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Properties

Label 1080.6
Level 1080
Weight 6
Dimension 63168
Nonzero newspaces 27
Sturm bound 373248
Trace bound 22

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Defining parameters

Level: \( N \) = \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 27 \)
Sturm bound: \(373248\)
Trace bound: \(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(1080))\).

Total New Old
Modular forms 156960 63552 93408
Cusp forms 154080 63168 90912
Eisenstein series 2880 384 2496

Trace form

\( 63168 q - 16 q^{2} - 24 q^{3} - 28 q^{4} + 50 q^{5} - 72 q^{6} + 20 q^{7} + 836 q^{8} - 48 q^{9} + O(q^{10}) \) \( 63168 q - 16 q^{2} - 24 q^{3} - 28 q^{4} + 50 q^{5} - 72 q^{6} + 20 q^{7} + 836 q^{8} - 48 q^{9} - 610 q^{10} - 3336 q^{11} - 24 q^{12} + 3068 q^{13} + 2132 q^{14} - 768 q^{15} + 7460 q^{16} - 8580 q^{17} - 24 q^{18} - 332 q^{19} - 2898 q^{20} + 7464 q^{21} + 10284 q^{22} + 18924 q^{23} + 2892 q^{24} + 14830 q^{25} + 56724 q^{26} - 28722 q^{27} - 76232 q^{28} - 57852 q^{29} - 34836 q^{30} + 4116 q^{31} + 44364 q^{32} + 12714 q^{33} + 120452 q^{34} + 88594 q^{35} + 142608 q^{36} + 55996 q^{37} + 65500 q^{38} - 6864 q^{39} - 64206 q^{40} + 71652 q^{41} - 241104 q^{42} - 76996 q^{43} - 310644 q^{44} - 117234 q^{45} + 125604 q^{46} + 184240 q^{47} + 235020 q^{48} - 148106 q^{49} - 153294 q^{50} + 171264 q^{51} - 111668 q^{52} + 145216 q^{53} - 24 q^{54} - 24766 q^{55} - 397148 q^{56} + 202002 q^{57} - 105644 q^{58} - 169370 q^{59} + 212304 q^{60} - 142996 q^{61} + 1312020 q^{62} - 838776 q^{63} + 205772 q^{64} - 216222 q^{65} - 5652 q^{66} - 9068 q^{67} - 1206468 q^{68} + 699648 q^{69} - 769926 q^{70} + 1368820 q^{71} - 834816 q^{72} + 430348 q^{73} - 490748 q^{74} + 188382 q^{75} + 196324 q^{76} - 643376 q^{77} + 459180 q^{78} - 816540 q^{79} + 874778 q^{80} - 792312 q^{81} + 42256 q^{82} - 2192188 q^{83} + 920148 q^{84} + 15204 q^{85} - 726468 q^{86} + 845244 q^{87} - 892452 q^{88} + 870678 q^{89} - 1495974 q^{90} + 770904 q^{91} + 1348820 q^{92} + 868320 q^{93} + 182524 q^{94} + 1536936 q^{95} + 3429120 q^{96} - 307964 q^{97} + 2997356 q^{98} + 510012 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(1080))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1080.6.a \(\chi_{1080}(1, \cdot)\) 1080.6.a.a 1 1
1080.6.a.b 1
1080.6.a.c 2
1080.6.a.d 2
1080.6.a.e 3
1080.6.a.f 3
1080.6.a.g 3
1080.6.a.h 3
1080.6.a.i 5
1080.6.a.j 5
1080.6.a.k 5
1080.6.a.l 5
1080.6.a.m 5
1080.6.a.n 5
1080.6.a.o 5
1080.6.a.p 5
1080.6.a.q 5
1080.6.a.r 5
1080.6.a.s 6
1080.6.a.t 6
1080.6.b \(\chi_{1080}(971, \cdot)\) n/a 320 1
1080.6.d \(\chi_{1080}(109, \cdot)\) n/a 480 1
1080.6.f \(\chi_{1080}(649, \cdot)\) n/a 120 1
1080.6.h \(\chi_{1080}(431, \cdot)\) None 0 1
1080.6.k \(\chi_{1080}(541, \cdot)\) n/a 320 1
1080.6.m \(\chi_{1080}(539, \cdot)\) n/a 480 1
1080.6.o \(\chi_{1080}(1079, \cdot)\) None 0 1
1080.6.q \(\chi_{1080}(361, \cdot)\) n/a 120 2
1080.6.s \(\chi_{1080}(377, \cdot)\) n/a 240 2
1080.6.t \(\chi_{1080}(487, \cdot)\) None 0 2
1080.6.w \(\chi_{1080}(163, \cdot)\) n/a 960 2
1080.6.x \(\chi_{1080}(53, \cdot)\) n/a 960 2
1080.6.bb \(\chi_{1080}(359, \cdot)\) None 0 2
1080.6.bd \(\chi_{1080}(179, \cdot)\) n/a 712 2
1080.6.bf \(\chi_{1080}(181, \cdot)\) n/a 480 2
1080.6.bg \(\chi_{1080}(71, \cdot)\) None 0 2
1080.6.bi \(\chi_{1080}(289, \cdot)\) n/a 180 2
1080.6.bk \(\chi_{1080}(469, \cdot)\) n/a 712 2
1080.6.bm \(\chi_{1080}(251, \cdot)\) n/a 480 2
1080.6.bo \(\chi_{1080}(121, \cdot)\) n/a 1080 6
1080.6.bp \(\chi_{1080}(307, \cdot)\) n/a 1424 4
1080.6.bs \(\chi_{1080}(197, \cdot)\) n/a 1424 4
1080.6.bt \(\chi_{1080}(17, \cdot)\) n/a 360 4
1080.6.bw \(\chi_{1080}(127, \cdot)\) None 0 4
1080.6.bx \(\chi_{1080}(59, \cdot)\) n/a 6456 6
1080.6.cc \(\chi_{1080}(61, \cdot)\) n/a 4320 6
1080.6.cd \(\chi_{1080}(119, \cdot)\) None 0 6
1080.6.cg \(\chi_{1080}(49, \cdot)\) n/a 1620 6
1080.6.ch \(\chi_{1080}(11, \cdot)\) n/a 4320 6
1080.6.ci \(\chi_{1080}(191, \cdot)\) None 0 6
1080.6.cj \(\chi_{1080}(229, \cdot)\) n/a 6456 6
1080.6.co \(\chi_{1080}(77, \cdot)\) n/a 12912 12
1080.6.cp \(\chi_{1080}(7, \cdot)\) None 0 12
1080.6.cs \(\chi_{1080}(113, \cdot)\) n/a 3240 12
1080.6.ct \(\chi_{1080}(43, \cdot)\) n/a 12912 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(1080))\) into lower level spaces

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