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Properties

Label 112.12
Level 112
Weight 12
Dimension 2255
Nonzero newspaces 8
Sturm bound 9216
Trace bound 3

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Defining parameters

Level: \( N \) = \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(9216\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(112))\).

Total New Old
Modular forms 4308 2299 2009
Cusp forms 4140 2255 1885
Eisenstein series 168 44 124

Trace form

\( 2255 q - 8 q^{2} - 493 q^{3} - 6172 q^{4} + 2633 q^{5} - 60716 q^{6} + 68143 q^{7} - 149696 q^{8} - 679637 q^{9} + O(q^{10}) \) \( 2255 q - 8 q^{2} - 493 q^{3} - 6172 q^{4} + 2633 q^{5} - 60716 q^{6} + 68143 q^{7} - 149696 q^{8} - 679637 q^{9} + 1977884 q^{10} + 656219 q^{11} - 4600532 q^{12} - 246058 q^{13} + 1829944 q^{14} + 4712886 q^{15} + 7442884 q^{16} - 4772615 q^{17} + 64438200 q^{18} + 31186741 q^{19} - 137310340 q^{20} - 12547831 q^{21} + 170022752 q^{22} + 32707781 q^{23} + 132361876 q^{24} - 267214417 q^{25} - 611370780 q^{26} + 557432066 q^{27} + 322075868 q^{28} + 94276742 q^{29} - 581287284 q^{30} - 938127041 q^{31} - 809397148 q^{32} + 1666989061 q^{33} + 1764923660 q^{34} - 459134975 q^{35} - 3708775280 q^{36} - 192498939 q^{37} + 2552505652 q^{38} + 3043040770 q^{39} + 966482020 q^{40} - 125267658 q^{41} + 1981485500 q^{42} - 13399931136 q^{43} + 8708234140 q^{44} + 11589287472 q^{45} + 4144436656 q^{46} + 9111271849 q^{47} - 29665869668 q^{48} - 68693842665 q^{49} + 5835325704 q^{50} - 24476521243 q^{51} + 55956666792 q^{52} + 5128619113 q^{53} - 65395518932 q^{54} + 19871819982 q^{55} - 47289827632 q^{56} + 1844116474 q^{57} + 75198645392 q^{58} - 31200702653 q^{59} + 71614819452 q^{60} + 9285446889 q^{61} - 6700796936 q^{62} - 15694422423 q^{63} - 123935662468 q^{64} - 39203023250 q^{65} + 43631301844 q^{66} - 54300901153 q^{67} + 92276333696 q^{68} + 53281890894 q^{69} - 144490896892 q^{70} + 38996687152 q^{71} + 144625482348 q^{72} + 44038460209 q^{73} - 28282841828 q^{74} - 219205930884 q^{75} + 23572009868 q^{76} - 73500728819 q^{77} - 74062401040 q^{78} - 2884070931 q^{79} + 17905172644 q^{80} + 271662680070 q^{81} + 163110776692 q^{82} - 122183413736 q^{83} - 61178517172 q^{84} + 93956011922 q^{85} - 20094595732 q^{86} + 31610946162 q^{87} + 325711244292 q^{88} - 312435588855 q^{89} - 324620820156 q^{90} + 122521456170 q^{91} - 233232588964 q^{92} + 276472767413 q^{93} + 438657172540 q^{94} - 5275557341 q^{95} - 1961531938276 q^{96} - 178619322738 q^{97} + 87346590780 q^{98} - 955268363132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(112))\)

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
112.12.a \(\chi_{112}(1, \cdot)\) 112.12.a.a 1 1
112.12.a.b 1
112.12.a.c 2
112.12.a.d 2
112.12.a.e 2
112.12.a.f 3
112.12.a.g 3
112.12.a.h 3
112.12.a.i 3
112.12.a.j 4
112.12.a.k 4
112.12.a.l 5
112.12.b \(\chi_{112}(57, \cdot)\) None 0 1
112.12.e \(\chi_{112}(55, \cdot)\) None 0 1
112.12.f \(\chi_{112}(111, \cdot)\) 112.12.f.a 16 1
112.12.f.b 28
112.12.i \(\chi_{112}(65, \cdot)\) 112.12.i.a 8 2
112.12.i.b 8
112.12.i.c 12
112.12.i.d 14
112.12.i.e 22
112.12.i.f 22
112.12.j \(\chi_{112}(27, \cdot)\) n/a 348 2
112.12.m \(\chi_{112}(29, \cdot)\) n/a 264 2
112.12.p \(\chi_{112}(31, \cdot)\) 112.12.p.a 28 2
112.12.p.b 30
112.12.p.c 30
112.12.q \(\chi_{112}(87, \cdot)\) None 0 2
112.12.t \(\chi_{112}(9, \cdot)\) None 0 2
112.12.v \(\chi_{112}(3, \cdot)\) n/a 696 4
112.12.w \(\chi_{112}(37, \cdot)\) n/a 696 4

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

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(112)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)