Properties

Label 2548.2
Level 2548
Weight 2
Dimension 108209
Nonzero newspaces 60
Sturm bound 790272
Trace bound 11

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Defining parameters

Level: N N = 2548=227213 2548 = 2^{2} \cdot 7^{2} \cdot 13
Weight: k k = 2 2
Nonzero newspaces: 60 60
Sturm bound: 790272790272
Trace bound: 1111

Dimensions

The following table gives the dimensions of various subspaces of M2(Γ1(2548))M_{2}(\Gamma_1(2548)).

Total New Old
Modular forms 201168 110345 90823
Cusp forms 193969 108209 85760
Eisenstein series 7199 2136 5063

Trace form

108209q156q24q3156q4324q5144q68q7264q8312q9120q10+6q1190q12334q13372q14+12q15108q16327q17114q18++90q99+O(q100) 108209 q - 156 q^{2} - 4 q^{3} - 156 q^{4} - 324 q^{5} - 144 q^{6} - 8 q^{7} - 264 q^{8} - 312 q^{9} - 120 q^{10} + 6 q^{11} - 90 q^{12} - 334 q^{13} - 372 q^{14} + 12 q^{15} - 108 q^{16} - 327 q^{17} - 114 q^{18}+ \cdots + 90 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(Γ1(2548))S_{2}^{\mathrm{new}}(\Gamma_1(2548))

