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Properties

Label 38.6
Level 38
Weight 6
Dimension 75
Nonzero newspaces 3
Newform subspaces 8
Sturm bound 540
Trace bound 1

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Defining parameters

Level: N N = 38=2⋅19 38 = 2 \cdot 19
Weight: k k = 6 6
Nonzero newspaces: 3 3
Newform subspaces: 8 8
Sturm bound: 540540
Trace bound: 11

Dimensions

The following table gives the dimensions of various subspaces of M6(Γ1(38))M_{6}(\Gamma_1(38)).

Total New Old
Modular forms 243 75 168
Cusp forms 207 75 132
Eisenstein series 36 0 36

Trace form

75q+864q12−4344q13−3960q14−3564q15+4302q17+8748q18+12810q19+3168q20−1890q21−8532q22−10278q23−23364q25−3960q26+41157q27+⋯−197541q99+O(q100) 75 q + 864 q^{12} - 4344 q^{13} - 3960 q^{14} - 3564 q^{15} + 4302 q^{17} + 8748 q^{18} + 12810 q^{19} + 3168 q^{20} - 1890 q^{21} - 8532 q^{22} - 10278 q^{23} - 23364 q^{25} - 3960 q^{26} + 41157 q^{27}+ \cdots - 197541 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S6new(Γ1(38))S_{6}^{\mathrm{new}}(\Gamma_1(38))

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
38.6.a χ38(1,⋅)\chi_{38}(1, \cdot) 38.6.a.a 1 1
38.6.a.b 1
38.6.a.c 2
38.6.a.d 3
38.6.c χ38(7,⋅)\chi_{38}(7, \cdot) 38.6.c.a 6 2
38.6.c.b 8
38.6.e χ38(5,⋅)\chi_{38}(5, \cdot) 38.6.e.a 24 6
38.6.e.b 30

Decomposition of S6old(Γ1(38))S_{6}^{\mathrm{old}}(\Gamma_1(38)) into lower level spaces

S6old(Γ1(38))≅ S_{6}^{\mathrm{old}}(\Gamma_1(38)) \cong S6new(Γ1(1))S_{6}^{\mathrm{new}}(\Gamma_1(1))⊕4^{\oplus 4}⊕\oplusS6new(Γ1(2))S_{6}^{\mathrm{new}}(\Gamma_1(2))⊕2^{\oplus 2}⊕\oplusS6new(Γ1(19))S_{6}^{\mathrm{new}}(\Gamma_1(19))⊕2^{\oplus 2}