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Properties

Label 891.6
Level 891
Weight 6
Dimension 112776
Nonzero newspaces 16
Sturm bound 349920
Trace bound 7

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Defining parameters

Level: \( N \) = \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(349920\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(891))\).

Total New Old
Modular forms 146880 113784 33096
Cusp forms 144720 112776 31944
Eisenstein series 2160 1008 1152

Trace form

\( 112776 q - 96 q^{2} - 144 q^{3} - 96 q^{4} - 270 q^{5} - 144 q^{6} + 14 q^{7} + 1062 q^{8} - 144 q^{9} + O(q^{10}) \) \( 112776 q - 96 q^{2} - 144 q^{3} - 96 q^{4} - 270 q^{5} - 144 q^{6} + 14 q^{7} + 1062 q^{8} - 144 q^{9} - 152 q^{10} + 9 q^{11} - 324 q^{12} - 3634 q^{13} - 3366 q^{14} - 144 q^{15} + 6456 q^{16} + 6846 q^{17} - 17496 q^{18} + 2300 q^{19} + 53298 q^{20} + 27342 q^{21} + 28 q^{22} - 15042 q^{23} - 32976 q^{24} - 18000 q^{25} - 88722 q^{26} - 35190 q^{27} - 62896 q^{28} - 48426 q^{29} + 30528 q^{30} + 24374 q^{31} + 224988 q^{32} + 36585 q^{33} + 102236 q^{34} + 110478 q^{35} - 35856 q^{36} - 48280 q^{37} - 191988 q^{38} - 144 q^{39} - 88322 q^{40} - 327618 q^{41} - 104454 q^{42} + 29822 q^{43} + 268695 q^{44} + 271728 q^{45} + 362512 q^{46} + 376698 q^{47} + 132714 q^{48} + 28972 q^{49} - 499164 q^{50} - 252774 q^{51} - 501814 q^{52} - 716286 q^{53} - 694404 q^{54} - 211145 q^{55} - 724914 q^{56} - 83196 q^{57} + 228118 q^{58} + 433854 q^{59} + 659502 q^{60} + 225878 q^{61} + 1414926 q^{62} + 532404 q^{63} + 649004 q^{64} + 1087338 q^{65} + 324486 q^{66} - 34146 q^{67} - 1949736 q^{68} - 1436004 q^{69} + 466762 q^{70} - 254766 q^{71} - 1963152 q^{72} + 163562 q^{73} + 115938 q^{74} + 112356 q^{75} - 427204 q^{76} + 220827 q^{77} + 1482534 q^{78} - 877378 q^{79} + 394284 q^{80} + 909792 q^{81} - 959276 q^{82} - 193920 q^{83} + 1648602 q^{84} + 500086 q^{85} + 1955832 q^{86} - 812016 q^{87} + 2409436 q^{88} - 1329906 q^{89} - 4275810 q^{90} + 233706 q^{91} - 1391634 q^{92} - 60228 q^{93} + 1260766 q^{94} + 2397282 q^{95} + 2829798 q^{96} - 1630 q^{97} + 3732240 q^{98} + 1736406 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(891))\)

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
891.6.a \(\chi_{891}(1, \cdot)\) 891.6.a.a 13 1
891.6.a.b 13
891.6.a.c 13
891.6.a.d 13
891.6.a.e 23
891.6.a.f 23
891.6.a.g 24
891.6.a.h 24
891.6.a.i 27
891.6.a.j 27
891.6.d \(\chi_{891}(890, \cdot)\) n/a 236 1
891.6.e \(\chi_{891}(298, \cdot)\) n/a 400 2
891.6.f \(\chi_{891}(82, \cdot)\) n/a 944 4
891.6.g \(\chi_{891}(296, \cdot)\) n/a 476 2
891.6.j \(\chi_{891}(100, \cdot)\) n/a 900 6
891.6.k \(\chi_{891}(161, \cdot)\) n/a 944 4
891.6.n \(\chi_{891}(136, \cdot)\) n/a 1904 8
891.6.o \(\chi_{891}(98, \cdot)\) n/a 1068 6
891.6.r \(\chi_{891}(34, \cdot)\) n/a 8100 18
891.6.u \(\chi_{891}(107, \cdot)\) n/a 1904 8
891.6.v \(\chi_{891}(37, \cdot)\) n/a 4272 24
891.6.y \(\chi_{891}(32, \cdot)\) n/a 9684 18
891.6.bb \(\chi_{891}(8, \cdot)\) n/a 4272 24
891.6.bc \(\chi_{891}(4, \cdot)\) n/a 38736 72
891.6.bd \(\chi_{891}(2, \cdot)\) n/a 38736 72

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(891))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(891)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(891))\)\(^{\oplus 1}\)