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
2548.2.a χ2548(1,)\chi_{2548}(1, \cdot) 2548.2.a.a 1 1
2548.2.a.b 1
2548.2.a.c 1
2548.2.a.d 1
2548.2.a.e 1
2548.2.a.f 1
2548.2.a.g 1
2548.2.a.h 1
2548.2.a.i 1
2548.2.a.j 1
2548.2.a.k 1
2548.2.a.l 2
2548.2.a.m 2
2548.2.a.n 3
2548.2.a.o 3
2548.2.a.p 4
2548.2.a.q 4
2548.2.a.r 6
2548.2.a.s 6
2548.2.f χ2548(391,)\chi_{2548}(391, \cdot) n/a 240 1
2548.2.g χ2548(2157,)\chi_{2548}(2157, \cdot) 2548.2.g.a 4 1
2548.2.g.b 4
2548.2.g.c 4
2548.2.g.d 4
2548.2.g.e 6
2548.2.g.f 6
2548.2.g.g 8
2548.2.g.h 12
2548.2.h χ2548(2547,)\chi_{2548}(2547, \cdot) n/a 272 1
2548.2.i χ2548(165,)\chi_{2548}(165, \cdot) 2548.2.i.a 2 2
2548.2.i.b 2
2548.2.i.c 2
2548.2.i.d 2
2548.2.i.e 2
2548.2.i.f 2
2548.2.i.g 2
2548.2.i.h 2
2548.2.i.i 4
2548.2.i.j 4
2548.2.i.k 4
2548.2.i.l 4
2548.2.i.m 12
2548.2.i.n 18
2548.2.i.o 32
2548.2.j χ2548(1145,)\chi_{2548}(1145, \cdot) 2548.2.j.a 2 2
2548.2.j.b 2
2548.2.j.c 2
2548.2.j.d 2
2548.2.j.e 2
2548.2.j.f 2
2548.2.j.g 2
2548.2.j.h 2
2548.2.j.i 2
2548.2.j.j 2
2548.2.j.k 4
2548.2.j.l 4
2548.2.j.m 4
2548.2.j.n 4
2548.2.j.o 6
2548.2.j.p 6
2548.2.j.q 8
2548.2.j.r 12
2548.2.j.s 12
2548.2.k χ2548(393,)\chi_{2548}(393, \cdot) 2548.2.k.a 2 2
2548.2.k.b 2
2548.2.k.c 2
2548.2.k.d 2
2548.2.k.e 4
2548.2.k.f 4
2548.2.k.g 12
2548.2.k.h 18
2548.2.k.i 18
2548.2.k.j 32
2548.2.l χ2548(373,)\chi_{2548}(373, \cdot) 2548.2.l.a 2 2
2548.2.l.b 2
2548.2.l.c 2
2548.2.l.d 2
2548.2.l.e 2
2548.2.l.f 2
2548.2.l.g 2
2548.2.l.h 2
2548.2.l.i 4
2548.2.l.j 4
2548.2.l.k 4
2548.2.l.l 4
2548.2.l.m 12
2548.2.l.n 18
2548.2.l.o 32
2548.2.m χ2548(99,)\chi_{2548}(99, \cdot) n/a 554 2
2548.2.n χ2548(489,)\chi_{2548}(489, \cdot) 2548.2.n.a 40 2
2548.2.n.b 56
2548.2.u χ2548(589,)\chi_{2548}(589, \cdot) 2548.2.u.a 2 2
2548.2.u.b 16
2548.2.u.c 16
2548.2.u.d 18
2548.2.u.e 18
2548.2.u.f 24
2548.2.v χ2548(783,)\chi_{2548}(783, \cdot) n/a 544 2
2548.2.w χ2548(803,)\chi_{2548}(803, \cdot) n/a 544 2
2548.2.x χ2548(1195,)\chi_{2548}(1195, \cdot) n/a 544 2
2548.2.y χ2548(753,)\chi_{2548}(753, \cdot) 2548.2.y.a 8 2
2548.2.y.b 8
2548.2.y.c 8
2548.2.y.d 12
2548.2.y.e 16
2548.2.y.f 16
2548.2.y.g 24
2548.2.z χ2548(1587,)\chi_{2548}(1587, \cdot) n/a 480 2
2548.2.ba χ2548(815,)\chi_{2548}(815, \cdot) n/a 544 2
2548.2.bb χ2548(569,)\chi_{2548}(569, \cdot) 2548.2.bb.a 2 2
2548.2.bb.b 2
2548.2.bb.c 16
2548.2.bb.d 16
2548.2.bb.e 16
2548.2.bb.f 18
2548.2.bb.g 24
2548.2.bc χ2548(979,)\chi_{2548}(979, \cdot) n/a 544 2
2548.2.bp χ2548(1011,)\chi_{2548}(1011, \cdot) n/a 544 2
2548.2.bq χ2548(361,)\chi_{2548}(361, \cdot) 2548.2.bq.a 2 2
2548.2.bq.b 2
2548.2.bq.c 16
2548.2.bq.d 16
2548.2.bq.e 16
2548.2.bq.f 18
2548.2.bq.g 24
2548.2.br χ2548(607,)\chi_{2548}(607, \cdot) n/a 544 2
2548.2.bs χ2548(365,)\chi_{2548}(365, \cdot) n/a 336 6
2548.2.bt χ2548(717,)\chi_{2548}(717, \cdot) n/a 188 4
2548.2.bu χ2548(67,)\chi_{2548}(67, \cdot) n/a 1088 4
2548.2.cb χ2548(275,)\chi_{2548}(275, \cdot) n/a 1088 4
2548.2.cc χ2548(97,)\chi_{2548}(97, \cdot) n/a 184 4
2548.2.cd χ2548(1097,)\chi_{2548}(1097, \cdot) n/a 184 4
2548.2.ce χ2548(687,)\chi_{2548}(687, \cdot) n/a 1108 4
2548.2.cf χ2548(655,)\chi_{2548}(655, \cdot) n/a 1088 4
2548.2.cg χ2548(509,)\chi_{2548}(509, \cdot) n/a 188 4
2548.2.cj χ2548(363,)\chi_{2548}(363, \cdot) n/a 2328 6
2548.2.ck χ2548(337,)\chi_{2548}(337, \cdot) n/a 384 6
2548.2.cl χ2548(27,)\chi_{2548}(27, \cdot) n/a 2016 6
2548.2.cq χ2548(9,)\chi_{2548}(9, \cdot) n/a 780 12
2548.2.cr χ2548(29,)\chi_{2548}(29, \cdot) n/a 792 12
2548.2.cs χ2548(53,)\chi_{2548}(53, \cdot) n/a 672 12
2548.2.ct χ2548(289,)\chi_{2548}(289, \cdot) n/a 780 12
2548.2.cw χ2548(125,)\chi_{2548}(125, \cdot) n/a 768 12
2548.2.cx χ2548(239,)\chi_{2548}(239, \cdot) n/a 4656 12
2548.2.cy χ2548(3,)\chi_{2548}(3, \cdot) n/a 4656 12
2548.2.cz χ2548(121,)\chi_{2548}(121, \cdot) n/a 780 12
2548.2.da χ2548(283,)\chi_{2548}(283, \cdot) n/a 4656 12
2548.2.dn χ2548(251,)\chi_{2548}(251, \cdot) n/a 4656 12
2548.2.do χ2548(205,)\chi_{2548}(205, \cdot) n/a 780 12
2548.2.dp χ2548(87,)\chi_{2548}(87, \cdot) n/a 4656 12
2548.2.dq χ2548(131,)\chi_{2548}(131, \cdot) n/a 4032 12
2548.2.dr χ2548(25,)\chi_{2548}(25, \cdot) n/a 792 12
2548.2.ds χ2548(103,)\chi_{2548}(103, \cdot) n/a 4656 12
2548.2.dt χ2548(75,)\chi_{2548}(75, \cdot) n/a 4656 12
2548.2.du χ2548(55,)\chi_{2548}(55, \cdot) n/a 4656 12
2548.2.dv χ2548(225,)\chi_{2548}(225, \cdot) n/a 792 12
2548.2.ec χ2548(45,)\chi_{2548}(45, \cdot) n/a 1560 24
2548.2.ed χ2548(135,)\chi_{2548}(135, \cdot) n/a 9312 24
2548.2.ee χ2548(15,)\chi_{2548}(15, \cdot) n/a 9312 24
2548.2.ef χ2548(5,)\chi_{2548}(5, \cdot) n/a 1584 24
2548.2.eg χ2548(41,)\chi_{2548}(41, \cdot) n/a 1584 24
2548.2.eh χ2548(123,)\chi_{2548}(123, \cdot) n/a 9312 24
2548.2.eo χ2548(11,)\chi_{2548}(11, \cdot) n/a 9312 24
2548.2.ep χ2548(33,)\chi_{2548}(33, \cdot) n/a 1560 24

