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Properties

Label 888.2
Level 888
Weight 2
Dimension 9080
Nonzero newspaces 27
Newform subspaces 70
Sturm bound 87552
Trace bound 6

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Defining parameters

Level: \( N \) = \( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 27 \)
Newform subspaces: \( 70 \)
Sturm bound: \(87552\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(888))\).

Total New Old
Modular forms 22752 9360 13392
Cusp forms 21025 9080 11945
Eisenstein series 1727 280 1447

Trace form

\( 9080 q + 4 q^{2} - 30 q^{3} - 64 q^{4} + 4 q^{5} - 40 q^{6} - 64 q^{7} - 8 q^{8} - 66 q^{9} + O(q^{10}) \) \( 9080 q + 4 q^{2} - 30 q^{3} - 64 q^{4} + 4 q^{5} - 40 q^{6} - 64 q^{7} - 8 q^{8} - 66 q^{9} - 80 q^{10} - 8 q^{11} - 52 q^{12} + 4 q^{13} - 8 q^{14} - 48 q^{15} - 72 q^{16} + 4 q^{17} - 24 q^{18} - 72 q^{19} + 16 q^{20} - 56 q^{22} - 12 q^{24} - 126 q^{25} + 16 q^{26} - 54 q^{27} - 72 q^{28} - 12 q^{29} - 28 q^{30} - 96 q^{31} - 16 q^{32} - 80 q^{33} - 112 q^{34} - 44 q^{36} - 6 q^{37} - 16 q^{38} - 24 q^{39} - 88 q^{40} + 4 q^{41} - 44 q^{42} - 40 q^{43} + 4 q^{45} - 56 q^{46} + 48 q^{47} - 20 q^{48} - 146 q^{49} + 4 q^{50} - 104 q^{52} + 4 q^{53} - 48 q^{54} - 56 q^{55} + 16 q^{56} - 88 q^{57} - 48 q^{58} + 64 q^{59} - 36 q^{60} + 94 q^{61} + 8 q^{62} + 64 q^{63} - 40 q^{64} + 122 q^{65} - 52 q^{66} - 48 q^{67} + 128 q^{69} - 56 q^{70} + 80 q^{71} - 60 q^{72} - 4 q^{73} - 16 q^{74} + 86 q^{75} - 24 q^{76} + 144 q^{77} - 52 q^{78} + 48 q^{79} + 94 q^{81} + 80 q^{83} - 20 q^{84} + 170 q^{85} + 16 q^{86} + 108 q^{87} - 104 q^{88} + 142 q^{89} - 28 q^{90} + 16 q^{93} - 120 q^{94} + 16 q^{95} - 84 q^{96} - 100 q^{97} - 12 q^{98} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(888))\)

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
888.2.a \(\chi_{888}(1, \cdot)\) 888.2.a.a 1 1
888.2.a.b 1
888.2.a.c 1
888.2.a.d 1
888.2.a.e 2
888.2.a.f 2
888.2.a.g 2
888.2.a.h 2
888.2.a.i 3
888.2.a.j 3
888.2.c \(\chi_{888}(443, \cdot)\) 888.2.c.a 16 1
888.2.c.b 16
888.2.c.c 20
888.2.c.d 96
888.2.e \(\chi_{888}(815, \cdot)\) None 0 1
888.2.f \(\chi_{888}(445, \cdot)\) 888.2.f.a 28 1
888.2.f.b 44
888.2.h \(\chi_{888}(73, \cdot)\) 888.2.h.a 2 1
888.2.h.b 6
888.2.h.c 10
888.2.j \(\chi_{888}(371, \cdot)\) 888.2.j.a 4 1
888.2.j.b 4
888.2.j.c 136
888.2.l \(\chi_{888}(887, \cdot)\) None 0 1
888.2.o \(\chi_{888}(517, \cdot)\) 888.2.o.a 76 1
888.2.q \(\chi_{888}(121, \cdot)\) 888.2.q.a 2 2
888.2.q.b 2
888.2.q.c 2
888.2.q.d 2
888.2.q.e 6
888.2.q.f 6
888.2.q.g 6
888.2.q.h 6
888.2.q.i 8
888.2.r \(\chi_{888}(43, \cdot)\) 888.2.r.a 2 2
888.2.r.b 2
888.2.r.c 2
888.2.r.d 2
888.2.r.e 72
888.2.r.f 72
888.2.t \(\chi_{888}(31, \cdot)\) None 0 2
888.2.w \(\chi_{888}(413, \cdot)\) 888.2.w.a 296 2
888.2.y \(\chi_{888}(401, \cdot)\) 888.2.y.a 4 2
888.2.y.b 16
888.2.y.c 56
888.2.z \(\chi_{888}(85, \cdot)\) 888.2.z.a 152 2
888.2.bd \(\chi_{888}(491, \cdot)\) 888.2.bd.a 296 2
888.2.bf \(\chi_{888}(455, \cdot)\) None 0 2
888.2.bh \(\chi_{888}(565, \cdot)\) 888.2.bh.a 152 2
888.2.bj \(\chi_{888}(529, \cdot)\) 888.2.bj.a 8 2
888.2.bj.b 8
888.2.bj.c 20
888.2.bk \(\chi_{888}(11, \cdot)\) 888.2.bk.a 296 2
888.2.bm \(\chi_{888}(47, \cdot)\) None 0 2
888.2.bo \(\chi_{888}(49, \cdot)\) 888.2.bo.a 6 6
888.2.bo.b 24
888.2.bo.c 24
888.2.bo.d 30
888.2.bo.e 36
888.2.bp \(\chi_{888}(29, \cdot)\) 888.2.bp.a 592 4
888.2.br \(\chi_{888}(473, \cdot)\) 888.2.br.a 152 4
888.2.bu \(\chi_{888}(547, \cdot)\) 888.2.bu.a 4 4
888.2.bu.b 4
888.2.bu.c 144
888.2.bu.d 152
888.2.bw \(\chi_{888}(103, \cdot)\) None 0 4
888.2.by \(\chi_{888}(71, \cdot)\) None 0 6
888.2.cb \(\chi_{888}(95, \cdot)\) None 0 6
888.2.cc \(\chi_{888}(25, \cdot)\) 888.2.cc.a 48 6
888.2.cc.b 60
888.2.cf \(\chi_{888}(83, \cdot)\) 888.2.cf.a 888 6
888.2.cg \(\chi_{888}(157, \cdot)\) 888.2.cg.a 456 6
888.2.cj \(\chi_{888}(373, \cdot)\) 888.2.cj.a 456 6
888.2.ck \(\chi_{888}(299, \cdot)\) 888.2.ck.a 888 6
888.2.co \(\chi_{888}(17, \cdot)\) 888.2.co.a 456 12
888.2.cp \(\chi_{888}(55, \cdot)\) None 0 12
888.2.cs \(\chi_{888}(19, \cdot)\) 888.2.cs.a 456 12
888.2.cs.b 456
888.2.ct \(\chi_{888}(5, \cdot)\) 888.2.ct.a 1776 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(888))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(888)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 2}\)