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Properties

Label 120.4
Level 120
Weight 4
Dimension 436
Nonzero newspaces 9
Newform subspaces 24
Sturm bound 3072
Trace bound 4

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Defining parameters

Level: \( N \) = \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 24 \)
Sturm bound: \(3072\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(120))\).

Total New Old
Modular forms 1248 460 788
Cusp forms 1056 436 620
Eisenstein series 192 24 168

Trace form

\( 436 q - 4 q^{2} - 6 q^{3} - 48 q^{4} + 8 q^{5} + 20 q^{6} - 40 q^{7} + 152 q^{8} + 68 q^{9} + O(q^{10}) \) \( 436 q - 4 q^{2} - 6 q^{3} - 48 q^{4} + 8 q^{5} + 20 q^{6} - 40 q^{7} + 152 q^{8} + 68 q^{9} - 44 q^{10} + 40 q^{13} - 64 q^{14} + 86 q^{15} + 400 q^{16} - 96 q^{17} + 140 q^{18} + 312 q^{19} + 704 q^{20} + 176 q^{21} - 384 q^{22} - 504 q^{23} - 1096 q^{24} + 532 q^{25} - 848 q^{26} + 42 q^{27} - 1120 q^{28} - 576 q^{29} + 564 q^{30} + 40 q^{31} + 1176 q^{32} + 456 q^{33} + 2080 q^{34} + 1248 q^{35} + 1832 q^{36} + 1144 q^{37} - 520 q^{38} + 1068 q^{39} - 2112 q^{40} + 312 q^{41} - 2760 q^{42} + 744 q^{43} - 3368 q^{44} - 536 q^{45} - 3360 q^{46} - 1168 q^{47} - 1496 q^{48} - 3364 q^{49} + 620 q^{50} - 4308 q^{51} + 248 q^{52} - 1264 q^{53} + 2716 q^{54} - 816 q^{55} + 3728 q^{56} - 1136 q^{57} + 4944 q^{58} + 120 q^{59} + 504 q^{60} + 2168 q^{61} + 4216 q^{62} + 1568 q^{63} + 6960 q^{64} - 896 q^{65} - 368 q^{66} + 5816 q^{67} - 2984 q^{68} - 1152 q^{69} - 4264 q^{70} + 176 q^{71} - 5432 q^{72} - 96 q^{73} - 7448 q^{74} - 1342 q^{75} - 9056 q^{76} + 96 q^{77} - 848 q^{78} - 6000 q^{79} - 4208 q^{80} + 3660 q^{81} - 1664 q^{82} - 4688 q^{83} + 3688 q^{84} + 1504 q^{85} - 8816 q^{86} - 1204 q^{87} + 1360 q^{88} - 80 q^{89} - 1492 q^{90} + 32 q^{91} + 5528 q^{92} + 3456 q^{93} + 2384 q^{94} + 6744 q^{95} + 976 q^{96} + 2600 q^{97} + 10468 q^{98} - 1896 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(120))\)

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
120.4.a \(\chi_{120}(1, \cdot)\) 120.4.a.a 1 1
120.4.a.b 1
120.4.a.c 1
120.4.a.d 1
120.4.a.e 1
120.4.a.f 1
120.4.b \(\chi_{120}(11, \cdot)\) 120.4.b.a 24 1
120.4.b.b 24
120.4.d \(\chi_{120}(109, \cdot)\) 120.4.d.a 18 1
120.4.d.b 18
120.4.f \(\chi_{120}(49, \cdot)\) 120.4.f.a 2 1
120.4.f.b 2
120.4.f.c 2
120.4.f.d 4
120.4.h \(\chi_{120}(71, \cdot)\) None 0 1
120.4.k \(\chi_{120}(61, \cdot)\) 120.4.k.a 2 1
120.4.k.b 8
120.4.k.c 14
120.4.m \(\chi_{120}(59, \cdot)\) 120.4.m.a 4 1
120.4.m.b 64
120.4.o \(\chi_{120}(119, \cdot)\) None 0 1
120.4.r \(\chi_{120}(17, \cdot)\) 120.4.r.a 36 2
120.4.s \(\chi_{120}(7, \cdot)\) None 0 2
120.4.v \(\chi_{120}(43, \cdot)\) 120.4.v.a 72 2
120.4.w \(\chi_{120}(53, \cdot)\) 120.4.w.a 4 2
120.4.w.b 4
120.4.w.c 128

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(120))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(120)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 1}\)