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Properties

Label 1584.4
Level 1584
Weight 4
Dimension 90437
Nonzero newspaces 32
Sturm bound 552960
Trace bound 25

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Defining parameters

Level: \( N \) = \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(552960\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1584))\).

Total New Old
Modular forms 209600 91165 118435
Cusp forms 205120 90437 114683
Eisenstein series 4480 728 3752

Trace form

\( 90437 q - 48 q^{2} - 48 q^{3} - 68 q^{4} - 61 q^{5} - 64 q^{6} - 63 q^{7} + 36 q^{8} + 24 q^{9} + O(q^{10}) \) \( 90437 q - 48 q^{2} - 48 q^{3} - 68 q^{4} - 61 q^{5} - 64 q^{6} - 63 q^{7} + 36 q^{8} + 24 q^{9} - 12 q^{10} + 30 q^{11} - 144 q^{12} + 39 q^{13} - 300 q^{14} - 6 q^{15} + 444 q^{16} + 97 q^{17} + 216 q^{18} - 379 q^{19} - 892 q^{20} - 678 q^{21} - 476 q^{22} - 728 q^{23} - 1536 q^{24} - 1365 q^{25} - 1700 q^{26} + 708 q^{27} - 996 q^{28} + 499 q^{29} + 936 q^{30} - 267 q^{31} + 1932 q^{32} - 117 q^{33} + 1800 q^{34} + 201 q^{35} - 1592 q^{36} + 1715 q^{37} - 2404 q^{38} + 402 q^{39} + 1468 q^{40} + 1699 q^{41} + 1296 q^{42} - 1704 q^{43} + 2156 q^{44} + 346 q^{45} + 3476 q^{46} - 6741 q^{47} + 4824 q^{48} - 2569 q^{49} + 7152 q^{50} - 3968 q^{51} + 3876 q^{52} + 237 q^{53} + 376 q^{54} - 799 q^{55} - 5880 q^{56} - 2316 q^{57} - 4580 q^{58} + 8645 q^{59} - 15928 q^{60} + 2247 q^{61} - 9516 q^{62} + 5034 q^{63} - 3332 q^{64} + 3678 q^{65} + 4848 q^{66} - 5776 q^{67} + 6820 q^{68} + 5626 q^{69} - 136 q^{70} - 1763 q^{71} + 15840 q^{72} - 1929 q^{73} + 17632 q^{74} + 1000 q^{75} + 4708 q^{76} + 7088 q^{77} + 888 q^{78} + 1523 q^{79} - 20256 q^{80} + 808 q^{81} - 18444 q^{82} - 353 q^{83} - 19168 q^{84} - 2375 q^{85} - 31260 q^{86} + 438 q^{87} - 23088 q^{88} - 8438 q^{89} - 2368 q^{90} + 6105 q^{91} + 14220 q^{92} - 1822 q^{93} + 13372 q^{94} + 1149 q^{95} + 12856 q^{96} - 4865 q^{97} + 33948 q^{98} + 1515 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1584))\)

