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Properties

Label 112.14
Level 112
Weight 14
Dimension 2669
Nonzero newspaces 8
Sturm bound 10752
Trace bound 3

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Defining parameters

Level: \( N \) = \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(10752\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(112))\).

Total New Old
Modular forms 5076 2713 2363
Cusp forms 4908 2669 2239
Eisenstein series 168 44 124

Trace form

\( 2669 q - 8 q^{2} + 1451 q^{3} - 732 q^{4} - 33811 q^{5} + 510100 q^{6} - 65241 q^{7} + 2153728 q^{8} - 4659935 q^{9} + O(q^{10}) \) \( 2669 q - 8 q^{2} + 1451 q^{3} - 732 q^{4} - 33811 q^{5} + 510100 q^{6} - 65241 q^{7} + 2153728 q^{8} - 4659935 q^{9} - 3619620 q^{10} + 24801347 q^{11} + 72933100 q^{12} - 17021174 q^{13} + 32192728 q^{14} - 116535546 q^{15} - 98108732 q^{16} + 5459989 q^{17} + 268370424 q^{18} - 788305275 q^{19} + 675031484 q^{20} + 1683019601 q^{21} - 1494261024 q^{22} - 2679405307 q^{23} - 8031994220 q^{24} + 4652079249 q^{25} + 14224843236 q^{26} - 1131253486 q^{27} - 10814980196 q^{28} + 11285624690 q^{29} + 14782394316 q^{30} + 21044519423 q^{31} - 322128028 q^{32} - 39188268683 q^{33} - 43036915316 q^{34} + 33871925401 q^{35} + 91713706000 q^{36} - 61406807199 q^{37} - 84501424268 q^{38} - 5536306358 q^{39} - 124336281116 q^{40} + 48063680898 q^{41} + 378221224700 q^{42} + 38162961664 q^{43} + 95060583388 q^{44} - 122967341700 q^{45} - 587105614800 q^{46} - 586842413207 q^{47} + 1812011172892 q^{48} - 3163602018443 q^{49} - 1474039781304 q^{50} + 982892520797 q^{51} - 874970978008 q^{52} - 790889514515 q^{53} + 2275740798124 q^{54} + 116901303294 q^{55} + 1298252440208 q^{56} - 92851793126 q^{57} - 4297224301488 q^{58} - 2010504490133 q^{59} - 223372184196 q^{60} + 1270258486365 q^{61} + 3732409341880 q^{62} + 627207681921 q^{63} - 2218197889092 q^{64} - 3028275413282 q^{65} - 4748583710060 q^{66} + 1413183561095 q^{67} + 3094687369664 q^{68} + 3371753049918 q^{69} - 2420496454652 q^{70} - 4969941619184 q^{71} + 8460887771436 q^{72} - 1461381797811 q^{73} - 5935098383396 q^{74} + 5598106308756 q^{75} + 12012551999052 q^{76} + 5623562353309 q^{77} - 67074316624 q^{78} - 23395502747091 q^{79} - 7600112683100 q^{80} + 17657182381980 q^{81} + 2708184566580 q^{82} + 4689375771112 q^{83} - 6692487540148 q^{84} - 8871678063590 q^{85} + 4350728588780 q^{86} - 28917671951910 q^{87} + 4017415195652 q^{88} + 18250695475413 q^{89} - 3644803204668 q^{90} + 6719410210466 q^{91} - 63360404408740 q^{92} - 52474793828131 q^{93} - 3825191862340 q^{94} + 57898108518643 q^{95} - 4103327214820 q^{96} + 6179526243866 q^{97} + 71186142002172 q^{98} - 76075847083580 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(112))\)

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
112.14.a \(\chi_{112}(1, \cdot)\) 112.14.a.a 1 1
112.14.a.b 1
112.14.a.c 2
112.14.a.d 2
112.14.a.e 3
112.14.a.f 3
112.14.a.g 3
112.14.a.h 4
112.14.a.i 4
112.14.a.j 5
112.14.a.k 5
112.14.a.l 6
112.14.b \(\chi_{112}(57, \cdot)\) None 0 1
112.14.e \(\chi_{112}(55, \cdot)\) None 0 1
112.14.f \(\chi_{112}(111, \cdot)\) 112.14.f.a 16 1
112.14.f.b 36
112.14.i \(\chi_{112}(65, \cdot)\) n/a 102 2
112.14.j \(\chi_{112}(27, \cdot)\) n/a 412 2
112.14.m \(\chi_{112}(29, \cdot)\) n/a 312 2
112.14.p \(\chi_{112}(31, \cdot)\) n/a 104 2
112.14.q \(\chi_{112}(87, \cdot)\) None 0 2
112.14.t \(\chi_{112}(9, \cdot)\) None 0 2
112.14.v \(\chi_{112}(3, \cdot)\) n/a 824 4
112.14.w \(\chi_{112}(37, \cdot)\) n/a 824 4

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

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces

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