Properties

Label 2600.2
Level 2600
Weight 2
Dimension 102371
Nonzero newspaces 64
Sturm bound 806400
Trace bound 13

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Defining parameters

Level: N N = 2600=235213 2600 = 2^{3} \cdot 5^{2} \cdot 13
Weight: k k = 2 2
Nonzero newspaces: 64 64
Sturm bound: 806400806400
Trace bound: 1313

Dimensions

The following table gives the dimensions of various subspaces of M2(Γ1(2600))M_{2}(\Gamma_1(2600)).

Total New Old
Modular forms 205632 104175 101457
Cusp forms 197569 102371 95198
Eisenstein series 8063 1804 6259

Trace form

102371q132q2132q3132q42q5212q6148q7132q8284q9160q10228q1184q124q13240q14144q15148q16259q17+340q99+O(q100) 102371 q - 132 q^{2} - 132 q^{3} - 132 q^{4} - 2 q^{5} - 212 q^{6} - 148 q^{7} - 132 q^{8} - 284 q^{9} - 160 q^{10} - 228 q^{11} - 84 q^{12} - 4 q^{13} - 240 q^{14} - 144 q^{15} - 148 q^{16} - 259 q^{17}+ \cdots - 340 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(Γ1(2600))S_{2}^{\mathrm{new}}(\Gamma_1(2600))

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space Sknew(N,χ) S_k^{\mathrm{new}}(N, \chi) we list available newforms together with their dimension.

