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Properties

Label 2669.2
Level 2669
Weight 2
Dimension 291371
Nonzero newspaces 40
Sturm bound 1183104
Trace bound 5

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Defining parameters

Level: \( N \) = \( 2669 = 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(1183104\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2669))\).

Total New Old
Modular forms 298272 296023 2249
Cusp forms 293281 291371 1910
Eisenstein series 4991 4652 339

Trace form

\( 291371 q - 1085 q^{2} - 1088 q^{3} - 1097 q^{4} - 1094 q^{5} - 1112 q^{6} - 1100 q^{7} - 1121 q^{8} - 1115 q^{9} + O(q^{10}) \) \( 291371 q - 1085 q^{2} - 1088 q^{3} - 1097 q^{4} - 1094 q^{5} - 1112 q^{6} - 1100 q^{7} - 1121 q^{8} - 1115 q^{9} - 1122 q^{10} - 1096 q^{11} - 1112 q^{12} - 1102 q^{13} - 1116 q^{14} - 1100 q^{15} - 1097 q^{16} - 1173 q^{17} - 2361 q^{18} - 1120 q^{19} - 1146 q^{20} - 1124 q^{21} - 1152 q^{22} - 1132 q^{23} - 1176 q^{24} - 1113 q^{25} - 1130 q^{26} - 1148 q^{27} - 1148 q^{28} - 1126 q^{29} - 1164 q^{30} - 1108 q^{31} - 1153 q^{32} - 1140 q^{33} - 1131 q^{34} - 2388 q^{35} - 1189 q^{36} - 1126 q^{37} - 1160 q^{38} - 1148 q^{39} - 1154 q^{40} - 1114 q^{41} - 1172 q^{42} - 1128 q^{43} - 1136 q^{44} - 1206 q^{45} - 1196 q^{46} - 1140 q^{47} - 1240 q^{48} - 1183 q^{49} - 1227 q^{50} - 1230 q^{51} - 2474 q^{52} - 1150 q^{53} - 1196 q^{54} - 1164 q^{55} - 1196 q^{56} - 1124 q^{57} - 1170 q^{58} - 1128 q^{59} - 1244 q^{60} - 1134 q^{61} - 1156 q^{62} - 1148 q^{63} - 1233 q^{64} - 1176 q^{65} - 1252 q^{66} - 1200 q^{67} - 1199 q^{68} - 2372 q^{69} - 1236 q^{70} - 1196 q^{71} - 1269 q^{72} - 1098 q^{73} - 1250 q^{74} - 1192 q^{75} - 1256 q^{76} - 1204 q^{77} - 1244 q^{78} - 1188 q^{79} - 1282 q^{80} - 1231 q^{81} - 1238 q^{82} - 1200 q^{83} - 1380 q^{84} - 1180 q^{85} - 2480 q^{86} - 1244 q^{87} - 1296 q^{88} - 1202 q^{89} - 1322 q^{90} - 1188 q^{91} - 1196 q^{92} - 1268 q^{93} - 1188 q^{94} - 1212 q^{95} - 1304 q^{96} - 1242 q^{97} - 1245 q^{98} - 1240 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2669))\)

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
2669.2.a \(\chi_{2669}(1, \cdot)\) 2669.2.a.a 44 1
2669.2.a.b 45
2669.2.a.c 60
2669.2.a.d 60
2669.2.b \(\chi_{2669}(2668, \cdot)\) n/a 236 1
2669.2.c \(\chi_{2669}(1412, \cdot)\) n/a 212 1
2669.2.d \(\chi_{2669}(1257, \cdot)\) n/a 234 1
2669.2.e \(\chi_{2669}(1582, \cdot)\) n/a 420 2
2669.2.f \(\chi_{2669}(472, \cdot)\) n/a 468 2
2669.2.k \(\chi_{2669}(1883, \cdot)\) n/a 472 2
2669.2.l \(\chi_{2669}(2211, \cdot)\) n/a 420 2
2669.2.m \(\chi_{2669}(798, \cdot)\) n/a 472 2
2669.2.n \(\chi_{2669}(169, \cdot)\) n/a 468 2
2669.2.p \(\chi_{2669}(627, \cdot)\) n/a 936 4
2669.2.q \(\chi_{2669}(315, \cdot)\) n/a 936 4
2669.2.s \(\chi_{2669}(2053, \cdot)\) n/a 936 4
2669.2.x \(\chi_{2669}(13, \cdot)\) n/a 944 4
2669.2.y \(\chi_{2669}(171, \cdot)\) n/a 2544 12
2669.2.ba \(\chi_{2669}(129, \cdot)\) n/a 1880 8
2669.2.bb \(\chi_{2669}(28, \cdot)\) n/a 1880 8
2669.2.be \(\chi_{2669}(144, \cdot)\) n/a 1888 8
2669.2.bf \(\chi_{2669}(145, \cdot)\) n/a 1872 8
2669.2.bh \(\chi_{2669}(16, \cdot)\) n/a 2808 12
2669.2.bi \(\chi_{2669}(239, \cdot)\) n/a 2544 12
2669.2.bj \(\chi_{2669}(118, \cdot)\) n/a 2832 12
2669.2.bk \(\chi_{2669}(35, \cdot)\) n/a 5040 24
2669.2.bm \(\chi_{2669}(207, \cdot)\) n/a 3760 16
2669.2.bn \(\chi_{2669}(22, \cdot)\) n/a 3760 16
2669.2.bp \(\chi_{2669}(4, \cdot)\) n/a 5664 24
2669.2.bu \(\chi_{2669}(310, \cdot)\) n/a 5616 24
2669.2.bv \(\chi_{2669}(560, \cdot)\) n/a 5616 24
2669.2.bw \(\chi_{2669}(33, \cdot)\) n/a 5664 24
2669.2.bx \(\chi_{2669}(86, \cdot)\) n/a 5040 24
2669.2.bz \(\chi_{2669}(93, \cdot)\) n/a 11328 48
2669.2.ca \(\chi_{2669}(49, \cdot)\) n/a 11232 48
2669.2.cc \(\chi_{2669}(140, \cdot)\) n/a 11328 48
2669.2.ch \(\chi_{2669}(30, \cdot)\) n/a 11232 48
2669.2.cj \(\chi_{2669}(41, \cdot)\) n/a 22560 96
2669.2.ck \(\chi_{2669}(7, \cdot)\) n/a 22560 96
2669.2.cn \(\chi_{2669}(25, \cdot)\) n/a 22464 96
2669.2.co \(\chi_{2669}(9, \cdot)\) n/a 22656 96
2669.2.cr \(\chi_{2669}(5, \cdot)\) n/a 45120 192
2669.2.cs \(\chi_{2669}(20, \cdot)\) n/a 45120 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2669))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2669)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(157))\)\(^{\oplus 2}\)