Properties

Label 18.16
Level 18
Weight 16
Dimension 36
Nonzero newspaces 2
Newform subspaces 8
Sturm bound 288
Trace bound 1

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Defining parameters

Level: N N = 18=232 18 = 2 \cdot 3^{2}
Weight: k k = 16 16
Nonzero newspaces: 2 2
Newform subspaces: 8 8
Sturm bound: 288288
Trace bound: 11

Dimensions

The following table gives the dimensions of various subspaces of M16(Γ1(18))M_{16}(\Gamma_1(18)).

Total New Old
Modular forms 143 36 107
Cusp forms 127 36 91
Eisenstein series 16 0 16

Trace form

36q+128q24065q3147456q4+410202q51319040q6+5316804q74194304q8+22300923q943425792q10+31054251q11+62619648q12171094572q13+907519744q14+48 ⁣ ⁣56q99+O(q100) 36 q + 128 q^{2} - 4065 q^{3} - 147456 q^{4} + 410202 q^{5} - 1319040 q^{6} + 5316804 q^{7} - 4194304 q^{8} + 22300923 q^{9} - 43425792 q^{10} + 31054251 q^{11} + 62619648 q^{12} - 171094572 q^{13} + 907519744 q^{14}+ \cdots - 48\!\cdots\!56 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S16new(Γ1(18))S_{16}^{\mathrm{new}}(\Gamma_1(18))

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
18.16.a χ18(1,)\chi_{18}(1, \cdot) 18.16.a.a 1 1
18.16.a.b 1
18.16.a.c 1
18.16.a.d 1
18.16.a.e 1
18.16.a.f 1
18.16.c χ18(7,)\chi_{18}(7, \cdot) 18.16.c.a 14 2
18.16.c.b 16

Decomposition of S16old(Γ1(18))S_{16}^{\mathrm{old}}(\Gamma_1(18)) into lower level spaces

S16old(Γ1(18)) S_{16}^{\mathrm{old}}(\Gamma_1(18)) \cong S16new(Γ1(1))S_{16}^{\mathrm{new}}(\Gamma_1(1))6^{\oplus 6}\oplusS16new(Γ1(2))S_{16}^{\mathrm{new}}(\Gamma_1(2))3^{\oplus 3}\oplusS16new(Γ1(3))S_{16}^{\mathrm{new}}(\Gamma_1(3))4^{\oplus 4}\oplusS16new(Γ1(6))S_{16}^{\mathrm{new}}(\Gamma_1(6))2^{\oplus 2}\oplusS16new(Γ1(9))S_{16}^{\mathrm{new}}(\Gamma_1(9))2^{\oplus 2}