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Properties

Label 3888.2
Level 3888
Weight 2
Dimension 185760
Nonzero newspaces 20
Sturm bound 1679616
Trace bound 46

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Defining parameters

Level: \( N \) = \( 3888 = 2^{4} \cdot 3^{5} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(1679616\)
Trace bound: \(46\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3888))\).

Total New Old
Modular forms 425196 187488 237708
Cusp forms 414613 185760 228853
Eisenstein series 10583 1728 8855

Trace form

\( 185760 q - 144 q^{2} - 162 q^{3} - 240 q^{4} - 180 q^{5} - 216 q^{6} - 180 q^{7} - 144 q^{8} - 54 q^{9} + O(q^{10}) \) \( 185760 q - 144 q^{2} - 162 q^{3} - 240 q^{4} - 180 q^{5} - 216 q^{6} - 180 q^{7} - 144 q^{8} - 54 q^{9} - 336 q^{10} - 108 q^{11} - 216 q^{12} - 300 q^{13} - 144 q^{14} - 162 q^{15} - 240 q^{16} - 324 q^{17} - 216 q^{18} - 252 q^{19} - 144 q^{20} - 270 q^{21} - 240 q^{22} - 108 q^{23} - 216 q^{24} - 60 q^{25} - 144 q^{26} - 162 q^{27} - 444 q^{28} - 180 q^{29} - 216 q^{30} - 180 q^{31} - 144 q^{32} - 486 q^{33} - 240 q^{34} - 108 q^{35} - 216 q^{36} - 420 q^{37} - 144 q^{38} - 162 q^{39} - 240 q^{40} - 36 q^{41} - 216 q^{42} - 180 q^{43} - 144 q^{44} - 270 q^{45} - 336 q^{46} - 108 q^{47} - 216 q^{48} - 540 q^{49} - 144 q^{50} - 162 q^{51} - 240 q^{52} - 189 q^{53} - 216 q^{54} - 333 q^{55} - 144 q^{56} - 54 q^{57} - 240 q^{58} - 108 q^{59} - 216 q^{60} - 300 q^{61} - 144 q^{62} - 162 q^{63} - 336 q^{64} - 324 q^{65} - 216 q^{66} - 180 q^{67} - 144 q^{68} - 270 q^{69} - 240 q^{70} - 108 q^{71} - 216 q^{72} - 84 q^{73} - 144 q^{74} - 162 q^{75} - 240 q^{76} - 180 q^{77} - 216 q^{78} - 180 q^{79} - 144 q^{80} - 486 q^{81} - 444 q^{82} - 108 q^{83} - 216 q^{84} - 330 q^{85} - 144 q^{86} - 162 q^{87} - 240 q^{88} - 72 q^{89} - 216 q^{90} - 306 q^{91} - 144 q^{92} - 270 q^{93} - 240 q^{94} - 270 q^{95} - 216 q^{96} - 612 q^{97} - 144 q^{98} - 162 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3888))\)

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
3888.2.a \(\chi_{3888}(1, \cdot)\) 3888.2.a.a 1 1
3888.2.a.b 1
3888.2.a.c 1
3888.2.a.d 1
3888.2.a.e 1
3888.2.a.f 1
3888.2.a.g 1
3888.2.a.h 1
3888.2.a.i 1
3888.2.a.j 1
3888.2.a.k 1
3888.2.a.l 1
3888.2.a.m 1
3888.2.a.n 1
3888.2.a.o 1
3888.2.a.p 1
3888.2.a.q 1
3888.2.a.r 1
3888.2.a.s 1
3888.2.a.t 1
3888.2.a.u 1
3888.2.a.v 1
3888.2.a.w 2
3888.2.a.x 2
3888.2.a.y 2
3888.2.a.z 2
3888.2.a.ba 2
3888.2.a.bb 2
3888.2.a.bc 2
3888.2.a.bd 3
3888.2.a.be 3
3888.2.a.bf 3
3888.2.a.bg 3
3888.2.a.bh 3
3888.2.a.bi 3
3888.2.a.bj 3
3888.2.a.bk 3
3888.2.a.bl 6
3888.2.a.bm 6
3888.2.c \(\chi_{3888}(3887, \cdot)\) 3888.2.c.a 2 1
3888.2.c.b 2
3888.2.c.c 2
3888.2.c.d 2
3888.2.c.e 2
3888.2.c.f 2
3888.2.c.g 2
3888.2.c.h 2
3888.2.c.i 2
3888.2.c.j 2
3888.2.c.k 2
3888.2.c.l 2
3888.2.c.m 4
3888.2.c.n 4
3888.2.c.o 4
3888.2.c.p 12
3888.2.c.q 24
3888.2.d \(\chi_{3888}(1945, \cdot)\) None 0 1
3888.2.f \(\chi_{3888}(1943, \cdot)\) None 0 1
3888.2.i \(\chi_{3888}(1297, \cdot)\) n/a 144 2
3888.2.k \(\chi_{3888}(973, \cdot)\) n/a 576 2
3888.2.l \(\chi_{3888}(971, \cdot)\) n/a 576 2
3888.2.p \(\chi_{3888}(647, \cdot)\) None 0 2
3888.2.r \(\chi_{3888}(649, \cdot)\) None 0 2
3888.2.s \(\chi_{3888}(1295, \cdot)\) n/a 144 2
3888.2.u \(\chi_{3888}(433, \cdot)\) n/a 408 6
3888.2.v \(\chi_{3888}(323, \cdot)\) n/a 1152 4
3888.2.y \(\chi_{3888}(325, \cdot)\) n/a 1152 4
3888.2.bb \(\chi_{3888}(217, \cdot)\) None 0 6
3888.2.bd \(\chi_{3888}(215, \cdot)\) None 0 6
3888.2.be \(\chi_{3888}(431, \cdot)\) n/a 432 6
3888.2.bg \(\chi_{3888}(145, \cdot)\) n/a 954 18
3888.2.bh \(\chi_{3888}(109, \cdot)\) n/a 3360 12
3888.2.bk \(\chi_{3888}(107, \cdot)\) n/a 3360 12
3888.2.bn \(\chi_{3888}(71, \cdot)\) None 0 18
3888.2.bp \(\chi_{3888}(73, \cdot)\) None 0 18
3888.2.bq \(\chi_{3888}(143, \cdot)\) n/a 972 18
3888.2.bs \(\chi_{3888}(49, \cdot)\) n/a 8694 54
3888.2.bt \(\chi_{3888}(35, \cdot)\) n/a 7704 36
3888.2.bw \(\chi_{3888}(37, \cdot)\) n/a 7704 36
3888.2.bz \(\chi_{3888}(25, \cdot)\) None 0 54
3888.2.cb \(\chi_{3888}(23, \cdot)\) None 0 54
3888.2.cc \(\chi_{3888}(47, \cdot)\) n/a 8748 54
3888.2.ce \(\chi_{3888}(13, \cdot)\) n/a 69768 108
3888.2.ch \(\chi_{3888}(11, \cdot)\) n/a 69768 108

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3888))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3888)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(486))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(972))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1296))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1944))\)\(^{\oplus 2}\)