Properties

Label 224.6
Level 224
Weight 6
Dimension 4090
Nonzero newspaces 12
Sturm bound 18432
Trace bound 13

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Defining parameters

Level: N N = 224=257 224 = 2^{5} \cdot 7
Weight: k k = 6 6
Nonzero newspaces: 12 12
Sturm bound: 1843218432
Trace bound: 1313

Dimensions

The following table gives the dimensions of various subspaces of M6(Γ1(224))M_{6}(\Gamma_1(224)).

Total New Old
Modular forms 7872 4190 3682
Cusp forms 7488 4090 3398
Eisenstein series 384 100 284

Trace form

4090q16q210q316q492q516q6+82q740q8598q9+384q1010q11+3152q12236q132500q14868q158376q163632q17+1410984q99+O(q100) 4090 q - 16 q^{2} - 10 q^{3} - 16 q^{4} - 92 q^{5} - 16 q^{6} + 82 q^{7} - 40 q^{8} - 598 q^{9} + 384 q^{10} - 10 q^{11} + 3152 q^{12} - 236 q^{13} - 2500 q^{14} - 868 q^{15} - 8376 q^{16} - 3632 q^{17}+ \cdots - 1410984 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S6new(Γ1(224))S_{6}^{\mathrm{new}}(\Gamma_1(224))

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
224.6.a χ224(1,)\chi_{224}(1, \cdot) 224.6.a.a 1 1
224.6.a.b 1
224.6.a.c 2
224.6.a.d 2
224.6.a.e 3
224.6.a.f 3
224.6.a.g 4
224.6.a.h 4
224.6.a.i 5
224.6.a.j 5
224.6.b χ224(113,)\chi_{224}(113, \cdot) 224.6.b.a 14 1
224.6.b.b 16
224.6.e χ224(111,)\chi_{224}(111, \cdot) 224.6.e.a 2 1
224.6.e.b 36
224.6.f χ224(223,)\chi_{224}(223, \cdot) 224.6.f.a 40 1
224.6.i χ224(65,)\chi_{224}(65, \cdot) 224.6.i.a 20 2
224.6.i.b 20
224.6.i.c 20
224.6.i.d 20
224.6.j χ224(55,)\chi_{224}(55, \cdot) None 0 2
224.6.m χ224(57,)\chi_{224}(57, \cdot) None 0 2
224.6.p χ224(31,)\chi_{224}(31, \cdot) 224.6.p.a 80 2
224.6.q χ224(47,)\chi_{224}(47, \cdot) 224.6.q.a 76 2
224.6.t χ224(81,)\chi_{224}(81, \cdot) 224.6.t.a 76 2
224.6.u χ224(29,)\chi_{224}(29, \cdot) n/a 480 4
224.6.x χ224(27,)\chi_{224}(27, \cdot) n/a 632 4
224.6.z χ224(87,)\chi_{224}(87, \cdot) None 0 4
224.6.ba χ224(9,)\chi_{224}(9, \cdot) None 0 4
224.6.bd χ224(37,)\chi_{224}(37, \cdot) n/a 1264 8
224.6.be χ224(3,)\chi_{224}(3, \cdot) n/a 1264 8

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

Decomposition of S6old(Γ1(224))S_{6}^{\mathrm{old}}(\Gamma_1(224)) into lower level spaces