# Properties

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

## 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

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

## 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

$$S_{4}^{\mathrm{old}}(\Gamma_1(1584)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 30}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 20}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 18}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 16}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 10}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 15}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 10}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 9}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(132))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(198))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(264))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(396))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(528))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(792))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(1584))$$$$^{\oplus 1}$$