## Defining parameters

 Level: $$N$$ = $$2268 = 2^{2} \cdot 3^{4} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$44$$ Sturm bound: $$559872$$ Trace bound: $$26$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2268))$$.

Total New Old
Modular forms 143208 62384 80824
Cusp forms 136729 61264 75465
Eisenstein series 6479 1120 5359

## Trace form

 $$61264 q - 48 q^{2} - 80 q^{4} - 90 q^{5} - 72 q^{6} + 3 q^{7} - 126 q^{8} - 144 q^{9} + O(q^{10})$$ $$61264 q - 48 q^{2} - 80 q^{4} - 90 q^{5} - 72 q^{6} + 3 q^{7} - 126 q^{8} - 144 q^{9} - 124 q^{10} + 6 q^{11} - 72 q^{12} - 166 q^{13} - 75 q^{14} - 104 q^{16} - 132 q^{17} - 72 q^{18} - 36 q^{19} - 90 q^{20} - 207 q^{21} - 216 q^{22} - 114 q^{23} - 72 q^{24} - 234 q^{25} - 18 q^{26} - 54 q^{27} - 141 q^{28} - 366 q^{29} - 72 q^{30} - 54 q^{31} + 12 q^{32} - 198 q^{33} - 16 q^{34} - 48 q^{35} - 180 q^{36} - 280 q^{37} + 26 q^{40} - 78 q^{41} - 45 q^{42} + 54 q^{43} + 234 q^{44} - 36 q^{45} + 60 q^{46} + 198 q^{47} + 126 q^{48} - 161 q^{49} + 300 q^{50} + 126 q^{51} + 62 q^{52} + 114 q^{53} + 180 q^{54} + 108 q^{55} + 171 q^{56} - 252 q^{57} + 62 q^{58} + 156 q^{59} + 162 q^{60} - 100 q^{61} + 360 q^{62} + 54 q^{63} - 110 q^{64} + 72 q^{65} + 72 q^{66} - 36 q^{67} + 156 q^{68} + 36 q^{69} - 39 q^{70} + 48 q^{71} - 72 q^{72} - 274 q^{73} + 6 q^{74} + 180 q^{75} + 12 q^{76} - 81 q^{77} - 234 q^{78} - 132 q^{79} - 72 q^{80} - 244 q^{82} + 54 q^{83} - 63 q^{84} - 344 q^{85} - 96 q^{86} + 288 q^{87} - 240 q^{88} + 66 q^{89} - 198 q^{90} + 15 q^{91} - 534 q^{92} + 252 q^{93} - 270 q^{94} + 264 q^{95} - 306 q^{96} - 82 q^{97} - 405 q^{98} + 180 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2268))$$

