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Properties

Label 88.5
Level 88
Weight 5
Dimension 514
Nonzero newspaces 6
Newform subspaces 9
Sturm bound 2400
Trace bound 2

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Defining parameters

Level: \( N \) = \( 88 = 2^{3} \cdot 11 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 9 \)
Sturm bound: \(2400\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(88))\).

Total New Old
Modular forms 1020 550 470
Cusp forms 900 514 386
Eisenstein series 120 36 84

Trace form

\( 514 q - 14 q^{2} - 6 q^{3} + 14 q^{4} + 126 q^{6} - 10 q^{7} - 314 q^{8} - 70 q^{9} + O(q^{10}) \) \( 514 q - 14 q^{2} - 6 q^{3} + 14 q^{4} + 126 q^{6} - 10 q^{7} - 314 q^{8} - 70 q^{9} - 490 q^{10} + 88 q^{11} + 764 q^{12} + 950 q^{14} + 350 q^{15} - 1066 q^{16} - 496 q^{17} - 1110 q^{18} - 2434 q^{19} + 950 q^{20} + 122 q^{22} + 820 q^{23} + 726 q^{24} + 2790 q^{25} + 470 q^{26} + 5586 q^{27} - 1930 q^{28} - 480 q^{29} - 3700 q^{30} - 3810 q^{31} - 4424 q^{32} - 5452 q^{33} + 796 q^{34} - 6250 q^{35} + 6670 q^{36} + 9804 q^{38} + 14870 q^{39} + 20660 q^{40} + 3176 q^{41} + 14880 q^{42} + 14512 q^{43} - 6092 q^{44} - 5160 q^{45} - 22240 q^{46} - 9370 q^{47} - 35156 q^{48} - 10226 q^{49} - 31340 q^{50} - 33166 q^{51} - 11320 q^{52} + 9120 q^{53} + 12214 q^{54} + 10230 q^{55} + 18100 q^{56} + 10136 q^{57} + 11060 q^{58} + 3318 q^{59} + 12000 q^{60} - 8480 q^{61} + 19190 q^{62} - 10580 q^{63} - 7306 q^{64} - 3860 q^{65} - 2898 q^{66} - 11376 q^{67} + 31014 q^{68} + 19520 q^{69} + 31680 q^{70} - 11050 q^{71} + 53940 q^{72} - 28456 q^{73} - 13720 q^{74} + 48790 q^{75} - 33674 q^{76} + 21000 q^{77} - 78140 q^{78} + 64550 q^{79} - 112360 q^{80} + 12786 q^{81} - 55566 q^{82} + 32334 q^{83} - 68770 q^{84} + 19920 q^{85} + 6638 q^{86} + 33222 q^{88} + 18756 q^{89} + 103830 q^{90} - 46450 q^{91} + 73190 q^{92} - 20400 q^{93} + 84110 q^{94} - 99130 q^{95} + 151176 q^{96} - 75308 q^{97} + 65776 q^{98} - 110860 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(88))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
88.5.b \(\chi_{88}(21, \cdot)\) 88.5.b.a 1 1
88.5.b.b 1
88.5.b.c 44
88.5.d \(\chi_{88}(23, \cdot)\) None 0 1
88.5.f \(\chi_{88}(67, \cdot)\) 88.5.f.a 40 1
88.5.h \(\chi_{88}(65, \cdot)\) 88.5.h.a 12 1
88.5.j \(\chi_{88}(17, \cdot)\) 88.5.j.a 48 4
88.5.l \(\chi_{88}(3, \cdot)\) 88.5.l.a 8 4
88.5.l.b 176
88.5.n \(\chi_{88}(15, \cdot)\) None 0 4
88.5.p \(\chi_{88}(13, \cdot)\) 88.5.p.a 184 4

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(88))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(88)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)