Properties

Label 112.7
Level 112
Weight 7
Dimension 1219
Nonzero newspaces 8
Sturm bound 5376
Trace bound 3

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Defining parameters

Level: \( N \) = \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(5376\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(112))\).

Total New Old
Modular forms 2388 1265 1123
Cusp forms 2220 1219 1001
Eisenstein series 168 46 122

Trace form

\( 1219 q - 8 q^{2} - 5 q^{3} - 188 q^{4} + 121 q^{5} + 1012 q^{6} - 5 q^{7} - 1952 q^{8} - 1305 q^{9} + O(q^{10}) \) \( 1219 q - 8 q^{2} - 5 q^{3} - 188 q^{4} + 121 q^{5} + 1012 q^{6} - 5 q^{7} - 1952 q^{8} - 1305 q^{9} + 2236 q^{10} - 2725 q^{11} + 4684 q^{12} + 7516 q^{13} - 7576 q^{14} - 18 q^{15} + 15940 q^{16} - 27871 q^{17} + 3736 q^{18} + 7243 q^{19} + 33116 q^{20} + 6077 q^{21} - 50528 q^{22} + 52951 q^{23} + 65172 q^{24} - 34197 q^{25} - 117916 q^{26} - 71564 q^{27} - 45188 q^{28} + 123362 q^{29} - 16916 q^{30} - 110889 q^{31} + 79332 q^{32} - 74179 q^{33} + 105164 q^{34} + 283627 q^{35} + 276944 q^{36} + 232369 q^{37} + 374548 q^{38} - 715108 q^{39} - 330332 q^{40} - 98604 q^{41} - 913380 q^{42} + 426874 q^{43} - 314244 q^{44} + 491814 q^{45} + 580976 q^{46} + 188487 q^{47} + 1001436 q^{48} + 2042131 q^{49} + 126824 q^{50} - 1178985 q^{51} - 478232 q^{52} - 666439 q^{53} - 338452 q^{54} + 465392 q^{55} + 405104 q^{56} + 1935930 q^{57} - 846416 q^{58} + 586299 q^{59} - 254212 q^{60} - 1291463 q^{61} + 980760 q^{62} - 30009 q^{63} - 789284 q^{64} + 75184 q^{65} + 1195252 q^{66} + 295459 q^{67} + 2251488 q^{68} + 618220 q^{69} + 2860804 q^{70} - 878298 q^{71} - 351476 q^{72} - 2288991 q^{73} - 7220804 q^{74} + 1362494 q^{75} - 8491988 q^{76} + 956229 q^{77} - 6358128 q^{78} + 2339055 q^{79} + 5797924 q^{80} + 3647966 q^{81} + 10009236 q^{82} + 576632 q^{83} + 7602764 q^{84} + 2304818 q^{85} + 6480940 q^{86} - 7814910 q^{87} - 6616316 q^{88} - 8171727 q^{89} - 19986940 q^{90} - 3963188 q^{91} - 9294116 q^{92} + 481609 q^{93} - 6047364 q^{94} + 11200383 q^{95} - 3249764 q^{96} + 2462708 q^{97} - 749860 q^{98} + 16643738 q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(112))\)

We only show spaces with odd 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
112.7.c \(\chi_{112}(97, \cdot)\) 112.7.c.a 1 1
112.7.c.b 2
112.7.c.c 4
112.7.c.d 4
112.7.c.e 12
112.7.d \(\chi_{112}(15, \cdot)\) 112.7.d.a 6 1
112.7.d.b 12
112.7.g \(\chi_{112}(71, \cdot)\) None 0 1
112.7.h \(\chi_{112}(41, \cdot)\) None 0 1
112.7.k \(\chi_{112}(43, \cdot)\) n/a 144 2
112.7.l \(\chi_{112}(13, \cdot)\) n/a 188 2
112.7.n \(\chi_{112}(73, \cdot)\) None 0 2
112.7.o \(\chi_{112}(23, \cdot)\) None 0 2
112.7.r \(\chi_{112}(79, \cdot)\) 112.7.r.a 16 2
112.7.r.b 16
112.7.r.c 16
112.7.s \(\chi_{112}(17, \cdot)\) 112.7.s.a 2 2
112.7.s.b 4
112.7.s.c 8
112.7.s.d 8
112.7.s.e 24
112.7.u \(\chi_{112}(11, \cdot)\) n/a 376 4
112.7.x \(\chi_{112}(5, \cdot)\) n/a 376 4

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces

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