# Properties

 Label 1155.2 Level 1155 Weight 2 Dimension 29305 Nonzero newspaces 48 Sturm bound 184320 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$1155 = 3 \cdot 5 \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$184320$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1155))$$.

Total New Old
Modular forms 48000 30393 17607
Cusp forms 44161 29305 14856
Eisenstein series 3839 1088 2751

## Trace form

 $$29305 q - 13 q^{2} - 31 q^{3} - 49 q^{4} + 13 q^{5} - 33 q^{6} - 39 q^{7} + 119 q^{8} + 41 q^{9} + O(q^{10})$$ $$29305 q - 13 q^{2} - 31 q^{3} - 49 q^{4} + 13 q^{5} - 33 q^{6} - 39 q^{7} + 119 q^{8} + 41 q^{9} + 23 q^{10} + 45 q^{11} + 47 q^{12} + 14 q^{13} + 111 q^{14} - 69 q^{15} + 119 q^{16} + 122 q^{17} + 31 q^{18} + 100 q^{19} + 147 q^{20} - 51 q^{21} + 75 q^{22} + 104 q^{23} + 3 q^{24} + 33 q^{25} + 154 q^{26} - 139 q^{27} + 15 q^{28} + 30 q^{29} - 127 q^{30} - 104 q^{31} - 153 q^{32} - 107 q^{33} - 122 q^{34} - 35 q^{35} - 409 q^{36} - 10 q^{37} + 28 q^{38} - 14 q^{39} - 325 q^{40} + 154 q^{41} - 137 q^{42} - 36 q^{43} + 39 q^{44} - 65 q^{45} + 32 q^{46} + 96 q^{47} - 181 q^{48} + 33 q^{49} + 7 q^{50} - 26 q^{51} - 262 q^{52} + 30 q^{53} - 81 q^{54} - 263 q^{55} - 89 q^{56} - 228 q^{57} - 622 q^{58} - 172 q^{59} - 647 q^{60} - 618 q^{61} - 512 q^{62} - 251 q^{63} - 1217 q^{64} - 458 q^{65} - 905 q^{66} - 668 q^{67} - 1026 q^{68} - 548 q^{69} - 941 q^{70} - 440 q^{71} - 909 q^{72} - 422 q^{73} - 542 q^{74} - 343 q^{75} - 1156 q^{76} - 275 q^{77} - 662 q^{78} - 184 q^{79} - 349 q^{80} - 543 q^{81} - 394 q^{82} + 100 q^{83} - 665 q^{84} - 182 q^{85} - 260 q^{86} - 18 q^{87} - 313 q^{88} + 26 q^{89} - 303 q^{90} - 218 q^{91} - 32 q^{92} - 12 q^{93} - 72 q^{94} + 104 q^{95} - 421 q^{96} + 98 q^{97} + 331 q^{98} - 267 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1155))$$