Label χ\chi Newforms Dimension χ\chi degree
2600.2.a χ2600(1,)\chi_{2600}(1, \cdot) 2600.2.a.a 1 1
2600.2.a.b 1
2600.2.a.c 1
2600.2.a.d 1
2600.2.a.e 1
2600.2.a.f 1
2600.2.a.g 1
2600.2.a.h 1
2600.2.a.i 1
2600.2.a.j 1
2600.2.a.k 1
2600.2.a.l 1
2600.2.a.m 1
2600.2.a.n 2
2600.2.a.o 2
2600.2.a.p 2
2600.2.a.q 2
2600.2.a.r 2
2600.2.a.s 2
2600.2.a.t 2
2600.2.a.u 2
2600.2.a.v 2
2600.2.a.w 2
2600.2.a.x 3
2600.2.a.y 3
2600.2.a.z 4
2600.2.a.ba 4
2600.2.a.bb 5
2600.2.a.bc 5
2600.2.d χ2600(1249,)\chi_{2600}(1249, \cdot) 2600.2.d.a 2 1
2600.2.d.b 2
2600.2.d.c 2
2600.2.d.d 2
2600.2.d.e 2
2600.2.d.f 2
2600.2.d.g 2
2600.2.d.h 4
2600.2.d.i 4
2600.2.d.j 4
2600.2.d.k 4
2600.2.d.l 4
2600.2.d.m 4
2600.2.d.n 4
2600.2.d.o 4
2600.2.d.p 8
2600.2.e χ2600(701,)\chi_{2600}(701, \cdot) n/a 260 1
2600.2.f χ2600(649,)\chi_{2600}(649, \cdot) 2600.2.f.a 4 1
2600.2.f.b 4
2600.2.f.c 6
2600.2.f.d 6
2600.2.f.e 8
2600.2.f.f 8
2600.2.f.g 14
2600.2.f.h 14
2600.2.g χ2600(1301,)\chi_{2600}(1301, \cdot) n/a 228 1
2600.2.j χ2600(2549,)\chi_{2600}(2549, \cdot) n/a 216 1
2600.2.k χ2600(2001,)\chi_{2600}(2001, \cdot) 2600.2.k.a 4 1
2600.2.k.b 6
2600.2.k.c 8
2600.2.k.d 14
2600.2.k.e 14
2600.2.k.f 20
2600.2.p χ2600(1949,)\chi_{2600}(1949, \cdot) n/a 248 1
2600.2.q χ2600(601,)\chi_{2600}(601, \cdot) n/a 134 2
2600.2.s χ2600(151,)\chi_{2600}(151, \cdot) None 0 2
2600.2.t χ2600(99,)\chi_{2600}(99, \cdot) n/a 496 2
2600.2.w χ2600(57,)\chi_{2600}(57, \cdot) n/a 126 2
2600.2.y χ2600(1357,)\chi_{2600}(1357, \cdot) n/a 496 2
2600.2.bb χ2600(807,)\chi_{2600}(807, \cdot) None 0 2
2600.2.bc χ2600(1507,)\chi_{2600}(1507, \cdot) n/a 496 2
2600.2.bd χ2600(207,)\chi_{2600}(207, \cdot) None 0 2
2600.2.be χ2600(443,)\chi_{2600}(443, \cdot) n/a 432 2
2600.2.bh χ2600(993,)\chi_{2600}(993, \cdot) n/a 126 2
2600.2.bj χ2600(957,)\chi_{2600}(957, \cdot) n/a 496 2
2600.2.bm χ2600(1451,)\chi_{2600}(1451, \cdot) n/a 520 2
2600.2.bn χ2600(1399,)\chi_{2600}(1399, \cdot) None 0 2
2600.2.bp χ2600(521,)\chi_{2600}(521, \cdot) n/a 360 4
2600.2.bq χ2600(1349,)\chi_{2600}(1349, \cdot) n/a 496 2
2600.2.bv χ2600(1401,)\chi_{2600}(1401, \cdot) n/a 132 2
2600.2.bw χ2600(549,)\chi_{2600}(549, \cdot) n/a 496 2
2600.2.bz χ2600(1101,)\chi_{2600}(1101, \cdot) n/a 520 2
2600.2.ca χ2600(49,)\chi_{2600}(49, \cdot) n/a 128 2
2600.2.cb χ2600(101,)\chi_{2600}(101, \cdot) n/a 520 2
2600.2.cc χ2600(1049,)\chi_{2600}(1049, \cdot) n/a 124 2
2600.2.ch χ2600(441,)\chi_{2600}(441, \cdot) n/a 424 4
2600.2.ci χ2600(469,)\chi_{2600}(469, \cdot) n/a 1440 4
2600.2.cj χ2600(389,)\chi_{2600}(389, \cdot) n/a 1664 4
2600.2.cm χ2600(181,)\chi_{2600}(181, \cdot) n/a 1664 4
2600.2.cn χ2600(209,)\chi_{2600}(209, \cdot) n/a 360 4
2600.2.cs χ2600(261,)\chi_{2600}(261, \cdot) n/a 1440 4
2600.2.ct χ2600(129,)\chi_{2600}(129, \cdot) n/a 416 4
2600.2.cv χ2600(799,)\chi_{2600}(799, \cdot) None 0 4
2600.2.cw χ2600(851,)\chi_{2600}(851, \cdot) n/a 1040 4
2600.2.cz χ2600(93,)\chi_{2600}(93, \cdot) n/a 992 4
2600.2.db χ2600(657,)\chi_{2600}(657, \cdot) n/a 252 4
2600.2.dc χ2600(107,)\chi_{2600}(107, \cdot) n/a 992 4
2600.2.dd χ2600(407,)\chi_{2600}(407, \cdot) None 0 4
2600.2.di χ2600(43,)\chi_{2600}(43, \cdot) n/a 992 4
2600.2.dj χ2600(607,)\chi_{2600}(607, \cdot) None 0 4
2600.2.dk χ2600(293,)\chi_{2600}(293, \cdot) n/a 992 4
2600.2.dm χ2600(193,)\chi_{2600}(193, \cdot) n/a 252 4
2600.2.dp χ2600(899,)\chi_{2600}(899, \cdot) n/a 992 4
2600.2.dq χ2600(951,)\chi_{2600}(951, \cdot) None 0 4
2600.2.ds χ2600(81,)\chi_{2600}(81, \cdot) n/a 832 8
2600.2.du χ2600(239,)\chi_{2600}(239, \cdot) None 0 8
2600.2.dv χ2600(291,)\chi_{2600}(291, \cdot) n/a 3328 8
2600.2.dx χ2600(317,)\chi_{2600}(317, \cdot) n/a 3328 8
2600.2.dz χ2600(73,)\chi_{2600}(73, \cdot) n/a 840 8
2600.2.ed χ2600(27,)\chi_{2600}(27, \cdot) n/a 2880 8
2600.2.ee χ2600(103,)\chi_{2600}(103, \cdot) None 0 8
2600.2.ef χ2600(363,)\chi_{2600}(363, \cdot) n/a 3328 8
2600.2.eg χ2600(183,)\chi_{2600}(183, \cdot) None 0 8
2600.2.ek χ2600(213,)\chi_{2600}(213, \cdot) n/a 3328 8
2600.2.em χ2600(177,)\chi_{2600}(177, \cdot) n/a 840 8
2600.2.eo χ2600(619,)\chi_{2600}(619, \cdot) n/a 3328 8
2600.2.ep χ2600(31,)\chi_{2600}(31, \cdot) None 0 8
2600.2.er χ2600(329,)\chi_{2600}(329, \cdot) n/a 832 8
2600.2.es χ2600(61,)\chi_{2600}(61, \cdot) n/a 3328 8
2600.2.ex χ2600(9,)\chi_{2600}(9, \cdot) n/a 848 8
2600.2.ey χ2600(381,)\chi_{2600}(381, \cdot) n/a 3328 8
2600.2.fb χ2600(69,)\chi_{2600}(69, \cdot) n/a 3328 8
2600.2.fc χ2600(29,)\chi_{2600}(29, \cdot) n/a 3328 8
2600.2.fd χ2600(121,)\chi_{2600}(121, \cdot) n/a 848 8
2600.2.fh χ2600(71,)\chi_{2600}(71, \cdot) None 0 16
2600.2.fi χ2600(19,)\chi_{2600}(19, \cdot) n/a 6656 16
2600.2.fk χ2600(137,)\chi_{2600}(137, \cdot) n/a 1680 16
2600.2.fm χ2600(37,)\chi_{2600}(37, \cdot) n/a 6656 16
2600.2.fo χ2600(87,)\chi_{2600}(87, \cdot) None 0 16
2600.2.fp χ2600(147,)\chi_{2600}(147, \cdot) n/a 6656 16
2600.2.fu χ2600(23,)\chi_{2600}(23, \cdot) None 0 16
2600.2.fv χ2600(3,)\chi_{2600}(3, \cdot) n/a 6656 16
2600.2.fx χ2600(33,)\chi_{2600}(33, \cdot) n/a 1680 16
2600.2.fz χ2600(197,)\chi_{2600}(197, \cdot) n/a 6656 16
2600.2.gb χ2600(11,)\chi_{2600}(11, \cdot) n/a 6656 16
2600.2.gc χ2600(119,)\chi_{2600}(119, \cdot) None 0 16

