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Properties

Label 3283.2
Level 3283
Weight 2
Dimension 418720
Nonzero newspaces 40
Sturm bound 1759296
Trace bound 2

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Defining parameters

Level: \( N \) = \( 3283 = 7^{2} \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(1759296\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3283))\).

Total New Old
Modular forms 443784 425024 18760
Cusp forms 435865 418720 17145
Eisenstein series 7919 6304 1615

Trace form

\( 418720 q - 987 q^{2} - 989 q^{3} - 995 q^{4} - 993 q^{5} - 1005 q^{6} - 1160 q^{7} - 1767 q^{8} - 1007 q^{9} + O(q^{10}) \) \( 418720 q - 987 q^{2} - 989 q^{3} - 995 q^{4} - 993 q^{5} - 1005 q^{6} - 1160 q^{7} - 1767 q^{8} - 1007 q^{9} - 1017 q^{10} - 1005 q^{11} - 1037 q^{12} - 1009 q^{13} - 1188 q^{14} - 1785 q^{15} - 1043 q^{16} - 1017 q^{17} - 1059 q^{18} - 1021 q^{19} - 1065 q^{20} - 1202 q^{21} - 1809 q^{22} - 1029 q^{23} - 1101 q^{24} - 1043 q^{25} - 1065 q^{26} - 1061 q^{27} - 1244 q^{28} - 1797 q^{29} - 1125 q^{30} - 1045 q^{31} - 1107 q^{32} - 1077 q^{33} - 1089 q^{34} - 1230 q^{35} - 1811 q^{36} - 1001 q^{37} - 1017 q^{38} - 995 q^{39} - 909 q^{40} - 981 q^{41} - 1146 q^{42} - 1741 q^{43} - 897 q^{44} - 927 q^{45} - 873 q^{46} - 993 q^{47} - 879 q^{48} - 1076 q^{49} - 3099 q^{50} - 957 q^{51} - 913 q^{52} - 1038 q^{53} - 1068 q^{54} - 1014 q^{55} - 1104 q^{56} - 1890 q^{57} - 1125 q^{58} - 1083 q^{59} - 1329 q^{60} - 1139 q^{61} - 1155 q^{62} - 1272 q^{63} - 2177 q^{64} - 1281 q^{65} - 1566 q^{66} - 1136 q^{67} - 2388 q^{68} - 1239 q^{69} - 1398 q^{70} - 2013 q^{71} - 1701 q^{72} - 1272 q^{73} - 1275 q^{74} - 1361 q^{75} - 1525 q^{76} - 1314 q^{77} - 1989 q^{78} - 1218 q^{79} - 1425 q^{80} - 1154 q^{81} - 1122 q^{82} - 1014 q^{83} - 1076 q^{84} - 1785 q^{85} - 951 q^{86} - 885 q^{87} - 879 q^{88} - 993 q^{89} - 651 q^{90} - 1174 q^{91} - 1779 q^{92} - 733 q^{93} - 891 q^{94} - 885 q^{95} - 687 q^{96} - 967 q^{97} - 852 q^{98} - 3057 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3283))\)

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
3283.2.a \(\chi_{3283}(1, \cdot)\) 3283.2.a.a 1 1
3283.2.a.b 1
3283.2.a.c 1
3283.2.a.d 1
3283.2.a.e 1
3283.2.a.f 2
3283.2.a.g 2
3283.2.a.h 2
3283.2.a.i 2
3283.2.a.j 2
3283.2.a.k 2
3283.2.a.l 2
3283.2.a.m 3
3283.2.a.n 3
3283.2.a.o 4
3283.2.a.p 4
3283.2.a.q 4
3283.2.a.r 4
3283.2.a.s 5
3283.2.a.t 7
3283.2.a.u 9
3283.2.a.v 10
3283.2.a.w 14
3283.2.a.x 14
3283.2.a.y 18
3283.2.a.z 18
3283.2.a.ba 20
3283.2.a.bb 22
3283.2.a.bc 22
3283.2.a.bd 26
3283.2.c \(\chi_{3283}(3282, \cdot)\) n/a 224 1
3283.2.e \(\chi_{3283}(1243, \cdot)\) n/a 446 2
3283.2.f \(\chi_{3283}(1341, \cdot)\) n/a 440 2
3283.2.g \(\chi_{3283}(2843, \cdot)\) n/a 454 2
3283.2.h \(\chi_{3283}(900, \cdot)\) n/a 446 2
3283.2.i \(\chi_{3283}(901, \cdot)\) n/a 446 2
3283.2.o \(\chi_{3283}(803, \cdot)\) n/a 444 2
3283.2.p \(\chi_{3283}(1244, \cdot)\) n/a 446 2
3283.2.s \(\chi_{3283}(97, \cdot)\) n/a 444 2
3283.2.u \(\chi_{3283}(470, \cdot)\) n/a 1848 6
3283.2.v \(\chi_{3283}(148, \cdot)\) n/a 2280 10
3283.2.x \(\chi_{3283}(468, \cdot)\) n/a 1884 6
3283.2.z \(\chi_{3283}(37, \cdot)\) n/a 3780 12
3283.2.ba \(\chi_{3283}(29, \cdot)\) n/a 3792 12
3283.2.bb \(\chi_{3283}(135, \cdot)\) n/a 3696 12
3283.2.bc \(\chi_{3283}(163, \cdot)\) n/a 3780 12
3283.2.be \(\chi_{3283}(244, \cdot)\) n/a 2240 10
3283.2.bg \(\chi_{3283}(361, \cdot)\) n/a 4460 20
3283.2.bh \(\chi_{3283}(540, \cdot)\) n/a 4540 20
3283.2.bi \(\chi_{3283}(226, \cdot)\) n/a 4440 20
3283.2.bj \(\chi_{3283}(116, \cdot)\) n/a 4460 20
3283.2.bl \(\chi_{3283}(566, \cdot)\) n/a 3792 12
3283.2.bo \(\chi_{3283}(164, \cdot)\) n/a 3780 12
3283.2.bp \(\chi_{3283}(66, \cdot)\) n/a 3792 12
3283.2.bv \(\chi_{3283}(38, \cdot)\) n/a 3780 12
3283.2.bx \(\chi_{3283}(48, \cdot)\) n/a 4440 20
3283.2.ca \(\chi_{3283}(80, \cdot)\) n/a 4460 20
3283.2.cb \(\chi_{3283}(276, \cdot)\) n/a 4440 20
3283.2.ch \(\chi_{3283}(31, \cdot)\) n/a 4460 20
3283.2.ci \(\chi_{3283}(15, \cdot)\) n/a 18840 60
3283.2.ck \(\chi_{3283}(27, \cdot)\) n/a 18840 60
3283.2.cm \(\chi_{3283}(39, \cdot)\) n/a 37800 120
3283.2.cn \(\chi_{3283}(9, \cdot)\) n/a 37920 120
3283.2.co \(\chi_{3283}(36, \cdot)\) n/a 37920 120
3283.2.cp \(\chi_{3283}(4, \cdot)\) n/a 37800 120
3283.2.cq \(\chi_{3283}(61, \cdot)\) n/a 37800 120
3283.2.cw \(\chi_{3283}(3, \cdot)\) n/a 37920 120
3283.2.cx \(\chi_{3283}(12, \cdot)\) n/a 37800 120
3283.2.da \(\chi_{3283}(13, \cdot)\) n/a 37920 120

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3283))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3283)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(469))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3283))\)\(^{\oplus 1}\)