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
1155.2.a $$\chi_{1155}(1, \cdot)$$ 1155.2.a.a 1 1
1155.2.a.b 1
1155.2.a.c 1
1155.2.a.d 1
1155.2.a.e 1
1155.2.a.f 1
1155.2.a.g 1
1155.2.a.h 1
1155.2.a.i 1
1155.2.a.j 1
1155.2.a.k 1
1155.2.a.l 1
1155.2.a.m 1
1155.2.a.n 1
1155.2.a.o 2
1155.2.a.p 2
1155.2.a.q 2
1155.2.a.r 2
1155.2.a.s 3
1155.2.a.t 3
1155.2.a.u 4
1155.2.a.v 4
1155.2.a.w 5
1155.2.c $$\chi_{1155}(694, \cdot)$$ 1155.2.c.a 2 1
1155.2.c.b 2
1155.2.c.c 6
1155.2.c.d 6
1155.2.c.e 20
1155.2.c.f 20
1155.2.d $$\chi_{1155}(881, \cdot)$$ n/a 104 1
1155.2.f $$\chi_{1155}(659, \cdot)$$ n/a 144 1
1155.2.i $$\chi_{1155}(76, \cdot)$$ 1155.2.i.a 8 1
1155.2.i.b 8
1155.2.i.c 16
1155.2.i.d 32
1155.2.k $$\chi_{1155}(769, \cdot)$$ 1155.2.k.a 48 1
1155.2.k.b 48
1155.2.l $$\chi_{1155}(1121, \cdot)$$ 1155.2.l.a 4 1
1155.2.l.b 4
1155.2.l.c 4
1155.2.l.d 4
1155.2.l.e 40
1155.2.l.f 40
1155.2.n $$\chi_{1155}(419, \cdot)$$ n/a 160 1
1155.2.q $$\chi_{1155}(331, \cdot)$$ 1155.2.q.a 2 2
1155.2.q.b 2
1155.2.q.c 2
1155.2.q.d 2
1155.2.q.e 2
1155.2.q.f 4
1155.2.q.g 10
1155.2.q.h 12
1155.2.q.i 14
1155.2.q.j 16
1155.2.q.k 18
1155.2.q.l 20
1155.2.s $$\chi_{1155}(617, \cdot)$$ n/a 240 2
1155.2.t $$\chi_{1155}(692, \cdot)$$ n/a 368 2
1155.2.v $$\chi_{1155}(727, \cdot)$$ n/a 160 2
1155.2.y $$\chi_{1155}(43, \cdot)$$ n/a 144 2
1155.2.z $$\chi_{1155}(421, \cdot)$$ n/a 192 4
1155.2.bb $$\chi_{1155}(296, \cdot)$$ n/a 256 2
1155.2.bc $$\chi_{1155}(439, \cdot)$$ n/a 192 2
1155.2.bg $$\chi_{1155}(89, \cdot)$$ n/a 320 2
1155.2.bi $$\chi_{1155}(551, \cdot)$$ n/a 216 2
1155.2.bj $$\chi_{1155}(529, \cdot)$$ n/a 160 2
1155.2.bl $$\chi_{1155}(241, \cdot)$$ n/a 128 2
1155.2.bo $$\chi_{1155}(494, \cdot)$$ n/a 368 2
1155.2.br $$\chi_{1155}(104, \cdot)$$ n/a 736 4
1155.2.bt $$\chi_{1155}(281, \cdot)$$ n/a 384 4
1155.2.bu $$\chi_{1155}(139, \cdot)$$ n/a 384 4
1155.2.bw $$\chi_{1155}(391, \cdot)$$ n/a 256 4
1155.2.bz $$\chi_{1155}(29, \cdot)$$ n/a 576 4
1155.2.cb $$\chi_{1155}(146, \cdot)$$ n/a 512 4
1155.2.cc $$\chi_{1155}(64, \cdot)$$ n/a 288 4
1155.2.ce $$\chi_{1155}(142, \cdot)$$ n/a 384 4
1155.2.ch $$\chi_{1155}(397, \cdot)$$ n/a 320 4
1155.2.cj $$\chi_{1155}(362, \cdot)$$ n/a 736 4
1155.2.ck $$\chi_{1155}(23, \cdot)$$ n/a 640 4
1155.2.cm $$\chi_{1155}(16, \cdot)$$ n/a 512 8
1155.2.cn $$\chi_{1155}(127, \cdot)$$ n/a 576 8
1155.2.cq $$\chi_{1155}(97, \cdot)$$ n/a 768 8
1155.2.cs $$\chi_{1155}(62, \cdot)$$ n/a 1472 8
1155.2.ct $$\chi_{1155}(92, \cdot)$$ n/a 1152 8
1155.2.cv $$\chi_{1155}(74, \cdot)$$ n/a 1472 8
1155.2.cy $$\chi_{1155}(61, \cdot)$$ n/a 512 8
1155.2.da $$\chi_{1155}(4, \cdot)$$ n/a 768 8
1155.2.db $$\chi_{1155}(26, \cdot)$$ n/a 1024 8
1155.2.dd $$\chi_{1155}(59, \cdot)$$ n/a 1472 8
1155.2.dh $$\chi_{1155}(19, \cdot)$$ n/a 768 8
1155.2.di $$\chi_{1155}(116, \cdot)$$ n/a 1024 8
1155.2.dl $$\chi_{1155}(53, \cdot)$$ n/a 2944 16
1155.2.dm $$\chi_{1155}(17, \cdot)$$ n/a 2944 16
1155.2.do $$\chi_{1155}(82, \cdot)$$ n/a 1536 16
1155.2.dr $$\chi_{1155}(172, \cdot)$$ n/a 1536 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1155))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1155)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(385))$$$$^{\oplus 2}$$