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

Decomposition of S2old(Γ1(2548))S_{2}^{\mathrm{old}}(\Gamma_1(2548)) into lower level spaces

S2old(Γ1(2548)) S_{2}^{\mathrm{old}}(\Gamma_1(2548)) \cong S2new(Γ1(1))S_{2}^{\mathrm{new}}(\Gamma_1(1))18^{\oplus 18}\oplusS2new(Γ1(2))S_{2}^{\mathrm{new}}(\Gamma_1(2))12^{\oplus 12}\oplusS2new(Γ1(4))S_{2}^{\mathrm{new}}(\Gamma_1(4))6^{\oplus 6}\oplusS2new(Γ1(7))S_{2}^{\mathrm{new}}(\Gamma_1(7))12^{\oplus 12}\oplusS2new(Γ1(13))S_{2}^{\mathrm{new}}(\Gamma_1(13))9^{\oplus 9}\oplusS2new(Γ1(14))S_{2}^{\mathrm{new}}(\Gamma_1(14))8^{\oplus 8}\oplusS2new(Γ1(26))S_{2}^{\mathrm{new}}(\Gamma_1(26))6^{\oplus 6}\oplusS2new(Γ1(28))S_{2}^{\mathrm{new}}(\Gamma_1(28))4^{\oplus 4}\oplusS2new(Γ1(49))S_{2}^{\mathrm{new}}(\Gamma_1(49))6^{\oplus 6}\oplusS2new(Γ1(52))S_{2}^{\mathrm{new}}(\Gamma_1(52))3^{\oplus 3}\oplusS2new(Γ1(91))S_{2}^{\mathrm{new}}(\Gamma_1(91))6^{\oplus 6}\oplusS2new(Γ1(98))S_{2}^{\mathrm{new}}(\Gamma_1(98))4^{\oplus 4}\oplusS2new(Γ1(182))S_{2}^{\mathrm{new}}(\Gamma_1(182))4^{\oplus 4}\oplusS2new(Γ1(196))S_{2}^{\mathrm{new}}(\Gamma_1(196))2^{\oplus 2}\oplusS2new(Γ1(364))S_{2}^{\mathrm{new}}(\Gamma_1(364))2^{\oplus 2}\oplusS2new(Γ1(637))S_{2}^{\mathrm{new}}(\Gamma_1(637))3^{\oplus 3}\oplusS2new(Γ1(1274))S_{2}^{\mathrm{new}}(\Gamma_1(1274))2^{\oplus 2}