Space of modular forms of level 60 and weight 4

• Label: 60.4
• Level: 60
• Weight: 4
• Dimension: 108
• Nonzero newspaces: 6
• Newform subspaces: 11
• Sturm bound: 768
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(768\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(60))\).

	Total	New	Old
Modular forms	328	116	212
Cusp forms	248	108	140
Eisenstein series	80	8	72

Trace form

108 * q - 10 * q^3 + 8 * q^4 - 20 * q^5 + 32 * q^6 + 16 * q^7 + 84 * q^8 + 16 * q^9 + 60 * q^10 - 16 * q^11 - 164 * q^12 - 76 * q^13 + 50 * q^15 + 64 * q^16 + 284 * q^17 + 256 * q^18 + 400 * q^19 - 380 * q^20 - 128 * q^21 - 776 * q^22 - 264 * q^23 - 552 * q^24 - 1068 * q^25 + 368 * q^26 - 346 * q^27 + 1368 * q^28 + 120 * q^29 + 316 * q^30 + 144 * q^31 + 340 * q^32 + 136 * q^33 - 936 * q^34 + 80 * q^35 - 208 * q^36 + 460 * q^37 - 2032 * q^38 + 60 * q^39 - 2704 * q^40 - 872 * q^41 - 888 * q^42 + 640 * q^43 + 1040 * q^45 + 3208 * q^46 + 336 * q^47 + 1740 * q^48 - 624 * q^49 + 3184 * q^50 + 1276 * q^51 + 3000 * q^52 + 44 * q^53 - 80 * q^54 - 1520 * q^55 - 1472 * q^56 - 352 * q^57 + 88 * q^58 - 760 * q^59 + 1216 * q^60 + 336 * q^61 - 1672 * q^62 - 3040 * q^63 - 952 * q^64 + 2620 * q^65 + 224 * q^66 + 1648 * q^67 + 4432 * q^68 + 712 * q^69 + 4552 * q^70 + 2400 * q^71 + 1068 * q^72 - 1212 * q^73 + 4270 * q^75 - 2432 * q^76 - 1680 * q^77 - 2864 * q^78 + 280 * q^79 - 4636 * q^80 + 2220 * q^81 - 2008 * q^82 - 1344 * q^83 - 4264 * q^84 - 10580 * q^85 - 448 * q^86 - 5236 * q^87 + 808 * q^88 - 320 * q^89 - 3780 * q^90 - 5248 * q^91 - 2888 * q^92 - 9632 * q^93 - 5048 * q^94 - 1800 * q^95 - 5248 * q^96 + 8492 * q^97 - 3288 * q^98 + 360 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)

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
60.4.a	\(\chi_{60}(1, \cdot)\)	60.4.a.a	1	1
		60.4.a.b	1
60.4.d	\(\chi_{60}(49, \cdot)\)	60.4.d.a	2	1
60.4.e	\(\chi_{60}(11, \cdot)\)	60.4.e.a	24	1
60.4.h	\(\chi_{60}(59, \cdot)\)	60.4.h.a	4	1
		60.4.h.b	4
		60.4.h.c	24
60.4.i	\(\chi_{60}(17, \cdot)\)	60.4.i.a	4	2
		60.4.i.b	8
60.4.j	\(\chi_{60}(7, \cdot)\)	60.4.j.a	8	2
		60.4.j.b	28

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(60))\) into lower level spaces

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