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Properties

Label 2088.2
Level 2088
Weight 2
Dimension 53251
Nonzero newspaces 36
Sturm bound 483840
Trace bound 22

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Defining parameters

Level: \( N \) = \( 2088 = 2^{3} \cdot 3^{2} \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(483840\)
Trace bound: \(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2088))\).

Total New Old
Modular forms 123648 54223 69425
Cusp forms 118273 53251 65022
Eisenstein series 5375 972 4403

Trace form

\( 53251 q - 80 q^{2} - 106 q^{3} - 80 q^{4} - 8 q^{5} - 96 q^{6} - 80 q^{7} - 56 q^{8} - 206 q^{9} + O(q^{10}) \) \( 53251 q - 80 q^{2} - 106 q^{3} - 80 q^{4} - 8 q^{5} - 96 q^{6} - 80 q^{7} - 56 q^{8} - 206 q^{9} - 204 q^{10} - 50 q^{11} - 84 q^{12} + 4 q^{13} - 56 q^{14} - 64 q^{15} - 64 q^{16} - 128 q^{17} - 112 q^{18} - 208 q^{19} - 104 q^{20} + 24 q^{21} - 112 q^{22} - 48 q^{23} - 160 q^{24} - 152 q^{25} - 140 q^{26} - 112 q^{27} - 268 q^{28} - 6 q^{29} - 316 q^{30} - 52 q^{31} - 160 q^{32} - 210 q^{33} - 56 q^{34} - 156 q^{35} - 212 q^{36} - 12 q^{37} - 160 q^{38} - 184 q^{39} - 104 q^{40} - 158 q^{41} - 212 q^{42} - 134 q^{43} - 168 q^{44} - 4 q^{45} - 284 q^{46} - 196 q^{47} - 152 q^{48} - 120 q^{49} - 140 q^{50} - 130 q^{51} - 32 q^{52} - 35 q^{53} - 88 q^{54} - 332 q^{55} - 20 q^{56} - 166 q^{57} - 74 q^{58} - 198 q^{59} + 20 q^{60} - 40 q^{61} + 44 q^{62} - 176 q^{63} - 212 q^{64} - 163 q^{65} + 96 q^{66} - 90 q^{67} + 84 q^{68} - 44 q^{69} + 8 q^{70} - 128 q^{71} + 92 q^{72} - 491 q^{73} + 136 q^{74} - 210 q^{75} - 16 q^{76} - 24 q^{77} + 36 q^{78} - 76 q^{79} + 108 q^{80} - 246 q^{81} - 292 q^{82} - 148 q^{83} + 16 q^{84} - 16 q^{85} + 16 q^{86} - 130 q^{87} - 196 q^{88} - 212 q^{89} - 84 q^{90} - 300 q^{91} - 192 q^{92} + 20 q^{93} - 132 q^{94} - 212 q^{95} - 208 q^{96} - 249 q^{97} - 136 q^{98} - 172 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2088))\)

