Space of modular forms of level 60 and weight 8

• Label: 60.8
• Level: 60
• Weight: 8
• Dimension: 258
• Nonzero newspaces: 6
• Newform subspaces: 12
• Sturm bound: 1536
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1536\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(60))\).

	Total	New	Old
Modular forms	712	266	446
Cusp forms	632	258	374
Eisenstein series	80	8	72

Trace form

258 * q + 26 * q^3 - 56 * q^4 + 170 * q^5 + 320 * q^6 - 2468 * q^7 + 2004 * q^8 - 3698 * q^9 + 8380 * q^10 + 10360 * q^11 - 12548 * q^12 - 22832 * q^13 + 3890 * q^15 + 118336 * q^16 + 36100 * q^17 - 32672 * q^18 + 12320 * q^19 - 113980 * q^20 - 33500 * q^21 + 29176 * q^22 + 6720 * q^23 + 170904 * q^24 - 1023438 * q^25 - 213008 * q^26 - 202 * q^27 + 67992 * q^28 + 307548 * q^29 - 275204 * q^30 + 294792 * q^31 + 35540 * q^32 + 38476 * q^33 - 6312 * q^34 - 819680 * q^35 - 1610896 * q^36 - 781000 * q^37 - 1098032 * q^38 + 1049760 * q^39 + 1068656 * q^40 - 666388 * q^41 + 3961896 * q^42 - 932476 * q^43 - 476770 * q^45 - 4076280 * q^46 + 408000 * q^47 - 3735540 * q^48 + 861174 * q^49 - 4816 * q^50 + 2219620 * q^51 + 12438200 * q^52 + 738412 * q^53 + 8756944 * q^54 - 4384680 * q^55 - 6547648 * q^56 - 2518300 * q^57 - 14951208 * q^58 + 6556888 * q^59 - 4238624 * q^60 + 1234492 * q^61 - 2193032 * q^62 - 13816 * q^63 + 22885192 * q^64 - 8808580 * q^65 + 17076512 * q^66 - 267668 * q^67 + 8043152 * q^68 + 24736 * q^69 + 7156552 * q^70 - 760800 * q^71 - 15593556 * q^72 + 15614424 * q^73 - 1583510 * q^75 + 12792064 * q^76 - 8807184 * q^77 + 30024208 * q^78 - 12149464 * q^79 - 20744156 * q^80 - 50734566 * q^81 - 8232408 * q^82 - 8690880 * q^83 - 45840424 * q^84 + 55312240 * q^85 - 15004352 * q^86 + 9911300 * q^87 + 73235752 * q^88 - 3586060 * q^89 + 19854300 * q^90 - 6248552 * q^91 + 18332792 * q^92 - 51792248 * q^93 - 39035704 * q^94 + 10879200 * q^95 - 62142208 * q^96 + 21847256 * q^97 - 40577688 * q^98 + 705672 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(60))\)

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
60.8.a	\(\chi_{60}(1, \cdot)\)	60.8.a.a	1	1
		60.8.a.b	1
		60.8.a.c	1
		60.8.a.d	1
60.8.d	\(\chi_{60}(49, \cdot)\)	60.8.d.a	2	1
		60.8.d.b	4
60.8.e	\(\chi_{60}(11, \cdot)\)	60.8.e.a	56	1
60.8.h	\(\chi_{60}(59, \cdot)\)	60.8.h.a	4	1
		60.8.h.b	4
		60.8.h.c	72
60.8.i	\(\chi_{60}(17, \cdot)\)	60.8.i.a	28	2
60.8.j	\(\chi_{60}(7, \cdot)\)	60.8.j.a	84	2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(60))\) into lower level spaces

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