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Properties

Label 3201.2
Level 3201
Weight 2
Dimension 275771
Nonzero newspaces 48
Sturm bound 1505280
Trace bound 10

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Defining parameters

Level: \( N \) = \( 3201 = 3 \cdot 11 \cdot 97 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(1505280\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3201))\).

Total New Old
Modular forms 380160 279187 100973
Cusp forms 372481 275771 96710
Eisenstein series 7679 3416 4263

Trace form

\( 275771 q + 9 q^{2} - 371 q^{3} - 727 q^{4} + 18 q^{5} - 375 q^{6} - 744 q^{7} + 5 q^{8} - 391 q^{9} + O(q^{10}) \) \( 275771 q + 9 q^{2} - 371 q^{3} - 727 q^{4} + 18 q^{5} - 375 q^{6} - 744 q^{7} + 5 q^{8} - 391 q^{9} - 754 q^{10} + 3 q^{11} - 863 q^{12} - 726 q^{13} + 12 q^{14} - 396 q^{15} - 775 q^{16} - 6 q^{17} - 395 q^{18} - 748 q^{19} + 26 q^{20} - 400 q^{21} - 895 q^{22} + 32 q^{23} - 379 q^{24} - 735 q^{25} + 26 q^{26} - 341 q^{27} - 680 q^{28} + 50 q^{29} - 330 q^{30} - 692 q^{31} + 149 q^{32} - 379 q^{33} - 1606 q^{34} + 64 q^{35} - 363 q^{36} - 714 q^{37} + 80 q^{38} - 382 q^{39} - 698 q^{40} + 6 q^{41} - 372 q^{42} - 756 q^{43} - 59 q^{44} - 916 q^{45} - 792 q^{46} + 4 q^{47} - 431 q^{48} - 797 q^{49} + 59 q^{50} - 430 q^{51} - 714 q^{52} + 22 q^{53} - 395 q^{54} - 866 q^{55} + 120 q^{56} - 304 q^{57} - 658 q^{58} + 120 q^{59} - 298 q^{60} - 662 q^{61} + 168 q^{62} - 320 q^{63} - 567 q^{64} + 132 q^{65} - 343 q^{66} - 1584 q^{67} + 178 q^{68} - 322 q^{69} - 616 q^{70} + 96 q^{71} - 319 q^{72} - 706 q^{73} + 162 q^{74} - 371 q^{75} - 708 q^{76} + 4 q^{77} - 818 q^{78} - 1024 q^{79} - 534 q^{80} - 391 q^{81} - 1358 q^{82} - 200 q^{83} - 1040 q^{84} - 1452 q^{85} - 1036 q^{86} - 606 q^{87} - 1683 q^{88} - 466 q^{89} - 546 q^{90} - 1784 q^{91} - 988 q^{92} - 854 q^{93} - 1384 q^{94} - 516 q^{95} - 1755 q^{96} - 1643 q^{97} - 695 q^{98} - 555 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3201))\)