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
2088.2.a \(\chi_{2088}(1, \cdot)\) 2088.2.a.a 1 1
2088.2.a.b 1
2088.2.a.c 1
2088.2.a.d 1
2088.2.a.e 1
2088.2.a.f 1
2088.2.a.g 1
2088.2.a.h 1
2088.2.a.i 1
2088.2.a.j 1
2088.2.a.k 1
2088.2.a.l 1
2088.2.a.m 1
2088.2.a.n 2
2088.2.a.o 2
2088.2.a.p 2
2088.2.a.q 2
2088.2.a.r 2
2088.2.a.s 3
2088.2.a.t 3
2088.2.a.u 3
2088.2.a.v 3
2088.2.c \(\chi_{2088}(2087, \cdot)\) None 0 1
2088.2.e \(\chi_{2088}(1799, \cdot)\) None 0 1
2088.2.f \(\chi_{2088}(1045, \cdot)\) n/a 140 1
2088.2.h \(\chi_{2088}(1333, \cdot)\) n/a 148 1
2088.2.j \(\chi_{2088}(755, \cdot)\) n/a 112 1
2088.2.l \(\chi_{2088}(1043, \cdot)\) n/a 120 1
2088.2.o \(\chi_{2088}(289, \cdot)\) 2088.2.o.a 2 1
2088.2.o.b 2
2088.2.o.c 4
2088.2.o.d 6
2088.2.o.e 8
2088.2.o.f 16
2088.2.q \(\chi_{2088}(697, \cdot)\) n/a 168 2
2088.2.r \(\chi_{2088}(1351, \cdot)\) None 0 2
2088.2.u \(\chi_{2088}(1061, \cdot)\) n/a 240 2
2088.2.w \(\chi_{2088}(307, \cdot)\) n/a 296 2
2088.2.x \(\chi_{2088}(17, \cdot)\) 2088.2.x.a 28 2
2088.2.x.b 32
2088.2.ba \(\chi_{2088}(985, \cdot)\) n/a 180 2
2088.2.bd \(\chi_{2088}(347, \cdot)\) n/a 712 2
2088.2.bf \(\chi_{2088}(59, \cdot)\) n/a 672 2
2088.2.bh \(\chi_{2088}(637, \cdot)\) n/a 712 2
2088.2.bj \(\chi_{2088}(349, \cdot)\) n/a 672 2
2088.2.bk \(\chi_{2088}(407, \cdot)\) None 0 2
2088.2.bm \(\chi_{2088}(695, \cdot)\) None 0 2
2088.2.bo \(\chi_{2088}(721, \cdot)\) n/a 222 6
2088.2.bq \(\chi_{2088}(41, \cdot)\) n/a 360 4
2088.2.br \(\chi_{2088}(331, \cdot)\) n/a 1424 4
2088.2.bt \(\chi_{2088}(365, \cdot)\) n/a 1424 4
2088.2.bw \(\chi_{2088}(655, \cdot)\) None 0 4
2088.2.by \(\chi_{2088}(361, \cdot)\) n/a 228 6
2088.2.cb \(\chi_{2088}(35, \cdot)\) n/a 720 6
2088.2.cd \(\chi_{2088}(107, \cdot)\) n/a 720 6
2088.2.cf \(\chi_{2088}(109, \cdot)\) n/a 888 6
2088.2.ch \(\chi_{2088}(181, \cdot)\) n/a 888 6
2088.2.ci \(\chi_{2088}(431, \cdot)\) None 0 6
2088.2.ck \(\chi_{2088}(71, \cdot)\) None 0 6
2088.2.cm \(\chi_{2088}(25, \cdot)\) n/a 1080 12
2088.2.co \(\chi_{2088}(89, \cdot)\) n/a 360 12
2088.2.cp \(\chi_{2088}(19, \cdot)\) n/a 1776 12
2088.2.cr \(\chi_{2088}(269, \cdot)\) n/a 1440 12
2088.2.cu \(\chi_{2088}(55, \cdot)\) None 0 12
2088.2.cw \(\chi_{2088}(167, \cdot)\) None 0 12
2088.2.cy \(\chi_{2088}(23, \cdot)\) None 0 12
2088.2.cz \(\chi_{2088}(277, \cdot)\) n/a 4272 12
2088.2.db \(\chi_{2088}(13, \cdot)\) n/a 4272 12
2088.2.dd \(\chi_{2088}(83, \cdot)\) n/a 4272 12
2088.2.df \(\chi_{2088}(299, \cdot)\) n/a 4272 12
2088.2.di \(\chi_{2088}(121, \cdot)\) n/a 1080 12
2088.2.dk \(\chi_{2088}(31, \cdot)\) None 0 24
2088.2.dn \(\chi_{2088}(77, \cdot)\) n/a 8544 24
2088.2.dp \(\chi_{2088}(43, \cdot)\) n/a 8544 24
2088.2.dq \(\chi_{2088}(113, \cdot)\) n/a 2160 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2088))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2088)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(348))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(522))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(696))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1044))\)\(^{\oplus 2}\)