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Properties

Label 72.5
Level 72
Weight 5
Dimension 247
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 1440
Trace bound 2

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Defining parameters

Level: N N = 72=23⋅32 72 = 2^{3} \cdot 3^{2}
Weight: k k = 5 5
Nonzero newspaces: 6 6
Newform subspaces: 11 11
Sturm bound: 14401440
Trace bound: 22

Dimensions

The following table gives the dimensions of various subspaces of M5(Γ1(72))M_{5}(\Gamma_1(72)).

Total New Old
Modular forms 624 265 359
Cusp forms 528 247 281
Eisenstein series 96 18 78

Trace form

247q−14q4+28q6−50q7−102q8−108q9−72q10+156q11+226q12+256q13+594q14+78q15+134q16−126q17−1954q19+1098q20+24q21+⋯+40566q99+O(q100) 247 q - 14 q^{4} + 28 q^{6} - 50 q^{7} - 102 q^{8} - 108 q^{9} - 72 q^{10} + 156 q^{11} + 226 q^{12} + 256 q^{13} + 594 q^{14} + 78 q^{15} + 134 q^{16} - 126 q^{17} - 1954 q^{19} + 1098 q^{20} + 24 q^{21}+ \cdots + 40566 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S5new(Γ1(72))S_{5}^{\mathrm{new}}(\Gamma_1(72))

We only show spaces with odd 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
72.5.b χ72(19,⋅)\chi_{72}(19, \cdot) 72.5.b.a 1 1
72.5.b.b 2
72.5.b.c 8
72.5.b.d 8
72.5.e χ72(17,⋅)\chi_{72}(17, \cdot) 72.5.e.a 2 1
72.5.e.b 2
72.5.g χ72(55,⋅)\chi_{72}(55, \cdot) None 0 1
72.5.h χ72(53,⋅)\chi_{72}(53, \cdot) 72.5.h.a 16 1
72.5.j χ72(5,⋅)\chi_{72}(5, \cdot) 72.5.j.a 92 2
72.5.k χ72(7,⋅)\chi_{72}(7, \cdot) None 0 2
72.5.m χ72(41,⋅)\chi_{72}(41, \cdot) 72.5.m.a 24 2
72.5.p χ72(43,⋅)\chi_{72}(43, \cdot) 72.5.p.a 4 2
72.5.p.b 88

Decomposition of S5old(Γ1(72))S_{5}^{\mathrm{old}}(\Gamma_1(72)) into lower level spaces

S5old(Γ1(72))≅ S_{5}^{\mathrm{old}}(\Gamma_1(72)) \cong S5new(Γ1(1))S_{5}^{\mathrm{new}}(\Gamma_1(1))⊕12^{\oplus 12}⊕\oplusS5new(Γ1(2))S_{5}^{\mathrm{new}}(\Gamma_1(2))⊕9^{\oplus 9}⊕\oplusS5new(Γ1(3))S_{5}^{\mathrm{new}}(\Gamma_1(3))⊕8^{\oplus 8}⊕\oplusS5new(Γ1(4))S_{5}^{\mathrm{new}}(\Gamma_1(4))⊕6^{\oplus 6}⊕\oplusS5new(Γ1(6))S_{5}^{\mathrm{new}}(\Gamma_1(6))⊕6^{\oplus 6}⊕\oplusS5new(Γ1(8))S_{5}^{\mathrm{new}}(\Gamma_1(8))⊕3^{\oplus 3}⊕\oplusS5new(Γ1(9))S_{5}^{\mathrm{new}}(\Gamma_1(9))⊕4^{\oplus 4}⊕\oplusS5new(Γ1(12))S_{5}^{\mathrm{new}}(\Gamma_1(12))⊕4^{\oplus 4}⊕\oplusS5new(Γ1(18))S_{5}^{\mathrm{new}}(\Gamma_1(18))⊕3^{\oplus 3}⊕\oplusS5new(Γ1(24))S_{5}^{\mathrm{new}}(\Gamma_1(24))⊕2^{\oplus 2}⊕\oplusS5new(Γ1(36))S_{5}^{\mathrm{new}}(\Gamma_1(36))⊕2^{\oplus 2}