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Properties

Label 88.4
Level 88
Weight 4
Dimension 379
Nonzero newspaces 6
Newform subspaces 12
Sturm bound 1920
Trace bound 2

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Defining parameters

Level: \( N \) = \( 88 = 2^{3} \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 12 \)
Sturm bound: \(1920\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(88))\).

Total New Old
Modular forms 780 415 365
Cusp forms 660 379 281
Eisenstein series 120 36 84

Trace form

\( 379 q - 6 q^{2} - 2 q^{3} + 14 q^{4} + 4 q^{5} - 66 q^{6} - 26 q^{7} - 90 q^{8} + 6 q^{9} + O(q^{10}) \) \( 379 q - 6 q^{2} - 2 q^{3} + 14 q^{4} + 4 q^{5} - 66 q^{6} - 26 q^{7} - 90 q^{8} + 6 q^{9} + 102 q^{10} + 34 q^{11} + 92 q^{12} - 44 q^{13} - 42 q^{14} - 460 q^{15} - 42 q^{16} - 54 q^{17} - 14 q^{18} + 127 q^{19} - 234 q^{20} + 612 q^{21} + 74 q^{22} + 890 q^{23} + 214 q^{24} + 350 q^{25} - 570 q^{26} - 449 q^{27} - 202 q^{28} - 746 q^{29} + 484 q^{30} - 1276 q^{31} + 1584 q^{32} + 641 q^{33} + 1804 q^{34} + 956 q^{35} + 1006 q^{36} + 324 q^{37} - 268 q^{38} - 94 q^{39} - 2628 q^{40} - 454 q^{41} - 4072 q^{42} - 1394 q^{43} - 3188 q^{44} - 1274 q^{45} - 3208 q^{46} - 3340 q^{47} - 3884 q^{48} + 240 q^{49} - 28 q^{50} + 445 q^{51} + 2560 q^{52} - 1336 q^{53} + 3894 q^{54} + 2008 q^{55} + 5140 q^{56} + 1353 q^{57} + 3340 q^{58} + 2131 q^{59} + 2584 q^{60} - 200 q^{61} + 886 q^{62} + 3116 q^{63} - 1162 q^{64} + 428 q^{65} + 158 q^{66} + 2124 q^{67} - 346 q^{68} + 1672 q^{69} - 4336 q^{70} + 3922 q^{71} - 7580 q^{72} + 4718 q^{73} - 7336 q^{74} + 3667 q^{75} - 4394 q^{76} - 934 q^{77} - 1500 q^{78} - 682 q^{79} + 6088 q^{80} - 1903 q^{81} + 5410 q^{82} - 8387 q^{83} + 8094 q^{84} - 4660 q^{85} + 11518 q^{86} - 12236 q^{87} + 13574 q^{88} - 5082 q^{89} + 12918 q^{90} - 12396 q^{91} + 1702 q^{92} - 9590 q^{93} + 6734 q^{94} - 3386 q^{95} + 2656 q^{96} - 4315 q^{97} - 3656 q^{98} + 3956 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(88))\)

We only show spaces with even 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
88.4.a \(\chi_{88}(1, \cdot)\) 88.4.a.a 1 1
88.4.a.b 1
88.4.a.c 2
88.4.a.d 3
88.4.c \(\chi_{88}(45, \cdot)\) 88.4.c.a 30 1
88.4.e \(\chi_{88}(87, \cdot)\) None 0 1
88.4.g \(\chi_{88}(43, \cdot)\) 88.4.g.a 2 1
88.4.g.b 32
88.4.i \(\chi_{88}(9, \cdot)\) 88.4.i.a 16 4
88.4.i.b 20
88.4.k \(\chi_{88}(19, \cdot)\) 88.4.k.a 8 4
88.4.k.b 128
88.4.m \(\chi_{88}(7, \cdot)\) None 0 4
88.4.o \(\chi_{88}(5, \cdot)\) 88.4.o.a 136 4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(88))\) into lower level spaces

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