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Properties

Label 3339.2
Level 3339
Weight 2
Dimension 304260
Nonzero newspaces 60
Sturm bound 1617408
Trace bound 9

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Defining parameters

Level: \( N \) = \( 3339 = 3^{2} \cdot 7 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(1617408\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3339))\).

Total New Old
Modular forms 409344 308852 100492
Cusp forms 399361 304260 95101
Eisenstein series 9983 4592 5391

Trace form

\( 304260 q - 294 q^{2} - 392 q^{3} - 286 q^{4} - 288 q^{5} - 392 q^{6} - 364 q^{7} - 726 q^{8} - 392 q^{9} + O(q^{10}) \) \( 304260 q - 294 q^{2} - 392 q^{3} - 286 q^{4} - 288 q^{5} - 392 q^{6} - 364 q^{7} - 726 q^{8} - 392 q^{9} - 852 q^{10} - 276 q^{11} - 416 q^{12} - 280 q^{13} - 384 q^{14} - 1016 q^{15} - 318 q^{16} - 336 q^{17} - 440 q^{18} - 904 q^{19} - 384 q^{20} - 532 q^{21} - 780 q^{22} - 324 q^{23} - 464 q^{24} - 294 q^{25} - 360 q^{26} - 428 q^{27} - 1104 q^{28} - 744 q^{29} - 476 q^{30} - 292 q^{31} - 390 q^{32} - 440 q^{33} - 336 q^{34} - 438 q^{35} - 1112 q^{36} - 908 q^{37} - 420 q^{38} - 464 q^{39} - 330 q^{40} - 380 q^{41} - 628 q^{42} - 660 q^{43} - 236 q^{44} - 488 q^{45} - 880 q^{46} - 296 q^{47} - 368 q^{48} - 344 q^{49} - 528 q^{50} - 392 q^{51} + 36 q^{52} - 114 q^{53} - 748 q^{54} - 684 q^{55} - 60 q^{56} - 896 q^{57} - 6 q^{58} - 16 q^{59} - 188 q^{60} - 216 q^{61} + 104 q^{62} - 328 q^{63} - 1878 q^{64} - 64 q^{65} - 308 q^{66} - 236 q^{67} + 6 q^{68} - 344 q^{69} - 438 q^{70} - 756 q^{71} - 284 q^{72} - 964 q^{73} - 336 q^{74} - 416 q^{75} - 388 q^{76} - 462 q^{77} - 1064 q^{78} - 384 q^{79} - 384 q^{80} - 560 q^{81} - 972 q^{82} - 444 q^{83} - 784 q^{84} - 828 q^{85} - 564 q^{86} - 572 q^{87} - 208 q^{88} - 446 q^{89} - 716 q^{90} - 1142 q^{91} - 576 q^{92} - 620 q^{93} + 132 q^{94} - 332 q^{95} - 752 q^{96} + 18 q^{97} - 610 q^{98} - 1184 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3339))\)

