# Properties

 Label 1100.4 Level 1100 Weight 4 Dimension 56729 Nonzero newspaces 42 Sturm bound 288000 Trace bound 13

## Defining parameters

 Level: $$N$$ = $$1100 = 2^{2} \cdot 5^{2} \cdot 11$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$42$$ Sturm bound: $$288000$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1100))$$.

Total New Old
Modular forms 109400 57469 51931
Cusp forms 106600 56729 49871
Eisenstein series 2800 740 2060

## Trace form

 $$56729 q - 53 q^{2} + 16 q^{3} - 45 q^{4} - 90 q^{5} - 37 q^{6} - 74 q^{7} - 221 q^{8} - 446 q^{9} + O(q^{10})$$ $$56729 q - 53 q^{2} + 16 q^{3} - 45 q^{4} - 90 q^{5} - 37 q^{6} - 74 q^{7} - 221 q^{8} - 446 q^{9} - 208 q^{10} + 10 q^{11} - 430 q^{12} + 442 q^{13} + 130 q^{14} + 344 q^{15} + 847 q^{16} - 84 q^{17} + 954 q^{18} - 481 q^{19} + 572 q^{20} - 1252 q^{21} + 35 q^{22} - 1168 q^{23} - 515 q^{24} - 1406 q^{25} - 2014 q^{26} - 1523 q^{27} - 3040 q^{28} - 296 q^{29} - 2540 q^{30} + 622 q^{31} - 2568 q^{32} + 2335 q^{33} - 1050 q^{34} + 1256 q^{35} + 2090 q^{36} + 1240 q^{37} + 1700 q^{38} - 466 q^{39} - 488 q^{40} + 1256 q^{41} + 5490 q^{42} + 4410 q^{43} + 2780 q^{44} + 6210 q^{45} - 22 q^{46} + 4012 q^{47} + 2560 q^{48} + 1478 q^{49} + 4332 q^{50} - 3831 q^{51} + 3214 q^{52} - 3304 q^{53} + 7460 q^{54} - 3580 q^{55} + 7848 q^{56} - 8701 q^{57} + 6388 q^{58} - 5567 q^{59} - 5700 q^{60} - 8642 q^{61} - 4960 q^{62} - 4936 q^{63} - 13485 q^{64} - 1590 q^{65} - 9400 q^{66} + 2466 q^{67} - 13592 q^{68} - 168 q^{69} - 6140 q^{70} - 1504 q^{71} - 13743 q^{72} + 3492 q^{73} - 1950 q^{74} - 7384 q^{75} + 4080 q^{76} + 6200 q^{77} + 18600 q^{78} + 542 q^{79} + 4132 q^{80} + 9641 q^{81} + 25649 q^{82} - 3823 q^{83} + 26490 q^{84} - 6714 q^{85} + 3043 q^{86} - 1036 q^{87} + 6065 q^{88} - 5604 q^{89} - 21648 q^{90} - 16132 q^{91} - 47480 q^{92} - 25684 q^{93} - 51520 q^{94} - 3672 q^{95} - 48272 q^{96} + 6275 q^{97} - 36176 q^{98} + 6910 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1100))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1100.4.a $$\chi_{1100}(1, \cdot)$$ 1100.4.a.a 1 1
1100.4.a.b 1
1100.4.a.c 1
1100.4.a.d 1
1100.4.a.e 2
1100.4.a.f 2
1100.4.a.g 2
1100.4.a.h 2
1100.4.a.i 3
1100.4.a.j 5
1100.4.a.k 5
1100.4.a.l 5
1100.4.a.m 5
1100.4.a.n 6
1100.4.a.o 6
1100.4.b $$\chi_{1100}(749, \cdot)$$ 1100.4.b.a 2 1
1100.4.b.b 2
1100.4.b.c 2
1100.4.b.d 2
1100.4.b.e 4
1100.4.b.f 4
1100.4.b.g 4
1100.4.b.h 6
1100.4.b.i 10
1100.4.b.j 10
1100.4.d $$\chi_{1100}(351, \cdot)$$ n/a 336 1
1100.4.g $$\chi_{1100}(1099, \cdot)$$ n/a 320 1
1100.4.k $$\chi_{1100}(593, \cdot)$$ n/a 108 2
1100.4.l $$\chi_{1100}(243, \cdot)$$ n/a 540 2
1100.4.m $$\chi_{1100}(361, \cdot)$$ n/a 360 4
1100.4.n $$\chi_{1100}(201, \cdot)$$ n/a 228 4
1100.4.o $$\chi_{1100}(581, \cdot)$$ n/a 360 4
1100.4.p $$\chi_{1100}(81, \cdot)$$ n/a 360 4
1100.4.q $$\chi_{1100}(221, \cdot)$$ n/a 304 4
1100.4.r $$\chi_{1100}(181, \cdot)$$ n/a 360 4
1100.4.s $$\chi_{1100}(491, \cdot)$$ n/a 2144 4
1100.4.u $$\chi_{1100}(229, \cdot)$$ n/a 360 4
1100.4.w $$\chi_{1100}(219, \cdot)$$ n/a 2144 4
1100.4.bc $$\chi_{1100}(299, \cdot)$$ n/a 1280 4
1100.4.bd $$\chi_{1100}(19, \cdot)$$ n/a 2144 4
1100.4.be $$\chi_{1100}(139, \cdot)$$ n/a 2144 4
1100.4.bf $$\chi_{1100}(39, \cdot)$$ n/a 2144 4
1100.4.bm $$\chi_{1100}(89, \cdot)$$ n/a 296 4
1100.4.br $$\chi_{1100}(371, \cdot)$$ n/a 2144 4
1100.4.bs $$\chi_{1100}(51, \cdot)$$ n/a 1344 4
1100.4.bt $$\chi_{1100}(211, \cdot)$$ n/a 2144 4
1100.4.bu $$\chi_{1100}(171, \cdot)$$ n/a 2144 4
1100.4.bz $$\chi_{1100}(9, \cdot)$$ n/a 360 4
1100.4.ca $$\chi_{1100}(69, \cdot)$$ n/a 360 4
1100.4.cb $$\chi_{1100}(49, \cdot)$$ n/a 216 4
1100.4.cc $$\chi_{1100}(389, \cdot)$$ n/a 360 4
1100.4.ce $$\chi_{1100}(131, \cdot)$$ n/a 2144 4
1100.4.ch $$\chi_{1100}(79, \cdot)$$ n/a 2144 4
1100.4.ci $$\chi_{1100}(223, \cdot)$$ n/a 4288 8
1100.4.cj $$\chi_{1100}(17, \cdot)$$ n/a 720 8
1100.4.co $$\chi_{1100}(57, \cdot)$$ n/a 432 8
1100.4.cp $$\chi_{1100}(103, \cdot)$$ n/a 4288 8
1100.4.cq $$\chi_{1100}(23, \cdot)$$ n/a 3600 8
1100.4.cr $$\chi_{1100}(3, \cdot)$$ n/a 4288 8
1100.4.cs $$\chi_{1100}(153, \cdot)$$ n/a 720 8
1100.4.ct $$\chi_{1100}(13, \cdot)$$ n/a 720 8
1100.4.cu $$\chi_{1100}(217, \cdot)$$ n/a 720 8
1100.4.cv $$\chi_{1100}(207, \cdot)$$ n/a 2560 8
1100.4.de $$\chi_{1100}(203, \cdot)$$ n/a 4288 8
1100.4.df $$\chi_{1100}(73, \cdot)$$ n/a 720 8

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1100))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(1100)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 9}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(220))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(275))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(550))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(1100))$$$$^{\oplus 1}$$