# Properties

 Label 2592.2 Level 2592 Weight 2 Dimension 82384 Nonzero newspaces 24 Sturm bound 746496 Trace bound 89

## Defining parameters

 Level: $$N$$ = $$2592 = 2^{5} \cdot 3^{4}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$746496$$ Trace bound: $$89$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2592))$$.

Total New Old
Modular forms 190080 83504 106576
Cusp forms 183169 82384 100785
Eisenstein series 6911 1120 5791

## Trace form

 $$82384 q - 96 q^{2} - 108 q^{3} - 160 q^{4} - 96 q^{5} - 144 q^{6} - 120 q^{7} - 96 q^{8} - 216 q^{9} + O(q^{10})$$ $$82384 q - 96 q^{2} - 108 q^{3} - 160 q^{4} - 96 q^{5} - 144 q^{6} - 120 q^{7} - 96 q^{8} - 216 q^{9} - 232 q^{10} - 72 q^{11} - 144 q^{12} - 160 q^{13} - 96 q^{14} - 108 q^{15} - 160 q^{16} - 48 q^{17} - 144 q^{18} - 174 q^{19} - 96 q^{20} - 144 q^{21} - 160 q^{22} - 72 q^{23} - 144 q^{24} - 240 q^{25} - 96 q^{26} - 108 q^{27} - 232 q^{28} - 96 q^{29} - 144 q^{30} - 120 q^{31} - 96 q^{32} - 360 q^{33} - 160 q^{34} - 78 q^{35} - 144 q^{36} - 232 q^{37} - 96 q^{38} - 108 q^{39} - 160 q^{40} - 144 q^{41} - 144 q^{42} - 120 q^{43} - 96 q^{44} - 144 q^{45} - 232 q^{46} - 72 q^{47} - 144 q^{48} - 80 q^{49} - 96 q^{50} - 108 q^{51} - 160 q^{52} - 96 q^{53} - 144 q^{54} - 194 q^{55} - 96 q^{56} - 216 q^{57} - 160 q^{58} - 108 q^{59} - 144 q^{60} - 208 q^{61} - 96 q^{62} - 108 q^{63} - 232 q^{64} - 336 q^{65} - 144 q^{66} - 168 q^{67} - 96 q^{68} - 144 q^{69} - 160 q^{70} - 150 q^{71} - 144 q^{72} - 396 q^{73} - 96 q^{74} - 108 q^{75} - 160 q^{76} - 192 q^{77} - 144 q^{78} - 168 q^{79} - 96 q^{80} - 72 q^{81} - 448 q^{82} - 132 q^{83} - 144 q^{84} - 208 q^{85} - 96 q^{86} - 108 q^{87} - 160 q^{88} - 168 q^{89} - 144 q^{90} - 202 q^{91} - 96 q^{92} - 144 q^{93} - 128 q^{94} - 102 q^{95} - 144 q^{96} - 400 q^{97} - 96 q^{98} - 108 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2592))$$