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
1584.4.a \(\chi_{1584}(1, \cdot)\) 1584.4.a.a 1 1
1584.4.a.b 1
1584.4.a.c 1
1584.4.a.d 1
1584.4.a.e 1
1584.4.a.f 1
1584.4.a.g 1
1584.4.a.h 1
1584.4.a.i 1
1584.4.a.j 1
1584.4.a.k 1
1584.4.a.l 1
1584.4.a.m 1
1584.4.a.n 1
1584.4.a.o 1
1584.4.a.p 1
1584.4.a.q 1
1584.4.a.r 1
1584.4.a.s 1
1584.4.a.t 1
1584.4.a.u 1
1584.4.a.v 1
1584.4.a.w 2
1584.4.a.x 2
1584.4.a.y 2
1584.4.a.z 2
1584.4.a.ba 2
1584.4.a.bb 2
1584.4.a.bc 2
1584.4.a.bd 2
1584.4.a.be 2
1584.4.a.bf 2
1584.4.a.bg 2
1584.4.a.bh 2
1584.4.a.bi 2
1584.4.a.bj 2
1584.4.a.bk 2
1584.4.a.bl 3
1584.4.a.bm 3
1584.4.a.bn 3
1584.4.a.bo 3
1584.4.a.bp 3
1584.4.a.bq 4
1584.4.a.br 4
1584.4.b \(\chi_{1584}(593, \cdot)\) 1584.4.b.a 2 1
1584.4.b.b 2
1584.4.b.c 6
1584.4.b.d 6
1584.4.b.e 6
1584.4.b.f 6
1584.4.b.g 8
1584.4.b.h 18
1584.4.b.i 18
1584.4.d \(\chi_{1584}(287, \cdot)\) 1584.4.d.a 10 1
1584.4.d.b 10
1584.4.d.c 20
1584.4.d.d 20
1584.4.f \(\chi_{1584}(793, \cdot)\) None 0 1
1584.4.h \(\chi_{1584}(1495, \cdot)\) None 0 1
1584.4.k \(\chi_{1584}(1079, \cdot)\) None 0 1
1584.4.m \(\chi_{1584}(1385, \cdot)\) None 0 1
1584.4.o \(\chi_{1584}(703, \cdot)\) 1584.4.o.a 2 1
1584.4.o.b 2
1584.4.o.c 2
1584.4.o.d 4
1584.4.o.e 4
1584.4.o.f 8
1584.4.o.g 8
1584.4.o.h 12
1584.4.o.i 24
1584.4.o.j 24
1584.4.q \(\chi_{1584}(529, \cdot)\) n/a 360 2
1584.4.r \(\chi_{1584}(307, \cdot)\) n/a 716 2
1584.4.u \(\chi_{1584}(397, \cdot)\) n/a 600 2
1584.4.v \(\chi_{1584}(683, \cdot)\) n/a 480 2
1584.4.y \(\chi_{1584}(197, \cdot)\) n/a 576 2
1584.4.z \(\chi_{1584}(289, \cdot)\) n/a 356 4
1584.4.bc \(\chi_{1584}(175, \cdot)\) n/a 432 2
1584.4.be \(\chi_{1584}(329, \cdot)\) None 0 2
1584.4.bg \(\chi_{1584}(23, \cdot)\) None 0 2
1584.4.bh \(\chi_{1584}(439, \cdot)\) None 0 2
1584.4.bj \(\chi_{1584}(265, \cdot)\) None 0 2
1584.4.bl \(\chi_{1584}(815, \cdot)\) n/a 360 2
1584.4.bn \(\chi_{1584}(65, \cdot)\) n/a 428 2
1584.4.bq \(\chi_{1584}(127, \cdot)\) n/a 360 4
1584.4.bs \(\chi_{1584}(233, \cdot)\) None 0 4
1584.4.bu \(\chi_{1584}(71, \cdot)\) None 0 4
1584.4.bx \(\chi_{1584}(343, \cdot)\) None 0 4
1584.4.bz \(\chi_{1584}(361, \cdot)\) None 0 4
1584.4.cb \(\chi_{1584}(575, \cdot)\) n/a 288 4
1584.4.cd \(\chi_{1584}(17, \cdot)\) n/a 288 4
1584.4.cf \(\chi_{1584}(155, \cdot)\) n/a 2880 4
1584.4.cg \(\chi_{1584}(461, \cdot)\) n/a 3440 4
1584.4.cj \(\chi_{1584}(43, \cdot)\) n/a 3440 4
1584.4.ck \(\chi_{1584}(133, \cdot)\) n/a 2880 4
1584.4.cm \(\chi_{1584}(49, \cdot)\) n/a 1712 8
1584.4.cn \(\chi_{1584}(413, \cdot)\) n/a 2304 8
1584.4.cq \(\chi_{1584}(179, \cdot)\) n/a 2304 8
1584.4.cr \(\chi_{1584}(37, \cdot)\) n/a 2864 8
1584.4.cu \(\chi_{1584}(19, \cdot)\) n/a 2864 8
1584.4.cw \(\chi_{1584}(497, \cdot)\) n/a 1712 8
1584.4.cy \(\chi_{1584}(47, \cdot)\) n/a 1728 8
1584.4.da \(\chi_{1584}(25, \cdot)\) None 0 8
1584.4.dc \(\chi_{1584}(7, \cdot)\) None 0 8
1584.4.dd \(\chi_{1584}(119, \cdot)\) None 0 8
1584.4.df \(\chi_{1584}(41, \cdot)\) None 0 8
1584.4.dh \(\chi_{1584}(79, \cdot)\) n/a 1728 8
1584.4.dl \(\chi_{1584}(157, \cdot)\) n/a 13760 16
1584.4.dm \(\chi_{1584}(139, \cdot)\) n/a 13760 16
1584.4.dp \(\chi_{1584}(29, \cdot)\) n/a 13760 16
1584.4.dq \(\chi_{1584}(59, \cdot)\) n/a 13760 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1584))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1584)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(792))\)\(^{\oplus 2}\)