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Properties

Label 16.18
Level 16
Weight 18
Dimension 74
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 288
Trace bound 1

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Defining parameters

Level: N N = 16=24 16 = 2^{4}
Weight: k k = 18 18
Nonzero newspaces: 2 2
Newform subspaces: 6 6
Sturm bound: 288288
Trace bound: 11

Dimensions

The following table gives the dimensions of various subspaces of M18(Γ1(16))M_{18}(\Gamma_1(16)).

Total New Old
Modular forms 143 79 64
Cusp forms 129 74 55
Eisenstein series 14 5 9

Trace form

74q−2q2−6562q3−54744q4−12242q5−9659408q6+13155520q7−101532236q8+381202024q9+284165324q10−629746270q11+647301316q12−795138962q13+6580735964q14+⋯+16 ⁣⋯ ⁣46q99+O(q100) 74 q - 2 q^{2} - 6562 q^{3} - 54744 q^{4} - 12242 q^{5} - 9659408 q^{6} + 13155520 q^{7} - 101532236 q^{8} + 381202024 q^{9} + 284165324 q^{10} - 629746270 q^{11} + 647301316 q^{12} - 795138962 q^{13} + 6580735964 q^{14}+ \cdots + 16\!\cdots\!46 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S18new(Γ1(16))S_{18}^{\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
16.18.a χ16(1,⋅)\chi_{16}(1, \cdot) 16.18.a.a 1 1
16.18.a.b 1
16.18.a.c 2
16.18.a.d 2
16.18.a.e 2
16.18.b χ16(9,⋅)\chi_{16}(9, \cdot) None 0 1
16.18.e χ16(5,⋅)\chi_{16}(5, \cdot) 16.18.e.a 66 2

Decomposition of S18old(Γ1(16))S_{18}^{\mathrm{old}}(\Gamma_1(16)) into lower level spaces

S18old(Γ1(16))≅ S_{18}^{\mathrm{old}}(\Gamma_1(16)) \cong S18new(Γ1(1))S_{18}^{\mathrm{new}}(\Gamma_1(1))⊕5^{\oplus 5}⊕\oplusS18new(Γ1(2))S_{18}^{\mathrm{new}}(\Gamma_1(2))⊕4^{\oplus 4}⊕\oplusS18new(Γ1(4))S_{18}^{\mathrm{new}}(\Gamma_1(4))⊕3^{\oplus 3}⊕\oplusS18new(Γ1(8))S_{18}^{\mathrm{new}}(\Gamma_1(8))⊕2^{\oplus 2}