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Properties

Label 912.6
Level 912
Weight 6
Dimension 48176
Nonzero newspaces 24
Sturm bound 276480
Trace bound 13

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Defining parameters

Level: \( N \) = \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(276480\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(912))\).

Total New Old
Modular forms 116208 48484 67724
Cusp forms 114192 48176 66016
Eisenstein series 2016 308 1708

Trace form

\( 48176 q - 41 q^{3} - 152 q^{4} - 76 q^{5} + 196 q^{6} + 282 q^{7} + 984 q^{8} - 951 q^{9} + O(q^{10}) \) \( 48176 q - 41 q^{3} - 152 q^{4} - 76 q^{5} + 196 q^{6} + 282 q^{7} + 984 q^{8} - 951 q^{9} - 1800 q^{10} - 3624 q^{11} - 20 q^{12} + 394 q^{13} - 648 q^{14} + 4473 q^{15} - 8424 q^{16} - 404 q^{17} + 8764 q^{18} - 9734 q^{19} + 15200 q^{20} - 3989 q^{21} - 2488 q^{22} + 9328 q^{23} - 15612 q^{24} + 3892 q^{25} + 25960 q^{26} + 5983 q^{27} + 3768 q^{28} + 16708 q^{29} + 1444 q^{30} - 40726 q^{31} - 88320 q^{32} - 15265 q^{33} - 62296 q^{34} + 38352 q^{35} + 64700 q^{36} + 25420 q^{37} + 72088 q^{38} + 80294 q^{39} + 180776 q^{40} + 21756 q^{41} + 5892 q^{42} - 44406 q^{43} - 87536 q^{44} - 65121 q^{45} - 244040 q^{46} - 70272 q^{47} - 71268 q^{48} - 162112 q^{49} - 212424 q^{50} - 59007 q^{51} + 329688 q^{52} + 223636 q^{53} + 68084 q^{54} + 198026 q^{55} + 317184 q^{56} + 42591 q^{57} + 70624 q^{58} + 61064 q^{59} + 71852 q^{60} + 337074 q^{61} - 382200 q^{62} - 82809 q^{63} - 715976 q^{64} - 820152 q^{65} - 310460 q^{66} - 1327614 q^{67} + 244672 q^{68} - 304061 q^{69} + 747912 q^{70} + 143228 q^{71} + 90388 q^{72} + 694970 q^{73} + 189992 q^{74} + 865856 q^{75} - 242296 q^{76} + 1014488 q^{77} - 426324 q^{78} + 1096422 q^{79} - 1246736 q^{80} + 997001 q^{81} + 333704 q^{82} - 244908 q^{83} + 10156 q^{84} - 376898 q^{85} + 1162336 q^{86} - 1252995 q^{87} + 1179960 q^{88} - 673716 q^{89} + 127340 q^{90} - 259878 q^{91} + 25504 q^{92} - 155609 q^{93} - 1021912 q^{94} - 119624 q^{95} + 19624 q^{96} - 1038990 q^{97} - 955472 q^{98} + 282149 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(912))\)

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
912.6.a \(\chi_{912}(1, \cdot)\) 912.6.a.a 1 1
912.6.a.b 1
912.6.a.c 1
912.6.a.d 1
912.6.a.e 1
912.6.a.f 1
912.6.a.g 2
912.6.a.h 2
912.6.a.i 2
912.6.a.j 2
912.6.a.k 3
912.6.a.l 3
912.6.a.m 3
912.6.a.n 3
912.6.a.o 3
912.6.a.p 4
912.6.a.q 4
912.6.a.r 4
912.6.a.s 4
912.6.a.t 5
912.6.a.u 5
912.6.a.v 5
912.6.a.w 5
912.6.a.x 5
912.6.a.y 6
912.6.a.z 7
912.6.a.ba 7
912.6.d \(\chi_{912}(191, \cdot)\) n/a 180 1
912.6.e \(\chi_{912}(151, \cdot)\) None 0 1
912.6.f \(\chi_{912}(113, \cdot)\) n/a 198 1
912.6.g \(\chi_{912}(457, \cdot)\) None 0 1
912.6.j \(\chi_{912}(647, \cdot)\) None 0 1
912.6.k \(\chi_{912}(607, \cdot)\) 912.6.k.a 16 1
912.6.k.b 16
912.6.k.c 34
912.6.k.d 34
912.6.p \(\chi_{912}(569, \cdot)\) None 0 1
912.6.q \(\chi_{912}(49, \cdot)\) n/a 200 2
912.6.r \(\chi_{912}(341, \cdot)\) n/a 1592 2
912.6.u \(\chi_{912}(229, \cdot)\) n/a 720 2
912.6.v \(\chi_{912}(419, \cdot)\) n/a 1440 2
912.6.y \(\chi_{912}(379, \cdot)\) n/a 800 2
912.6.bb \(\chi_{912}(31, \cdot)\) n/a 200 2
912.6.bc \(\chi_{912}(311, \cdot)\) None 0 2
912.6.bd \(\chi_{912}(521, \cdot)\) None 0 2
912.6.bg \(\chi_{912}(103, \cdot)\) None 0 2
912.6.bh \(\chi_{912}(239, \cdot)\) n/a 400 2
912.6.bm \(\chi_{912}(121, \cdot)\) None 0 2
912.6.bn \(\chi_{912}(65, \cdot)\) n/a 396 2
912.6.bo \(\chi_{912}(289, \cdot)\) n/a 600 6
912.6.bq \(\chi_{912}(277, \cdot)\) n/a 1600 4
912.6.br \(\chi_{912}(221, \cdot)\) n/a 3184 4
912.6.bu \(\chi_{912}(259, \cdot)\) n/a 1600 4
912.6.bv \(\chi_{912}(11, \cdot)\) n/a 3184 4
912.6.bz \(\chi_{912}(41, \cdot)\) None 0 6
912.6.ca \(\chi_{912}(25, \cdot)\) None 0 6
912.6.cc \(\chi_{912}(257, \cdot)\) n/a 1188 6
912.6.cf \(\chi_{912}(295, \cdot)\) None 0 6
912.6.ch \(\chi_{912}(47, \cdot)\) n/a 1200 6
912.6.ci \(\chi_{912}(79, \cdot)\) n/a 600 6
912.6.ck \(\chi_{912}(23, \cdot)\) None 0 6
912.6.cn \(\chi_{912}(67, \cdot)\) n/a 4800 12
912.6.cp \(\chi_{912}(35, \cdot)\) n/a 9552 12
912.6.cq \(\chi_{912}(61, \cdot)\) n/a 4800 12
912.6.cs \(\chi_{912}(29, \cdot)\) n/a 9552 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(912))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(912)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 2}\)