Space of modular forms of level 120 and weight 2

• Label: 120.2
• Level: 120
• Weight: 2
• Dimension: 136
• Nonzero newspaces: 9
• Newform subspaces: 18
• Sturm bound: 1536
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1536\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(120))\).

	Total	New	Old
Modular forms	480	160	320
Cusp forms	289	136	153
Eisenstein series	191	24	167

Trace form

136 * q + 4 * q^2 + 2 * q^3 + 4 * q^5 - 12 * q^6 + 8 * q^7 - 8 * q^8 - 12 * q^10 - 32 * q^12 + 8 * q^13 - 32 * q^14 - 18 * q^15 - 48 * q^16 - 20 * q^18 - 40 * q^19 - 32 * q^20 - 16 * q^21 - 32 * q^22 - 24 * q^23 - 8 * q^24 - 8 * q^25 - 16 * q^26 - 46 * q^27 - 24 * q^29 - 4 * q^30 - 72 * q^31 + 24 * q^32 - 40 * q^33 + 16 * q^34 - 48 * q^35 - 8 * q^36 - 40 * q^37 + 40 * q^38 - 20 * q^39 + 64 * q^40 + 32 * q^42 - 24 * q^43 + 56 * q^44 + 12 * q^45 + 64 * q^46 + 16 * q^47 + 72 * q^48 - 24 * q^49 + 52 * q^50 + 60 * q^51 - 8 * q^52 + 16 * q^53 + 36 * q^54 - 16 * q^55 + 16 * q^56 + 16 * q^58 + 24 * q^59 + 72 * q^60 + 48 * q^61 + 8 * q^62 + 64 * q^63 + 48 * q^64 - 16 * q^65 + 64 * q^66 + 24 * q^67 + 56 * q^68 + 72 * q^70 + 16 * q^71 + 72 * q^72 - 80 * q^73 + 56 * q^74 + 42 * q^75 + 32 * q^76 + 72 * q^78 + 64 * q^79 + 80 * q^80 - 48 * q^81 + 128 * q^82 + 80 * q^83 + 72 * q^84 - 64 * q^85 - 16 * q^86 + 60 * q^87 - 48 * q^88 - 40 * q^89 + 36 * q^90 - 64 * q^91 - 8 * q^92 - 32 * q^93 - 128 * q^94 + 24 * q^95 - 112 * q^96 - 24 * q^97 - 100 * q^98 + 88 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)

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
120.2.a	\(\chi_{120}(1, \cdot)\)	120.2.a.a	1	1
		120.2.a.b	1
120.2.b	\(\chi_{120}(11, \cdot)\)	120.2.b.a	8	1
		120.2.b.b	8
120.2.d	\(\chi_{120}(109, \cdot)\)	120.2.d.a	6	1
		120.2.d.b	6
120.2.f	\(\chi_{120}(49, \cdot)\)	120.2.f.a	2	1
120.2.h	\(\chi_{120}(71, \cdot)\)	None	0	1
120.2.k	\(\chi_{120}(61, \cdot)\)	120.2.k.a	2	1
		120.2.k.b	6
120.2.m	\(\chi_{120}(59, \cdot)\)	120.2.m.a	4	1
		120.2.m.b	16
120.2.o	\(\chi_{120}(119, \cdot)\)	None	0	1
120.2.r	\(\chi_{120}(17, \cdot)\)	120.2.r.a	4	2
		120.2.r.b	4
		120.2.r.c	4
120.2.s	\(\chi_{120}(7, \cdot)\)	None	0	2
120.2.v	\(\chi_{120}(43, \cdot)\)	120.2.v.a	24	2
120.2.w	\(\chi_{120}(53, \cdot)\)	120.2.w.a	4	2
		120.2.w.b	4
		120.2.w.c	32

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(120))\) into lower level spaces

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