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
3339.2.a \(\chi_{3339}(1, \cdot)\) 3339.2.a.a 1 1
3339.2.a.b 1
3339.2.a.c 1
3339.2.a.d 1
3339.2.a.e 1
3339.2.a.f 1
3339.2.a.g 1
3339.2.a.h 2
3339.2.a.i 2
3339.2.a.j 2
3339.2.a.k 3
3339.2.a.l 3
3339.2.a.m 3
3339.2.a.n 3
3339.2.a.o 4
3339.2.a.p 4
3339.2.a.q 4
3339.2.a.r 4
3339.2.a.s 5
3339.2.a.t 5
3339.2.a.u 7
3339.2.a.v 9
3339.2.a.w 11
3339.2.a.x 13
3339.2.a.y 13
3339.2.a.z 13
3339.2.a.ba 13
3339.2.c \(\chi_{3339}(1324, \cdot)\) n/a 134 1
3339.2.d \(\chi_{3339}(2015, \cdot)\) n/a 136 1
3339.2.f \(\chi_{3339}(3338, \cdot)\) n/a 144 1
3339.2.i \(\chi_{3339}(478, \cdot)\) n/a 348 2
3339.2.j \(\chi_{3339}(1114, \cdot)\) n/a 624 2
3339.2.k \(\chi_{3339}(319, \cdot)\) n/a 832 2
3339.2.l \(\chi_{3339}(2545, \cdot)\) n/a 832 2
3339.2.m \(\chi_{3339}(1189, \cdot)\) n/a 356 2
3339.2.p \(\chi_{3339}(1772, \cdot)\) n/a 216 2
3339.2.r \(\chi_{3339}(2651, \cdot)\) n/a 832 2
3339.2.s \(\chi_{3339}(529, \cdot)\) n/a 856 2
3339.2.u \(\chi_{3339}(1748, \cdot)\) n/a 856 2
3339.2.z \(\chi_{3339}(1112, \cdot)\) n/a 856 2
3339.2.bb \(\chi_{3339}(1907, \cdot)\) n/a 288 2
3339.2.be \(\chi_{3339}(1642, \cdot)\) n/a 856 2
3339.2.bg \(\chi_{3339}(902, \cdot)\) n/a 832 2
3339.2.bi \(\chi_{3339}(584, \cdot)\) n/a 280 2
3339.2.bj \(\chi_{3339}(1801, \cdot)\) n/a 356 2
3339.2.bl \(\chi_{3339}(211, \cdot)\) n/a 648 2
3339.2.bn \(\chi_{3339}(425, \cdot)\) n/a 832 2
3339.2.br \(\chi_{3339}(635, \cdot)\) n/a 856 2
3339.2.bs \(\chi_{3339}(23, \cdot)\) n/a 1712 4
3339.2.bv \(\chi_{3339}(871, \cdot)\) n/a 1712 4
3339.2.bx \(\chi_{3339}(76, \cdot)\) n/a 1712 4
3339.2.bz \(\chi_{3339}(242, \cdot)\) n/a 576 4
3339.2.cb \(\chi_{3339}(977, \cdot)\) n/a 1712 4
3339.2.cc \(\chi_{3339}(1825, \cdot)\) n/a 1712 4
3339.2.ce \(\chi_{3339}(136, \cdot)\) n/a 712 4
3339.2.cg \(\chi_{3339}(659, \cdot)\) n/a 1296 4
3339.2.ci \(\chi_{3339}(505, \cdot)\) n/a 1632 12
3339.2.cl \(\chi_{3339}(62, \cdot)\) n/a 1728 12
3339.2.cn \(\chi_{3339}(314, \cdot)\) n/a 1728 12
3339.2.co \(\chi_{3339}(64, \cdot)\) n/a 1608 12
3339.2.cq \(\chi_{3339}(121, \cdot)\) n/a 10272 24
3339.2.cr \(\chi_{3339}(16, \cdot)\) n/a 10272 24
3339.2.cs \(\chi_{3339}(148, \cdot)\) n/a 7776 24
3339.2.ct \(\chi_{3339}(46, \cdot)\) n/a 4272 24
3339.2.cu \(\chi_{3339}(8, \cdot)\) n/a 2592 24
3339.2.cx \(\chi_{3339}(55, \cdot)\) n/a 4272 24
3339.2.cy \(\chi_{3339}(38, \cdot)\) n/a 10272 24
3339.2.dc \(\chi_{3339}(47, \cdot)\) n/a 10272 24
3339.2.de \(\chi_{3339}(43, \cdot)\) n/a 7776 24
3339.2.dg \(\chi_{3339}(37, \cdot)\) n/a 4272 24
3339.2.dh \(\chi_{3339}(89, \cdot)\) n/a 3456 24
3339.2.dj \(\chi_{3339}(293, \cdot)\) n/a 10272 24
3339.2.dl \(\chi_{3339}(4, \cdot)\) n/a 10272 24
3339.2.do \(\chi_{3339}(17, \cdot)\) n/a 3456 24
3339.2.dq \(\chi_{3339}(146, \cdot)\) n/a 10272 24
3339.2.dv \(\chi_{3339}(59, \cdot)\) n/a 10272 24
3339.2.dx \(\chi_{3339}(25, \cdot)\) n/a 10272 24
3339.2.dy \(\chi_{3339}(68, \cdot)\) n/a 10272 24
3339.2.eb \(\chi_{3339}(50, \cdot)\) n/a 15552 48
3339.2.ed \(\chi_{3339}(19, \cdot)\) n/a 8544 48
3339.2.ef \(\chi_{3339}(31, \cdot)\) n/a 20544 48
3339.2.eg \(\chi_{3339}(2, \cdot)\) n/a 20544 48
3339.2.ei \(\chi_{3339}(179, \cdot)\) n/a 6912 48
3339.2.ek \(\chi_{3339}(34, \cdot)\) n/a 20544 48
3339.2.em \(\chi_{3339}(103, \cdot)\) n/a 20544 48
3339.2.ep \(\chi_{3339}(74, \cdot)\) n/a 20544 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3339))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3339)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(159))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(371))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(477))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1113))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3339))\)\(^{\oplus 1}\)