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
3201.2.a \(\chi_{3201}(1, \cdot)\) 3201.2.a.a 1 1
3201.2.a.b 1
3201.2.a.c 1
3201.2.a.d 1
3201.2.a.e 1
3201.2.a.f 1
3201.2.a.g 1
3201.2.a.h 1
3201.2.a.i 2
3201.2.a.j 2
3201.2.a.k 2
3201.2.a.l 2
3201.2.a.m 2
3201.2.a.n 3
3201.2.a.o 7
3201.2.a.p 12
3201.2.a.q 13
3201.2.a.r 13
3201.2.a.s 13
3201.2.a.t 17
3201.2.a.u 19
3201.2.a.v 20
3201.2.a.w 24
3201.2.f \(\chi_{3201}(3103, \cdot)\) n/a 160 1
3201.2.g \(\chi_{3201}(98, \cdot)\) n/a 384 1
3201.2.h \(\chi_{3201}(3200, \cdot)\) n/a 388 1
3201.2.i \(\chi_{3201}(1684, \cdot)\) n/a 324 2
3201.2.j \(\chi_{3201}(560, \cdot)\) n/a 776 2
3201.2.k \(\chi_{3201}(463, \cdot)\) n/a 320 2
3201.2.n \(\chi_{3201}(874, \cdot)\) n/a 768 4
3201.2.o \(\chi_{3201}(230, \cdot)\) n/a 776 2
3201.2.p \(\chi_{3201}(1781, \cdot)\) n/a 776 2
3201.2.q \(\chi_{3201}(133, \cdot)\) n/a 324 2
3201.2.x \(\chi_{3201}(826, \cdot)\) n/a 640 4
3201.2.y \(\chi_{3201}(923, \cdot)\) n/a 1552 4
3201.2.z \(\chi_{3201}(1163, \cdot)\) n/a 1552 4
3201.2.ba \(\chi_{3201}(1262, \cdot)\) n/a 1536 4
3201.2.bb \(\chi_{3201}(775, \cdot)\) n/a 784 4
3201.2.bi \(\chi_{3201}(760, \cdot)\) n/a 648 4
3201.2.bj \(\chi_{3201}(857, \cdot)\) n/a 1552 4
3201.2.bk \(\chi_{3201}(229, \cdot)\) n/a 1568 8
3201.2.bn \(\chi_{3201}(758, \cdot)\) n/a 3104 8
3201.2.bo \(\chi_{3201}(661, \cdot)\) n/a 1312 8
3201.2.br \(\chi_{3201}(701, \cdot)\) n/a 3104 8
3201.2.bs \(\chi_{3201}(313, \cdot)\) n/a 1568 8
3201.2.bt \(\chi_{3201}(461, \cdot)\) n/a 3104 8
3201.2.bu \(\chi_{3201}(364, \cdot)\) n/a 1296 8
3201.2.cb \(\chi_{3201}(256, \cdot)\) n/a 1568 8
3201.2.cc \(\chi_{3201}(35, \cdot)\) n/a 3104 8
3201.2.cd \(\chi_{3201}(62, \cdot)\) n/a 3104 8
3201.2.ce \(\chi_{3201}(142, \cdot)\) n/a 3136 16
3201.2.cf \(\chi_{3201}(1112, \cdot)\) n/a 5248 16
3201.2.ci \(\chi_{3201}(64, \cdot)\) n/a 3136 16
3201.2.cj \(\chi_{3201}(50, \cdot)\) n/a 6208 16
3201.2.cm \(\chi_{3201}(100, \cdot)\) n/a 2656 16
3201.2.cn \(\chi_{3201}(32, \cdot)\) n/a 6208 16
3201.2.cq \(\chi_{3201}(16, \cdot)\) n/a 3136 16
3201.2.cr \(\chi_{3201}(200, \cdot)\) n/a 6208 16
3201.2.cu \(\chi_{3201}(70, \cdot)\) n/a 6272 32
3201.2.cv \(\chi_{3201}(8, \cdot)\) n/a 12416 32
3201.2.da \(\chi_{3201}(23, \cdot)\) n/a 10432 32
3201.2.db \(\chi_{3201}(10, \cdot)\) n/a 6272 32
3201.2.de \(\chi_{3201}(101, \cdot)\) n/a 12416 32
3201.2.df \(\chi_{3201}(4, \cdot)\) n/a 6272 32
3201.2.di \(\chi_{3201}(20, \cdot)\) n/a 24832 64
3201.2.dj \(\chi_{3201}(19, \cdot)\) n/a 12544 64
3201.2.dm \(\chi_{3201}(2, \cdot)\) n/a 24832 64
3201.2.dn \(\chi_{3201}(25, \cdot)\) n/a 12544 64
3201.2.do \(\chi_{3201}(7, \cdot)\) n/a 25088 128
3201.2.dp \(\chi_{3201}(5, \cdot)\) n/a 49664 128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3201))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3201)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(97))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(291))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1067))\)\(^{\oplus 2}\)