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
2592.2.a $$\chi_{2592}(1, \cdot)$$ 2592.2.a.a 1 1
2592.2.a.b 1
2592.2.a.c 1
2592.2.a.d 1
2592.2.a.e 1
2592.2.a.f 1
2592.2.a.g 1
2592.2.a.h 1
2592.2.a.i 2
2592.2.a.j 2
2592.2.a.k 2
2592.2.a.l 2
2592.2.a.m 2
2592.2.a.n 2
2592.2.a.o 2
2592.2.a.p 2
2592.2.a.q 2
2592.2.a.r 2
2592.2.a.s 2
2592.2.a.t 2
2592.2.a.u 4
2592.2.a.v 4
2592.2.a.w 4
2592.2.a.x 4
2592.2.c $$\chi_{2592}(2591, \cdot)$$ 2592.2.c.a 8 1
2592.2.c.b 16
2592.2.c.c 24
2592.2.d $$\chi_{2592}(1297, \cdot)$$ 2592.2.d.a 2 1
2592.2.d.b 2
2592.2.d.c 2
2592.2.d.d 2
2592.2.d.e 4
2592.2.d.f 4
2592.2.d.g 4
2592.2.d.h 4
2592.2.d.i 4
2592.2.d.j 8
2592.2.d.k 8
2592.2.f $$\chi_{2592}(1295, \cdot)$$ 2592.2.f.a 4 1
2592.2.f.b 16
2592.2.f.c 24
2592.2.i $$\chi_{2592}(865, \cdot)$$ 2592.2.i.a 2 2
2592.2.i.b 2
2592.2.i.c 2
2592.2.i.d 2
2592.2.i.e 2
2592.2.i.f 2
2592.2.i.g 2
2592.2.i.h 2
2592.2.i.i 2
2592.2.i.j 2
2592.2.i.k 2
2592.2.i.l 2
2592.2.i.m 2
2592.2.i.n 2
2592.2.i.o 2
2592.2.i.p 2
2592.2.i.q 2
2592.2.i.r 2
2592.2.i.s 2
2592.2.i.t 2
2592.2.i.u 2
2592.2.i.v 2
2592.2.i.w 2
2592.2.i.x 2
2592.2.i.y 4
2592.2.i.z 4
2592.2.i.ba 4
2592.2.i.bb 4
2592.2.i.bc 4
2592.2.i.bd 4
2592.2.i.be 4
2592.2.i.bf 4
2592.2.i.bg 8
2592.2.i.bh 8
2592.2.k $$\chi_{2592}(649, \cdot)$$ None 0 2
2592.2.l $$\chi_{2592}(647, \cdot)$$ None 0 2
2592.2.p $$\chi_{2592}(431, \cdot)$$ 2592.2.p.a 4 2
2592.2.p.b 4
2592.2.p.c 4
2592.2.p.d 8
2592.2.p.e 8
2592.2.p.f 16
2592.2.p.g 48
2592.2.r $$\chi_{2592}(433, \cdot)$$ 2592.2.r.a 4 2
2592.2.r.b 4
2592.2.r.c 4
2592.2.r.d 4
2592.2.r.e 4
2592.2.r.f 4
2592.2.r.g 4
2592.2.r.h 4
2592.2.r.i 4
2592.2.r.j 4
2592.2.r.k 4
2592.2.r.l 4
2592.2.r.m 4
2592.2.r.n 8
2592.2.r.o 8
2592.2.r.p 8
2592.2.r.q 16
2592.2.s $$\chi_{2592}(863, \cdot)$$ 2592.2.s.a 8 2
2592.2.s.b 8
2592.2.s.c 8
2592.2.s.d 8
2592.2.s.e 8
2592.2.s.f 8
2592.2.s.g 8
2592.2.s.h 8
2592.2.s.i 16
2592.2.s.j 16
2592.2.v $$\chi_{2592}(325, \cdot)$$ n/a 752 4
2592.2.w $$\chi_{2592}(323, \cdot)$$ n/a 752 4
2592.2.y $$\chi_{2592}(289, \cdot)$$ n/a 216 6
2592.2.z $$\chi_{2592}(215, \cdot)$$ None 0 4
2592.2.bc $$\chi_{2592}(217, \cdot)$$ None 0 4
2592.2.bf $$\chi_{2592}(145, \cdot)$$ n/a 204 6
2592.2.bh $$\chi_{2592}(143, \cdot)$$ n/a 204 6
2592.2.bi $$\chi_{2592}(287, \cdot)$$ n/a 216 6
2592.2.bk $$\chi_{2592}(109, \cdot)$$ n/a 1520 8
2592.2.bn $$\chi_{2592}(107, \cdot)$$ n/a 1520 8
2592.2.bo $$\chi_{2592}(97, \cdot)$$ n/a 1944 18
2592.2.bp $$\chi_{2592}(73, \cdot)$$ None 0 12
2592.2.bs $$\chi_{2592}(71, \cdot)$$ None 0 12
2592.2.bv $$\chi_{2592}(47, \cdot)$$ n/a 1908 18
2592.2.bx $$\chi_{2592}(49, \cdot)$$ n/a 1908 18
2592.2.by $$\chi_{2592}(95, \cdot)$$ n/a 1944 18
2592.2.cb $$\chi_{2592}(35, \cdot)$$ n/a 3408 24
2592.2.cc $$\chi_{2592}(37, \cdot)$$ n/a 3408 24
2592.2.ce $$\chi_{2592}(23, \cdot)$$ None 0 36
2592.2.ch $$\chi_{2592}(25, \cdot)$$ None 0 36
2592.2.ci $$\chi_{2592}(11, \cdot)$$ n/a 30960 72
2592.2.cl $$\chi_{2592}(13, \cdot)$$ n/a 30960 72

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2592))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2592)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 25}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(162))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(288))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(324))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(432))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(648))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(864))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1296))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2592))$$$$^{\oplus 1}$$