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Properties

Label 168.4
Level 168
Weight 4
Dimension 914
Nonzero newspaces 12
Newform subspaces 29
Sturm bound 6144
Trace bound 3

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Defining parameters

Level: N N = 168=23⋅3⋅7 168 = 2^{3} \cdot 3 \cdot 7
Weight: k k = 4 4
Nonzero newspaces: 12 12
Newform subspaces: 29 29
Sturm bound: 61446144
Trace bound: 33

Dimensions

The following table gives the dimensions of various subspaces of M4(Γ1(168))M_{4}(\Gamma_1(168)).

Total New Old
Modular forms 2448 954 1494
Cusp forms 2160 914 1246
Eisenstein series 288 40 248

Trace form

914q−4q2−8q3−52q4−28q5+22q6−16q7+152q8+124q9−84q10−28q11+106q12−8q13+100q14−108q15+180q16−280q17−338q18+⋯−5560q99+O(q100) 914 q - 4 q^{2} - 8 q^{3} - 52 q^{4} - 28 q^{5} + 22 q^{6} - 16 q^{7} + 152 q^{8} + 124 q^{9} - 84 q^{10} - 28 q^{11} + 106 q^{12} - 8 q^{13} + 100 q^{14} - 108 q^{15} + 180 q^{16} - 280 q^{17} - 338 q^{18}+ \cdots - 5560 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(Γ1(168))S_{4}^{\mathrm{new}}(\Gamma_1(168))

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
168.4.a χ168(1,⋅)\chi_{168}(1, \cdot) 168.4.a.a 1 1
168.4.a.b 1
168.4.a.c 1
168.4.a.d 1
168.4.a.e 1
168.4.a.f 1
168.4.a.g 2
168.4.a.h 2
168.4.b χ168(55,⋅)\chi_{168}(55, \cdot) None 0 1
168.4.c χ168(85,⋅)\chi_{168}(85, \cdot) 168.4.c.a 16 1
168.4.c.b 20
168.4.h χ168(71,⋅)\chi_{168}(71, \cdot) None 0 1
168.4.i χ168(125,⋅)\chi_{168}(125, \cdot) 168.4.i.a 4 1
168.4.i.b 8
168.4.i.c 80
168.4.j χ168(155,⋅)\chi_{168}(155, \cdot) 168.4.j.a 72 1
168.4.k χ168(41,⋅)\chi_{168}(41, \cdot) 168.4.k.a 24 1
168.4.p χ168(139,⋅)\chi_{168}(139, \cdot) 168.4.p.a 48 1
168.4.q χ168(25,⋅)\chi_{168}(25, \cdot) 168.4.q.a 2 2
168.4.q.b 2
168.4.q.c 2
168.4.q.d 4
168.4.q.e 6
168.4.q.f 8
168.4.t χ168(19,⋅)\chi_{168}(19, \cdot) 168.4.t.a 96 2
168.4.u χ168(17,⋅)\chi_{168}(17, \cdot) 168.4.u.a 48 2
168.4.v χ168(11,⋅)\chi_{168}(11, \cdot) 168.4.v.a 184 2
168.4.ba χ168(5,⋅)\chi_{168}(5, \cdot) 168.4.ba.a 4 2
168.4.ba.b 4
168.4.ba.c 176
168.4.bb χ168(23,⋅)\chi_{168}(23, \cdot) None 0 2
168.4.bc χ168(37,⋅)\chi_{168}(37, \cdot) 168.4.bc.a 96 2
168.4.bd χ168(31,⋅)\chi_{168}(31, \cdot) None 0 2

Decomposition of S4old(Γ1(168))S_{4}^{\mathrm{old}}(\Gamma_1(168)) into lower level spaces

S4old(Γ1(168))≅ S_{4}^{\mathrm{old}}(\Gamma_1(168)) \cong S4new(Γ1(1))S_{4}^{\mathrm{new}}(\Gamma_1(1))⊕16^{\oplus 16}⊕\oplusS4new(Γ1(2))S_{4}^{\mathrm{new}}(\Gamma_1(2))⊕12^{\oplus 12}⊕\oplusS4new(Γ1(3))S_{4}^{\mathrm{new}}(\Gamma_1(3))⊕8^{\oplus 8}⊕\oplusS4new(Γ1(4))S_{4}^{\mathrm{new}}(\Gamma_1(4))⊕8^{\oplus 8}⊕\oplusS4new(Γ1(6))S_{4}^{\mathrm{new}}(\Gamma_1(6))⊕6^{\oplus 6}⊕\oplusS4new(Γ1(7))S_{4}^{\mathrm{new}}(\Gamma_1(7))⊕8^{\oplus 8}⊕\oplusS4new(Γ1(8))S_{4}^{\mathrm{new}}(\Gamma_1(8))⊕4^{\oplus 4}⊕\oplusS4new(Γ1(12))S_{4}^{\mathrm{new}}(\Gamma_1(12))⊕4^{\oplus 4}⊕\oplusS4new(Γ1(14))S_{4}^{\mathrm{new}}(\Gamma_1(14))⊕6^{\oplus 6}⊕\oplusS4new(Γ1(21))S_{4}^{\mathrm{new}}(\Gamma_1(21))⊕4^{\oplus 4}⊕\oplusS4new(Γ1(24))S_{4}^{\mathrm{new}}(\Gamma_1(24))⊕2^{\oplus 2}⊕\oplusS4new(Γ1(28))S_{4}^{\mathrm{new}}(\Gamma_1(28))⊕4^{\oplus 4}⊕\oplusS4new(Γ1(42))S_{4}^{\mathrm{new}}(\Gamma_1(42))⊕3^{\oplus 3}⊕\oplusS4new(Γ1(56))S_{4}^{\mathrm{new}}(\Gamma_1(56))⊕2^{\oplus 2}⊕\oplusS4new(Γ1(84))S_{4}^{\mathrm{new}}(\Gamma_1(84))⊕2^{\oplus 2}