Space of modular forms of level 120 and weight 4

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

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 - 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

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

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