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Properties

Label 21.10
Level 21
Weight 10
Dimension 98
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 320
Trace bound 1

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Defining parameters

Level: N N = 21=3⋅7 21 = 3 \cdot 7
Weight: k k = 10 10
Nonzero newspaces: 4 4
Newform subspaces: 9 9
Sturm bound: 320320
Trace bound: 11

Dimensions

The following table gives the dimensions of various subspaces of M10(Γ1(21))M_{10}(\Gamma_1(21)).

Total New Old
Modular forms 156 110 46
Cusp forms 132 98 34
Eisenstein series 24 12 12

Trace form

98q+36q2−165q3−1198q4+3984q5−972q6−7390q7−57114q8+24447q9+60816q10−193392q11+73032q12+777964q13+6072q14−804582q15−1249678q16+⋯+8253694242q99+O(q100) 98 q + 36 q^{2} - 165 q^{3} - 1198 q^{4} + 3984 q^{5} - 972 q^{6} - 7390 q^{7} - 57114 q^{8} + 24447 q^{9} + 60816 q^{10} - 193392 q^{11} + 73032 q^{12} + 777964 q^{13} + 6072 q^{14} - 804582 q^{15} - 1249678 q^{16}+ \cdots + 8253694242 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S10new(Γ1(21))S_{10}^{\mathrm{new}}(\Gamma_1(21))

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
21.10.a χ21(1,⋅)\chi_{21}(1, \cdot) 21.10.a.a 1 1
21.10.a.b 2
21.10.a.c 2
21.10.a.d 3
21.10.c χ21(20,⋅)\chi_{21}(20, \cdot) 21.10.c.a 2 1
21.10.c.b 20
21.10.e χ21(4,⋅)\chi_{21}(4, \cdot) 21.10.e.a 10 2
21.10.e.b 14
21.10.g χ21(5,⋅)\chi_{21}(5, \cdot) 21.10.g.a 44 2

Decomposition of S10old(Γ1(21))S_{10}^{\mathrm{old}}(\Gamma_1(21)) into lower level spaces

S10old(Γ1(21))≅ S_{10}^{\mathrm{old}}(\Gamma_1(21)) \cong S10new(Γ1(1))S_{10}^{\mathrm{new}}(\Gamma_1(1))⊕4^{\oplus 4}⊕\oplusS10new(Γ1(3))S_{10}^{\mathrm{new}}(\Gamma_1(3))⊕2^{\oplus 2}⊕\oplusS10new(Γ1(7))S_{10}^{\mathrm{new}}(\Gamma_1(7))⊕2^{\oplus 2}