Properties

Label 189.6
Level 189
Weight 6
Dimension 4826
Nonzero newspaces 16
Sturm bound 15552
Trace bound 9

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Defining parameters

Level: N N = 189=337 189 = 3^{3} \cdot 7
Weight: k k = 6 6
Nonzero newspaces: 16 16
Sturm bound: 1555215552
Trace bound: 99

Dimensions

The following table gives the dimensions of various subspaces of M6(Γ1(189))M_{6}(\Gamma_1(189)).

Total New Old
Modular forms 6660 4986 1674
Cusp forms 6300 4826 1474
Eisenstein series 360 160 200

Trace form

4826q6q224q3168q4+318q5+216q6171q72694q8684q9120q10+642q11+5502q12+4322q13+3249q144050q157024q1614064q17++56574q99+O(q100) 4826 q - 6 q^{2} - 24 q^{3} - 168 q^{4} + 318 q^{5} + 216 q^{6} - 171 q^{7} - 2694 q^{8} - 684 q^{9} - 120 q^{10} + 642 q^{11} + 5502 q^{12} + 4322 q^{13} + 3249 q^{14} - 4050 q^{15} - 7024 q^{16} - 14064 q^{17}+ \cdots + 56574 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S6new(Γ1(189))S_{6}^{\mathrm{new}}(\Gamma_1(189))

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
189.6.a χ189(1,)\chi_{189}(1, \cdot) 189.6.a.a 1 1
189.6.a.b 1
189.6.a.c 1
189.6.a.d 1
189.6.a.e 2
189.6.a.f 2
189.6.a.g 2
189.6.a.h 4
189.6.a.i 4
189.6.a.j 4
189.6.a.k 4
189.6.a.l 4
189.6.a.m 5
189.6.a.n 5
189.6.c χ189(188,)\chi_{189}(188, \cdot) 189.6.c.a 2 1
189.6.c.b 24
189.6.c.c 28
189.6.e χ189(109,)\chi_{189}(109, \cdot) n/a 106 2
189.6.f χ189(64,)\chi_{189}(64, \cdot) 189.6.f.a 30 2
189.6.f.b 30
189.6.g χ189(100,)\chi_{189}(100, \cdot) 189.6.g.a 76 2
189.6.h χ189(37,)\chi_{189}(37, \cdot) 189.6.h.a 76 2
189.6.i χ189(143,)\chi_{189}(143, \cdot) 189.6.i.a 76 2
189.6.o χ189(62,)\chi_{189}(62, \cdot) 189.6.o.a 76 2
189.6.p χ189(26,)\chi_{189}(26, \cdot) n/a 106 2
189.6.s χ189(17,)\chi_{189}(17, \cdot) 189.6.s.a 76 2
189.6.u χ189(4,)\chi_{189}(4, \cdot) n/a 708 6
189.6.v χ189(22,)\chi_{189}(22, \cdot) n/a 540 6
189.6.w χ189(25,)\chi_{189}(25, \cdot) n/a 708 6
189.6.ba χ189(5,)\chi_{189}(5, \cdot) n/a 708 6
189.6.bd χ189(47,)\chi_{189}(47, \cdot) n/a 708 6
189.6.be χ189(20,)\chi_{189}(20, \cdot) n/a 708 6

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

Decomposition of S6old(Γ1(189))S_{6}^{\mathrm{old}}(\Gamma_1(189)) into lower level spaces