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
2268.2.a $$\chi_{2268}(1, \cdot)$$ 2268.2.a.a 1 1
2268.2.a.b 1
2268.2.a.c 1
2268.2.a.d 1
2268.2.a.e 2
2268.2.a.f 2
2268.2.a.g 3
2268.2.a.h 3
2268.2.a.i 3
2268.2.a.j 3
2268.2.a.k 4
2268.2.b $$\chi_{2268}(811, \cdot)$$ n/a 184 1
2268.2.e $$\chi_{2268}(323, \cdot)$$ n/a 144 1
2268.2.f $$\chi_{2268}(1133, \cdot)$$ 2268.2.f.a 16 1
2268.2.f.b 16
2268.2.i $$\chi_{2268}(865, \cdot)$$ 2268.2.i.a 2 2
2268.2.i.b 2
2268.2.i.c 2
2268.2.i.d 2
2268.2.i.e 2
2268.2.i.f 2
2268.2.i.g 2
2268.2.i.h 2
2268.2.i.i 4
2268.2.i.j 6
2268.2.i.k 6
2268.2.i.l 8
2268.2.i.m 8
2268.2.i.n 16
2268.2.j $$\chi_{2268}(757, \cdot)$$ 2268.2.j.a 2 2
2268.2.j.b 2
2268.2.j.c 2
2268.2.j.d 2
2268.2.j.e 2
2268.2.j.f 2
2268.2.j.g 2
2268.2.j.h 2
2268.2.j.i 2
2268.2.j.j 2
2268.2.j.k 2
2268.2.j.l 2
2268.2.j.m 2
2268.2.j.n 2
2268.2.j.o 4
2268.2.j.p 4
2268.2.j.q 4
2268.2.j.r 8
2268.2.k $$\chi_{2268}(1297, \cdot)$$ 2268.2.k.a 2 2
2268.2.k.b 2
2268.2.k.c 8
2268.2.k.d 8
2268.2.k.e 14
2268.2.k.f 14
2268.2.k.g 16
2268.2.l $$\chi_{2268}(109, \cdot)$$ 2268.2.l.a 2 2
2268.2.l.b 2
2268.2.l.c 2
2268.2.l.d 2
2268.2.l.e 2
2268.2.l.f 2
2268.2.l.g 2
2268.2.l.h 2
2268.2.l.i 4
2268.2.l.j 6
2268.2.l.k 6
2268.2.l.l 8
2268.2.l.m 8
2268.2.l.n 16
2268.2.n $$\chi_{2268}(1027, \cdot)$$ n/a 376 2
2268.2.o $$\chi_{2268}(107, \cdot)$$ n/a 376 2
2268.2.t $$\chi_{2268}(1781, \cdot)$$ 2268.2.t.a 16 2
2268.2.t.b 16
2268.2.t.c 32
2268.2.w $$\chi_{2268}(269, \cdot)$$ 2268.2.w.a 2 2
2268.2.w.b 2
2268.2.w.c 2
2268.2.w.d 2
2268.2.w.e 2
2268.2.w.f 2
2268.2.w.g 4
2268.2.w.h 4
2268.2.w.i 12
2268.2.w.j 32
2268.2.x $$\chi_{2268}(377, \cdot)$$ 2268.2.x.a 2 2
2268.2.x.b 2
2268.2.x.c 2
2268.2.x.d 2
2268.2.x.e 2
2268.2.x.f 2
2268.2.x.g 2
2268.2.x.h 2
2268.2.x.i 8
2268.2.x.j 8
2268.2.x.k 32
2268.2.ba $$\chi_{2268}(1079, \cdot)$$ n/a 288 2
2268.2.bb $$\chi_{2268}(431, \cdot)$$ n/a 376 2
2268.2.be $$\chi_{2268}(1619, \cdot)$$ n/a 368 2
2268.2.bf $$\chi_{2268}(1459, \cdot)$$ n/a 368 2
2268.2.bi $$\chi_{2268}(55, \cdot)$$ n/a 376 2
2268.2.bj $$\chi_{2268}(271, \cdot)$$ n/a 376 2
2268.2.bm $$\chi_{2268}(593, \cdot)$$ 2268.2.bm.a 2 2
2268.2.bm.b 2
2268.2.bm.c 2
2268.2.bm.d 2
2268.2.bm.e 2
2268.2.bm.f 2
2268.2.bm.g 4
2268.2.bm.h 4
2268.2.bm.i 12
2268.2.bm.j 32
2268.2.bo $$\chi_{2268}(253, \cdot)$$ n/a 108 6
2268.2.bp $$\chi_{2268}(289, \cdot)$$ n/a 144 6
2268.2.bq $$\chi_{2268}(37, \cdot)$$ n/a 144 6
2268.2.bs $$\chi_{2268}(611, \cdot)$$ n/a 840 6
2268.2.bt $$\chi_{2268}(451, \cdot)$$ n/a 840 6
2268.2.bx $$\chi_{2268}(125, \cdot)$$ n/a 144 6
2268.2.ca $$\chi_{2268}(17, \cdot)$$ n/a 144 6
2268.2.cc $$\chi_{2268}(307, \cdot)$$ n/a 840 6
2268.2.cd $$\chi_{2268}(19, \cdot)$$ n/a 840 6
2268.2.cf $$\chi_{2268}(71, \cdot)$$ n/a 648 6
2268.2.ci $$\chi_{2268}(179, \cdot)$$ n/a 840 6
2268.2.ck $$\chi_{2268}(341, \cdot)$$ n/a 144 6
2268.2.cm $$\chi_{2268}(193, \cdot)$$ n/a 1296 18
2268.2.cn $$\chi_{2268}(85, \cdot)$$ n/a 972 18
2268.2.co $$\chi_{2268}(25, \cdot)$$ n/a 1296 18
2268.2.cr $$\chi_{2268}(5, \cdot)$$ n/a 1296 18
2268.2.cs $$\chi_{2268}(11, \cdot)$$ n/a 7704 18
2268.2.ct $$\chi_{2268}(139, \cdot)$$ n/a 7704 18
2268.2.cu $$\chi_{2268}(31, \cdot)$$ n/a 7704 18
2268.2.dd $$\chi_{2268}(155, \cdot)$$ n/a 5832 18
2268.2.de $$\chi_{2268}(95, \cdot)$$ n/a 7704 18
2268.2.df $$\chi_{2268}(173, \cdot)$$ n/a 1296 18
2268.2.dg $$\chi_{2268}(41, \cdot)$$ n/a 1296 18
2268.2.dh $$\chi_{2268}(103, \cdot)$$ n/a 7704 18

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2268))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2268)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(162))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(189))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(252))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(324))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(378))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(567))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(756))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1134))$$$$^{\oplus 2}$$