Properties

Label 440.4
Level 440
Weight 4
Dimension 8656
Nonzero newspaces 18
Sturm bound 46080
Trace bound 6

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Defining parameters

Level: N N = 440=23511 440 = 2^{3} \cdot 5 \cdot 11
Weight: k k = 4 4
Nonzero newspaces: 18 18
Sturm bound: 4608046080
Trace bound: 66

Dimensions

The following table gives the dimensions of various subspaces of M4(Γ1(440))M_{4}(\Gamma_1(440)).

Total New Old
Modular forms 17760 8872 8888
Cusp forms 16800 8656 8144
Eisenstein series 960 216 744

Trace form

8656q20q228q360q4+18q5+68q64q7+148q8166q9134q10168q11472q1220q13212q14+572q15+244q16+216q17+948q18+4548q99+O(q100) 8656 q - 20 q^{2} - 28 q^{3} - 60 q^{4} + 18 q^{5} + 68 q^{6} - 4 q^{7} + 148 q^{8} - 166 q^{9} - 134 q^{10} - 168 q^{11} - 472 q^{12} - 20 q^{13} - 212 q^{14} + 572 q^{15} + 244 q^{16} + 216 q^{17} + 948 q^{18}+ \cdots - 4548 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(Γ1(440))S_{4}^{\mathrm{new}}(\Gamma_1(440))

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
440.4.a χ440(1,)\chi_{440}(1, \cdot) 440.4.a.a 1 1
440.4.a.b 1
440.4.a.c 1
440.4.a.d 1
440.4.a.e 2
440.4.a.f 3
440.4.a.g 3
440.4.a.h 4
440.4.a.i 4
440.4.a.j 5
440.4.a.k 5
440.4.b χ440(89,)\chi_{440}(89, \cdot) 440.4.b.a 2 1
440.4.b.b 20
440.4.b.c 24
440.4.c χ440(219,)\chi_{440}(219, \cdot) n/a 212 1
440.4.f χ440(351,)\chi_{440}(351, \cdot) None 0 1
440.4.g χ440(221,)\chi_{440}(221, \cdot) n/a 120 1
440.4.l χ440(309,)\chi_{440}(309, \cdot) n/a 180 1
440.4.m χ440(439,)\chi_{440}(439, \cdot) None 0 1
440.4.p χ440(131,)\chi_{440}(131, \cdot) n/a 144 1
440.4.r χ440(67,)\chi_{440}(67, \cdot) n/a 360 2
440.4.t χ440(197,)\chi_{440}(197, \cdot) n/a 424 2
440.4.v χ440(153,)\chi_{440}(153, \cdot) n/a 108 2
440.4.x χ440(23,)\chi_{440}(23, \cdot) None 0 2
440.4.y χ440(81,)\chi_{440}(81, \cdot) n/a 144 4
440.4.z χ440(51,)\chi_{440}(51, \cdot) n/a 576 4
440.4.bc χ440(39,)\chi_{440}(39, \cdot) None 0 4
440.4.bd χ440(69,)\chi_{440}(69, \cdot) n/a 848 4
440.4.bi χ440(141,)\chi_{440}(141, \cdot) n/a 576 4
440.4.bj χ440(151,)\chi_{440}(151, \cdot) None 0 4
440.4.bm χ440(19,)\chi_{440}(19, \cdot) n/a 848 4
440.4.bn χ440(9,)\chi_{440}(9, \cdot) n/a 216 4
440.4.bo χ440(17,)\chi_{440}(17, \cdot) n/a 432 8
440.4.bq χ440(47,)\chi_{440}(47, \cdot) None 0 8
440.4.bs χ440(3,)\chi_{440}(3, \cdot) n/a 1696 8
440.4.bu χ440(13,)\chi_{440}(13, \cdot) n/a 1696 8

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

Decomposition of S4old(Γ1(440))S_{4}^{\mathrm{old}}(\Gamma_1(440)) into lower level spaces

S4old(Γ1(440)) S_{4}^{\mathrm{old}}(\Gamma_1(440)) \cong S4new(Γ1(1))S_{4}^{\mathrm{new}}(\Gamma_1(1))16^{\oplus 16}\oplusS4new(Γ1(2))S_{4}^{\mathrm{new}}(\Gamma_1(2))12^{\oplus 12}\oplusS4new(Γ1(4))S_{4}^{\mathrm{new}}(\Gamma_1(4))8^{\oplus 8}\oplusS4new(Γ1(5))S_{4}^{\mathrm{new}}(\Gamma_1(5))8^{\oplus 8}\oplusS4new(Γ1(8))S_{4}^{\mathrm{new}}(\Gamma_1(8))4^{\oplus 4}\oplusS4new(Γ1(10))S_{4}^{\mathrm{new}}(\Gamma_1(10))6^{\oplus 6}\oplusS4new(Γ1(11))S_{4}^{\mathrm{new}}(\Gamma_1(11))8^{\oplus 8}\oplusS4new(Γ1(20))S_{4}^{\mathrm{new}}(\Gamma_1(20))4^{\oplus 4}\oplusS4new(Γ1(22))S_{4}^{\mathrm{new}}(\Gamma_1(22))6^{\oplus 6}\oplusS4new(Γ1(40))S_{4}^{\mathrm{new}}(\Gamma_1(40))2^{\oplus 2}\oplusS4new(Γ1(44))S_{4}^{\mathrm{new}}(\Gamma_1(44))4^{\oplus 4}\oplusS4new(Γ1(55))S_{4}^{\mathrm{new}}(\Gamma_1(55))4^{\oplus 4}\oplusS4new(Γ1(88))S_{4}^{\mathrm{new}}(\Gamma_1(88))2^{\oplus 2}\oplusS4new(Γ1(110))S_{4}^{\mathrm{new}}(\Gamma_1(110))3^{\oplus 3}\oplusS4new(Γ1(220))S_{4}^{\mathrm{new}}(\Gamma_1(220))2^{\oplus 2}