Space of modular forms of level 72 and weight 6

• Label: 72.6
• Level: 72
• Weight: 6
• Dimension: 312
• Nonzero newspaces: 6
• Newform subspaces: 16
• Sturm bound: 1728
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(1728\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(72))\).

	Total	New	Old
Modular forms	768	330	438
Cusp forms	672	312	360
Eisenstein series	96	18	78

Trace form

312 * q - 4 * q^2 - 15 * q^3 + 18 * q^4 + 26 * q^5 - 68 * q^6 + 118 * q^7 + 602 * q^8 - 165 * q^9 - 512 * q^10 - 1105 * q^11 - 1094 * q^12 - 36 * q^13 - 238 * q^14 + 456 * q^15 + 4230 * q^16 + 854 * q^17 - 4488 * q^18 + 5414 * q^19 - 1126 * q^20 + 2268 * q^21 + 4290 * q^22 - 12810 * q^23 + 9048 * q^24 - 9149 * q^25 + 12752 * q^26 - 3312 * q^27 - 3992 * q^28 + 12780 * q^29 - 38666 * q^30 + 9856 * q^31 + 6406 * q^32 - 6331 * q^33 + 1766 * q^34 - 13740 * q^35 + 66818 * q^36 - 10716 * q^37 - 8582 * q^38 - 19524 * q^39 - 28598 * q^40 + 50417 * q^41 - 96070 * q^42 + 29177 * q^43 - 31854 * q^44 + 4490 * q^45 + 33336 * q^46 + 32034 * q^47 + 141236 * q^48 - 93791 * q^49 + 146450 * q^50 + 13053 * q^51 + 42630 * q^52 + 44072 * q^53 - 44496 * q^54 - 72088 * q^55 - 244768 * q^56 + 22255 * q^57 - 226802 * q^58 - 165367 * q^59 + 62814 * q^60 + 15678 * q^61 + 153532 * q^62 - 42880 * q^63 - 142932 * q^64 - 13022 * q^65 + 65044 * q^66 - 7777 * q^67 + 30492 * q^68 + 32854 * q^69 + 343406 * q^70 + 508240 * q^71 - 84246 * q^72 - 2766 * q^73 + 78566 * q^74 + 137317 * q^75 + 73286 * q^76 + 52188 * q^77 + 248314 * q^78 - 70556 * q^79 - 85248 * q^80 - 91321 * q^81 - 703864 * q^82 - 557540 * q^83 - 186568 * q^84 - 7140 * q^85 - 750142 * q^86 - 286422 * q^87 - 178482 * q^88 - 187504 * q^89 + 319150 * q^90 + 154344 * q^91 + 765990 * q^92 - 111322 * q^93 + 638244 * q^94 + 636560 * q^95 + 36624 * q^96 + 36129 * q^97 + 398826 * q^98 + 81678 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(72))\)

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
72.6.a	\(\chi_{72}(1, \cdot)\)	72.6.a.a	1	1
		72.6.a.b	1
		72.6.a.c	1
		72.6.a.d	1
		72.6.a.e	1
		72.6.a.f	1
72.6.c	\(\chi_{72}(71, \cdot)\)	None	0	1
72.6.d	\(\chi_{72}(37, \cdot)\)	72.6.d.a	2	1
		72.6.d.b	4
		72.6.d.c	8
		72.6.d.d	10
72.6.f	\(\chi_{72}(35, \cdot)\)	72.6.f.a	20	1
72.6.i	\(\chi_{72}(25, \cdot)\)	72.6.i.a	14	2
		72.6.i.b	16
72.6.l	\(\chi_{72}(11, \cdot)\)	72.6.l.a	4	2
		72.6.l.b	112
72.6.n	\(\chi_{72}(13, \cdot)\)	72.6.n.a	116	2
72.6.o	\(\chi_{72}(23, \cdot)\)	None	0	2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(72)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)