Space of modular forms of level 60 and weight 2

• Label: 60.2
• Level: 60
• Weight: 2
• Dimension: 34
• Nonzero newspaces: 5
• Newform subspaces: 6
• Sturm bound: 384
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(384\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(60))\).

	Total	New	Old
Modular forms	136	42	94
Cusp forms	57	34	23
Eisenstein series	79	8	71

Trace form

34 * q + 2 * q^3 - 8 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 - 12 * q^8 - 10 * q^9 - 20 * q^10 - 8 * q^11 - 4 * q^12 - 24 * q^13 - 14 * q^15 - 20 * q^17 + 16 * q^18 + 20 * q^20 - 12 * q^21 + 8 * q^22 + 24 * q^24 - 14 * q^25 + 16 * q^26 + 14 * q^27 + 24 * q^28 + 12 * q^29 + 36 * q^30 + 24 * q^31 + 20 * q^32 + 12 * q^33 + 24 * q^34 + 16 * q^35 + 16 * q^38 + 16 * q^40 - 4 * q^41 + 8 * q^42 - 12 * q^43 - 2 * q^45 - 24 * q^46 - 20 * q^48 - 18 * q^49 - 16 * q^50 - 12 * q^51 - 40 * q^52 + 4 * q^53 - 56 * q^54 - 8 * q^55 - 64 * q^56 + 20 * q^57 - 56 * q^58 - 8 * q^59 - 64 * q^60 - 36 * q^61 - 56 * q^62 + 8 * q^63 - 56 * q^64 + 20 * q^65 - 64 * q^66 - 4 * q^67 - 16 * q^68 + 32 * q^69 - 8 * q^70 + 12 * q^72 + 48 * q^73 + 2 * q^75 + 32 * q^76 + 48 * q^77 + 16 * q^78 + 24 * q^79 + 4 * q^80 + 26 * q^81 + 56 * q^82 + 56 * q^84 + 56 * q^85 + 64 * q^86 + 20 * q^87 + 104 * q^88 + 20 * q^89 + 60 * q^90 + 24 * q^91 + 56 * q^92 + 24 * q^93 + 104 * q^94 + 64 * q^96 - 32 * q^97 + 24 * q^98 + 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)

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
60.2.a	\(\chi_{60}(1, \cdot)\)	None	0	1
60.2.d	\(\chi_{60}(49, \cdot)\)	60.2.d.a	2	1
60.2.e	\(\chi_{60}(11, \cdot)\)	60.2.e.a	8	1
60.2.h	\(\chi_{60}(59, \cdot)\)	60.2.h.a	4	1
		60.2.h.b	4
60.2.i	\(\chi_{60}(17, \cdot)\)	60.2.i.a	4	2
60.2.j	\(\chi_{60}(7, \cdot)\)	60.2.j.a	12	2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(60))\) into lower level spaces

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