↑

Properties

Label 16.22
Level 16
Weight 22
Dimension 92
Nonzero newspaces 2
Newform subspaces 7
Sturm bound 352
Trace bound 1

Downloads

Learn more

Defining parameters

Level: N N = 16=24 16 = 2^{4}
Weight: k k = 22 22
Nonzero newspaces: 2 2
Newform subspaces: 7 7
Sturm bound: 352352
Trace bound: 11

Dimensions

The following table gives the dimensions of various subspaces of M22(Γ1(16))M_{22}(\Gamma_1(16)).

Total New Old
Modular forms 175 97 78
Cusp forms 161 92 69
Eisenstein series 14 5 9

Trace form

92q−2q2−59050q3+1604328q4−10391782q5−142760912q6−286396624q7−5437750796q8+36243817378q9−101897120756q10+23187707306q11+366511438084q12+⋯+19 ⁣⋯ ⁣66q99+O(q100) 92 q - 2 q^{2} - 59050 q^{3} + 1604328 q^{4} - 10391782 q^{5} - 142760912 q^{6} - 286396624 q^{7} - 5437750796 q^{8} + 36243817378 q^{9} - 101897120756 q^{10} + 23187707306 q^{11} + 366511438084 q^{12}+ \cdots + 19\!\cdots\!66 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S22new(Γ1(16))S_{22}^{\mathrm{new}}(\Gamma_1(16))

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
16.22.a χ16(1,⋅)\chi_{16}(1, \cdot) 16.22.a.a 1 1
16.22.a.b 1
16.22.a.c 1
16.22.a.d 2
16.22.a.e 2
16.22.a.f 3
16.22.b χ16(9,⋅)\chi_{16}(9, \cdot) None 0 1
16.22.e χ16(5,⋅)\chi_{16}(5, \cdot) 16.22.e.a 82 2

Decomposition of S22old(Γ1(16))S_{22}^{\mathrm{old}}(\Gamma_1(16)) into lower level spaces

S22old(Γ1(16))≅ S_{22}^{\mathrm{old}}(\Gamma_1(16)) \cong S22new(Γ1(1))S_{22}^{\mathrm{new}}(\Gamma_1(1))⊕5^{\oplus 5}⊕\oplusS22new(Γ1(2))S_{22}^{\mathrm{new}}(\Gamma_1(2))⊕4^{\oplus 4}⊕\oplusS22new(Γ1(4))S_{22}^{\mathrm{new}}(\Gamma_1(4))⊕3^{\oplus 3}⊕\oplusS22new(Γ1(8))S_{22}^{\mathrm{new}}(\Gamma_1(8))⊕2^{\oplus 2}