Properties

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

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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

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

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 \(\chi_{1155}(331, \cdot)\) n/a 104 2
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

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