$\chi_{1100}(371, \cdot)$$ n/a 704 4
1100.2.bs $$\chi_{1100}(51, \cdot)$$ n/a 432 4
1100.2.bt $$\chi_{1100}(211, \cdot)$$ n/a 704 4
1100.2.bu $$\chi_{1100}(171, \cdot)$$ n/a 704 4
1100.2.bz $$\chi_{1100}(9, \cdot)$$ n/a 120 4
1100.2.ca $$\chi_{1100}(69, \cdot)$$ n/a 120 4
1100.2.cb $$\chi_{1100}(49, \cdot)$$ 1100.2.cb.a 8 4
1100.2.cb.b 16
1100.2.cb.c 16
1100.2.cb.d 32
1100.2.cc $$\chi_{1100}(389, \cdot)$$ n/a 120 4
1100.2.ce $$\chi_{1100}(131, \cdot)$$ n/a 704 4
1100.2.ch $$\chi_{1100}(79, \cdot)$$ n/a 704 4
1100.2.ci $$\chi_{1100}(223, \cdot)$$ n/a 1408 8
1100.2.cj $$\chi_{1100}(17, \cdot)$$ n/a 240 8
1100.2.co $$\chi_{1100}(57, \cdot)$$ n/a 144 8
1100.2.cp $$\chi_{1100}(103, \cdot)$$ n/a 1408 8
1100.2.cq $$\chi_{1100}(23, \cdot)$$ n/a 1200 8
1100.2.cr $$\chi_{1100}(3, \cdot)$$ n/a 1408 8
1100.2.cs $$\chi_{1100}(153, \cdot)$$ n/a 240 8
1100.2.ct $$\chi_{1100}(13, \cdot)$$ n/a 240 8
1100.2.cu $$\chi_{1100}(217, \cdot)$$ n/a 240 8
1100.2.cv $$\chi_{1100}(207, \cdot)$$ n/a 832 8
1100.2.de $$\chi_{1100}(203, \cdot)$$ n/a 1408 8
1100.2.df $$\chi_{1100}(73, \cdot)$$ n/a 240 8

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1100))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1100)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(220))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(275))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(550))$$$$^{\oplus 2}$$