↑

Properties

Label 1080.4
Level 1080
Weight 4
Dimension 37824
Nonzero newspaces 27
Sturm bound 248832
Trace bound 22

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 27 \)
Sturm bound: \(248832\)
Trace bound: \(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1080))\).

Total New Old
Modular forms 94752 38208 56544
Cusp forms 91872 37824 54048
Eisenstein series 2880 384 2496

Trace form

\( 37824 q - 16 q^{2} - 24 q^{3} - 28 q^{4} - 10 q^{5} - 72 q^{6} - 76 q^{7} - 28 q^{8} - 48 q^{9} + O(q^{10}) \) \( 37824 q - 16 q^{2} - 24 q^{3} - 28 q^{4} - 10 q^{5} - 72 q^{6} - 76 q^{7} - 28 q^{8} - 48 q^{9} + 30 q^{10} - 120 q^{11} - 24 q^{12} - 12 q^{13} + 116 q^{14} + 96 q^{15} + 36 q^{16} + 420 q^{17} - 24 q^{18} + 20 q^{19} - 306 q^{20} + 120 q^{21} - 468 q^{22} - 84 q^{23} + 300 q^{24} + 138 q^{25} + 2676 q^{26} + 870 q^{27} + 1208 q^{28} + 684 q^{29} - 276 q^{30} - 780 q^{31} - 3636 q^{32} - 570 q^{33} - 2236 q^{34} - 2126 q^{35} - 4272 q^{36} - 2220 q^{37} - 4580 q^{38} - 1680 q^{39} - 558 q^{40} + 444 q^{41} + 816 q^{42} - 964 q^{43} + 4620 q^{44} + 1674 q^{45} + 4196 q^{46} + 4432 q^{47} + 4332 q^{48} + 2794 q^{49} + 786 q^{50} - 3696 q^{51} - 500 q^{52} - 1088 q^{53} - 24 q^{54} - 190 q^{55} - 8540 q^{56} - 498 q^{57} - 7852 q^{58} + 8494 q^{59} - 3696 q^{60} + 900 q^{61} - 5388 q^{62} + 2760 q^{63} - 820 q^{64} - 1482 q^{65} + 7308 q^{66} - 9676 q^{67} + 13116 q^{68} - 192 q^{69} + 8090 q^{70} - 21068 q^{71} + 11904 q^{72} + 772 q^{73} + 22180 q^{74} + 1542 q^{75} + 12708 q^{76} + 1264 q^{77} + 3852 q^{78} + 3908 q^{79} + 5594 q^{80} + 408 q^{81} + 4496 q^{82} + 12932 q^{83} - 11244 q^{84} + 12 q^{85} - 22596 q^{86} + 7164 q^{87} - 7332 q^{88} - 8406 q^{89} - 21126 q^{90} - 3448 q^{91} - 27244 q^{92} - 12960 q^{93} - 452 q^{94} - 13080 q^{95} - 7872 q^{96} - 2900 q^{97} - 7828 q^{98} + 7596 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1080))\)

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
1080.4.a \(\chi_{1080}(1, \cdot)\) 1080.4.a.a 2 1
1080.4.a.b 2
1080.4.a.c 3
1080.4.a.d 3
1080.4.a.e 3
1080.4.a.f 3
1080.4.a.g 3
1080.4.a.h 3
1080.4.a.i 3
1080.4.a.j 3
1080.4.a.k 3
1080.4.a.l 3
1080.4.a.m 3
1080.4.a.n 3
1080.4.a.o 4
1080.4.a.p 4
1080.4.b \(\chi_{1080}(971, \cdot)\) n/a 192 1
1080.4.d \(\chi_{1080}(109, \cdot)\) n/a 288 1
1080.4.f \(\chi_{1080}(649, \cdot)\) 1080.4.f.a 16 1
1080.4.f.b 18
1080.4.f.c 18
1080.4.f.d 20
1080.4.h \(\chi_{1080}(431, \cdot)\) None 0 1
1080.4.k \(\chi_{1080}(541, \cdot)\) n/a 192 1
1080.4.m \(\chi_{1080}(539, \cdot)\) n/a 288 1
1080.4.o \(\chi_{1080}(1079, \cdot)\) None 0 1
1080.4.q \(\chi_{1080}(361, \cdot)\) 1080.4.q.a 2 2
1080.4.q.b 16
1080.4.q.c 16
1080.4.q.d 18
1080.4.q.e 20
1080.4.s \(\chi_{1080}(377, \cdot)\) n/a 144 2
1080.4.t \(\chi_{1080}(487, \cdot)\) None 0 2
1080.4.w \(\chi_{1080}(163, \cdot)\) n/a 576 2
1080.4.x \(\chi_{1080}(53, \cdot)\) n/a 576 2
1080.4.bb \(\chi_{1080}(359, \cdot)\) None 0 2
1080.4.bd \(\chi_{1080}(179, \cdot)\) n/a 424 2
1080.4.bf \(\chi_{1080}(181, \cdot)\) n/a 288 2
1080.4.bg \(\chi_{1080}(71, \cdot)\) None 0 2
1080.4.bi \(\chi_{1080}(289, \cdot)\) n/a 108 2
1080.4.bk \(\chi_{1080}(469, \cdot)\) n/a 424 2
1080.4.bm \(\chi_{1080}(251, \cdot)\) n/a 288 2
1080.4.bo \(\chi_{1080}(121, \cdot)\) n/a 648 6
1080.4.bp \(\chi_{1080}(307, \cdot)\) n/a 848 4
1080.4.bs \(\chi_{1080}(197, \cdot)\) n/a 848 4
1080.4.bt \(\chi_{1080}(17, \cdot)\) n/a 216 4
1080.4.bw \(\chi_{1080}(127, \cdot)\) None 0 4
1080.4.bx \(\chi_{1080}(59, \cdot)\) n/a 3864 6
1080.4.cc \(\chi_{1080}(61, \cdot)\) n/a 2592 6
1080.4.cd \(\chi_{1080}(119, \cdot)\) None 0 6
1080.4.cg \(\chi_{1080}(49, \cdot)\) n/a 972 6
1080.4.ch \(\chi_{1080}(11, \cdot)\) n/a 2592 6
1080.4.ci \(\chi_{1080}(191, \cdot)\) None 0 6
1080.4.cj \(\chi_{1080}(229, \cdot)\) n/a 3864 6
1080.4.co \(\chi_{1080}(77, \cdot)\) n/a 7728 12
1080.4.cp \(\chi_{1080}(7, \cdot)\) None 0 12
1080.4.cs \(\chi_{1080}(113, \cdot)\) n/a 1944 12
1080.4.ct \(\chi_{1080}(43, \cdot)\) n/a 7728 12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1080))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1080)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 2}\)