## Defining parameters

 Level: $$N$$ = $$891 = 3^{4} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Newform subspaces: $$89$$ Sturm bound: $$116640$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(891))$$.

Total New Old
Modular forms 30240 23160 7080
Cusp forms 28081 22152 5929
Eisenstein series 2159 1008 1151

## Trace form

 $$22152 q - 96 q^{2} - 144 q^{3} - 156 q^{4} - 90 q^{5} - 144 q^{6} - 154 q^{7} - 72 q^{8} - 144 q^{9} + O(q^{10})$$ $$22152 q - 96 q^{2} - 144 q^{3} - 156 q^{4} - 90 q^{5} - 144 q^{6} - 154 q^{7} - 72 q^{8} - 144 q^{9} - 212 q^{10} - 99 q^{11} - 324 q^{12} - 142 q^{13} - 54 q^{14} - 144 q^{15} - 156 q^{16} - 66 q^{17} - 162 q^{18} - 244 q^{19} - 162 q^{20} - 198 q^{21} - 185 q^{22} - 282 q^{23} - 252 q^{24} - 180 q^{25} - 270 q^{26} - 198 q^{27} - 280 q^{28} - 150 q^{29} - 252 q^{30} - 178 q^{31} - 192 q^{32} - 189 q^{33} - 382 q^{34} - 114 q^{35} - 216 q^{36} - 208 q^{37} - 18 q^{38} - 144 q^{39} - 206 q^{40} - 90 q^{41} - 234 q^{42} - 154 q^{43} - 171 q^{44} - 432 q^{45} - 320 q^{46} - 222 q^{47} - 342 q^{48} - 200 q^{49} - 384 q^{50} - 270 q^{51} - 238 q^{52} - 246 q^{53} - 396 q^{54} - 305 q^{55} - 558 q^{56} - 252 q^{57} - 206 q^{58} - 234 q^{59} - 378 q^{60} - 190 q^{61} - 306 q^{62} - 252 q^{63} - 298 q^{64} - 114 q^{65} - 162 q^{66} - 378 q^{67} + 96 q^{68} - 36 q^{69} - 242 q^{70} + 114 q^{71} + 288 q^{72} - 154 q^{73} + 270 q^{74} + 36 q^{75} - 202 q^{76} + 57 q^{77} - 90 q^{78} - 154 q^{79} + 300 q^{80} - 380 q^{82} + 48 q^{83} + 306 q^{84} - 338 q^{85} + 96 q^{86} + 144 q^{87} - 473 q^{88} - 210 q^{89} + 18 q^{90} - 342 q^{91} - 270 q^{92} - 180 q^{93} - 482 q^{94} - 462 q^{95} - 126 q^{96} - 382 q^{97} - 672 q^{98} - 234 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(891))$$

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
891.2.a $$\chi_{891}(1, \cdot)$$ 891.2.a.a 1 1
891.2.a.b 1
891.2.a.c 1
891.2.a.d 1
891.2.a.e 1
891.2.a.f 1
891.2.a.g 1
891.2.a.h 1
891.2.a.i 2
891.2.a.j 2
891.2.a.k 3
891.2.a.l 3
891.2.a.m 3
891.2.a.n 3
891.2.a.o 4
891.2.a.p 4
891.2.a.q 4
891.2.a.r 4
891.2.d $$\chi_{891}(890, \cdot)$$ 891.2.d.a 4 1
891.2.d.b 16
891.2.d.c 24
891.2.e $$\chi_{891}(298, \cdot)$$ 891.2.e.a 2 2
891.2.e.b 2
891.2.e.c 2
891.2.e.d 2
891.2.e.e 2
891.2.e.f 2
891.2.e.g 2
891.2.e.h 2
891.2.e.i 2
891.2.e.j 2
891.2.e.k 2
891.2.e.l 2
891.2.e.m 4
891.2.e.n 4
891.2.e.o 4
891.2.e.p 4
891.2.e.q 6
891.2.e.r 6
891.2.e.s 6
891.2.e.t 6
891.2.e.u 8
891.2.e.v 8
891.2.f $$\chi_{891}(82, \cdot)$$ 891.2.f.a 4 4
891.2.f.b 4
891.2.f.c 24
891.2.f.d 24
891.2.f.e 36
891.2.f.f 36
891.2.f.g 48
891.2.g $$\chi_{891}(296, \cdot)$$ 891.2.g.a 4 2
891.2.g.b 8
891.2.g.c 8
891.2.g.d 8
891.2.g.e 16
891.2.g.f 48
891.2.j $$\chi_{891}(100, \cdot)$$ 891.2.j.a 6 6
891.2.j.b 72
891.2.j.c 102
891.2.k $$\chi_{891}(161, \cdot)$$ 891.2.k.a 80 4
891.2.k.b 96
891.2.n $$\chi_{891}(136, \cdot)$$ 891.2.n.a 8 8
891.2.n.b 8
891.2.n.c 8
891.2.n.d 8
891.2.n.e 16
891.2.n.f 32
891.2.n.g 32
891.2.n.h 32
891.2.n.i 32
891.2.n.j 48
891.2.n.k 48
891.2.n.l 96
891.2.o $$\chi_{891}(98, \cdot)$$ 891.2.o.a 12 6
891.2.o.b 192
891.2.r $$\chi_{891}(34, \cdot)$$ 891.2.r.a 774 18
891.2.r.b 846
891.2.u $$\chi_{891}(107, \cdot)$$ 891.2.u.a 16 8
891.2.u.b 32
891.2.u.c 32
891.2.u.d 32
891.2.u.e 64
891.2.u.f 192
891.2.v $$\chi_{891}(37, \cdot)$$ 891.2.v.a 816 24
891.2.y $$\chi_{891}(32, \cdot)$$ 891.2.y.a 36 18
891.2.y.b 1872
891.2.bb $$\chi_{891}(8, \cdot)$$ 891.2.bb.a 816 24
891.2.bc $$\chi_{891}(4, \cdot)$$ 891.2.bc.a 7632 72
891.2.bd $$\chi_{891}(2, \cdot)$$ 891.2.bd.a 7632 72

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(891))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(891)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(297))$$$$^{\oplus 2}$$