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Properties

Label 3179.2
Level 3179
Weight 2
Dimension 403082
Nonzero newspaces 20
Sturm bound 1664640
Trace bound 3

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Defining parameters

Level: \( N \) = \( 3179 = 11 \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(1664640\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3179))\).

Total New Old
Modular forms 420160 409714 10446
Cusp forms 412161 403082 9079
Eisenstein series 7999 6632 1367

Trace form

\( 403082 q - 959 q^{2} - 957 q^{3} - 951 q^{4} - 953 q^{5} - 946 q^{6} - 954 q^{7} - 945 q^{8} - 949 q^{9} + O(q^{10}) \) \( 403082 q - 959 q^{2} - 957 q^{3} - 951 q^{4} - 953 q^{5} - 946 q^{6} - 954 q^{7} - 945 q^{8} - 949 q^{9} - 960 q^{10} - 1094 q^{11} - 2230 q^{12} - 974 q^{13} - 996 q^{14} - 1033 q^{15} - 1077 q^{16} - 1040 q^{17} - 1941 q^{18} - 972 q^{19} - 1028 q^{20} - 1022 q^{21} - 1111 q^{22} - 2169 q^{23} - 1060 q^{24} - 1045 q^{25} - 1070 q^{26} - 1011 q^{27} - 1100 q^{28} - 1010 q^{29} - 1142 q^{30} - 1049 q^{31} - 1113 q^{32} - 1157 q^{33} - 2432 q^{34} - 1938 q^{35} - 1193 q^{36} - 1047 q^{37} - 1092 q^{38} - 1100 q^{39} - 1254 q^{40} - 1102 q^{41} - 1252 q^{42} - 1082 q^{43} - 1263 q^{44} - 2292 q^{45} - 1078 q^{46} - 1064 q^{47} - 1248 q^{48} - 1034 q^{49} - 1115 q^{50} - 1088 q^{51} - 2006 q^{52} - 1088 q^{53} - 1330 q^{54} - 1201 q^{55} - 2520 q^{56} - 1264 q^{57} - 1222 q^{58} - 1151 q^{59} - 1466 q^{60} - 1142 q^{61} - 1294 q^{62} - 1332 q^{63} - 1289 q^{64} - 1176 q^{65} - 1322 q^{66} - 2259 q^{67} - 1224 q^{68} - 2207 q^{69} - 1356 q^{70} - 1083 q^{71} - 1549 q^{72} - 1282 q^{73} - 1188 q^{74} - 1344 q^{75} - 1300 q^{76} - 1234 q^{77} - 2656 q^{78} - 1146 q^{79} - 1482 q^{80} - 1254 q^{81} - 1250 q^{82} - 1138 q^{83} - 1468 q^{84} - 1208 q^{85} - 2160 q^{86} - 1224 q^{87} - 1385 q^{88} - 2343 q^{89} - 1634 q^{90} - 1304 q^{91} - 1562 q^{92} - 1223 q^{93} - 1472 q^{94} - 1288 q^{95} - 1772 q^{96} - 1125 q^{97} - 1471 q^{98} - 1373 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3179))\)

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
3179.2.a \(\chi_{3179}(1, \cdot)\) 3179.2.a.a 1 1
3179.2.a.b 1
3179.2.a.c 1
3179.2.a.d 1
3179.2.a.e 1
3179.2.a.f 1
3179.2.a.g 1
3179.2.a.h 2
3179.2.a.i 2
3179.2.a.j 2
3179.2.a.k 2
3179.2.a.l 2
3179.2.a.m 2
3179.2.a.n 2
3179.2.a.o 2
3179.2.a.p 3
3179.2.a.q 3
3179.2.a.r 3
3179.2.a.s 3
3179.2.a.t 3
3179.2.a.u 3
3179.2.a.v 3
3179.2.a.w 4
3179.2.a.x 6
3179.2.a.y 6
3179.2.a.z 6
3179.2.a.ba 6
3179.2.a.bb 8
3179.2.a.bc 8
3179.2.a.bd 14
3179.2.a.be 14
3179.2.a.bf 27
3179.2.a.bg 27
3179.2.a.bh 28
3179.2.a.bi 28
3179.2.d \(\chi_{3179}(2311, \cdot)\) n/a 224 1
3179.2.e \(\chi_{3179}(540, \cdot)\) n/a 448 2
3179.2.g \(\chi_{3179}(290, \cdot)\) n/a 1024 4
3179.2.h \(\chi_{3179}(155, \cdot)\) n/a 904 4
3179.2.j \(\chi_{3179}(577, \cdot)\) n/a 1024 4
3179.2.m \(\chi_{3179}(65, \cdot)\) n/a 2048 8
3179.2.o \(\chi_{3179}(188, \cdot)\) n/a 4096 16
3179.2.q \(\chi_{3179}(38, \cdot)\) n/a 2048 8
3179.2.r \(\chi_{3179}(67, \cdot)\) n/a 4096 16
3179.2.v \(\chi_{3179}(179, \cdot)\) n/a 4096 16
3179.2.x \(\chi_{3179}(89, \cdot)\) n/a 8192 32
3179.2.z \(\chi_{3179}(40, \cdot)\) n/a 8192 32
3179.2.ba \(\chi_{3179}(69, \cdot)\) n/a 19456 64
3179.2.bc \(\chi_{3179}(100, \cdot)\) n/a 16256 64
3179.2.bf \(\chi_{3179}(16, \cdot)\) n/a 19456 64
3179.2.bh \(\chi_{3179}(10, \cdot)\) n/a 38912 128
3179.2.bi \(\chi_{3179}(4, \cdot)\) n/a 38912 128
3179.2.bk \(\chi_{3179}(9, \cdot)\) n/a 77824 256
3179.2.bm \(\chi_{3179}(6, \cdot)\) n/a 155648 512

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3179))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3179)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 2}\)