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

Decomposition of S2old(Γ1(2600))S_{2}^{\mathrm{old}}(\Gamma_1(2600)) into lower level spaces

S2old(Γ1(2600)) S_{2}^{\mathrm{old}}(\Gamma_1(2600)) \cong S2new(Γ1(1))S_{2}^{\mathrm{new}}(\Gamma_1(1))24^{\oplus 24}\oplusS2new(Γ1(2))S_{2}^{\mathrm{new}}(\Gamma_1(2))18^{\oplus 18}\oplusS2new(Γ1(4))S_{2}^{\mathrm{new}}(\Gamma_1(4))12^{\oplus 12}\oplusS2new(Γ1(5))S_{2}^{\mathrm{new}}(\Gamma_1(5))16^{\oplus 16}\oplusS2new(Γ1(8))S_{2}^{\mathrm{new}}(\Gamma_1(8))6^{\oplus 6}\oplusS2new(Γ1(10))S_{2}^{\mathrm{new}}(\Gamma_1(10))12^{\oplus 12}\oplusS2new(Γ1(13))S_{2}^{\mathrm{new}}(\Gamma_1(13))12^{\oplus 12}\oplusS2new(Γ1(20))S_{2}^{\mathrm{new}}(\Gamma_1(20))8^{\oplus 8}\oplusS2new(Γ1(25))S_{2}^{\mathrm{new}}(\Gamma_1(25))8^{\oplus 8}\oplusS2new(Γ1(26))S_{2}^{\mathrm{new}}(\Gamma_1(26))9^{\oplus 9}\oplusS2new(Γ1(40))S_{2}^{\mathrm{new}}(\Gamma_1(40))4^{\oplus 4}\oplusS2new(Γ1(50))S_{2}^{\mathrm{new}}(\Gamma_1(50))6^{\oplus 6}\oplusS2new(Γ1(52))S_{2}^{\mathrm{new}}(\Gamma_1(52))6^{\oplus 6}\oplusS2new(Γ1(65))S_{2}^{\mathrm{new}}(\Gamma_1(65))8^{\oplus 8}\oplusS2new(Γ1(100))S_{2}^{\mathrm{new}}(\Gamma_1(100))4^{\oplus 4}\oplusS2new(Γ1(104))S_{2}^{\mathrm{new}}(\Gamma_1(104))3^{\oplus 3}\oplusS2new(Γ1(130))S_{2}^{\mathrm{new}}(\Gamma_1(130))6^{\oplus 6}\oplusS2new(Γ1(200))S_{2}^{\mathrm{new}}(\Gamma_1(200))2^{\oplus 2}\oplusS2new(Γ1(260))S_{2}^{\mathrm{new}}(\Gamma_1(260))4^{\oplus 4}\oplusS2new(Γ1(325))S_{2}^{\mathrm{new}}(\Gamma_1(325))4^{\oplus 4}\oplusS2new(Γ1(520))S_{2}^{\mathrm{new}}(\Gamma_1(520))2^{\oplus 2}\oplusS2new(Γ1(650))S_{2}^{\mathrm{new}}(\Gamma_1(650))3^{\oplus 3}\oplusS2new(Γ1(1300))S_{2}^{\mathrm{new}}(\Gamma_1(1300))2^{\oplus 2}