Space of modular forms of level 72 and weight 7

• Label: 72.7
• Level: 72
• Weight: 7
• Dimension: 375
• Nonzero newspaces: 6
• Newform subspaces: 11
• Sturm bound: 2016
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(2016\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(72))\).

	Total	New	Old
Modular forms	912	393	519
Cusp forms	816	375	441
Eisenstein series	96	18	78

Trace form

375 * q - 8 * q^2 + 6 * q^3 + 18 * q^4 + 124 * q^6 - 314 * q^7 - 806 * q^8 + 66 * q^9 + 2248 * q^10 - 10 * q^11 - 3854 * q^12 - 1968 * q^13 - 4398 * q^14 + 9366 * q^15 + 4230 * q^16 + 2438 * q^17 + 16656 * q^18 + 3386 * q^19 - 31830 * q^20 + 3828 * q^21 + 10626 * q^22 + 30882 * q^23 + 23208 * q^24 - 30419 * q^25 + 43920 * q^26 - 22932 * q^27 + 39592 * q^28 + 38556 * q^29 - 128474 * q^30 + 187822 * q^31 - 334058 * q^32 + 36422 * q^33 + 144014 * q^34 - 174924 * q^35 + 85058 * q^36 - 215148 * q^37 + 586970 * q^38 + 259806 * q^39 - 12806 * q^40 + 237680 * q^41 - 321166 * q^42 - 130378 * q^43 - 936094 * q^44 - 185620 * q^45 + 98088 * q^46 + 187590 * q^47 + 388076 * q^48 - 808811 * q^49 + 395950 * q^50 + 222582 * q^51 + 385014 * q^52 + 603624 * q^54 + 735044 * q^55 + 1057200 * q^56 - 758 * q^57 - 127802 * q^58 + 34454 * q^59 - 2117154 * q^60 - 515844 * q^61 - 1346628 * q^62 - 141754 * q^63 - 1377588 * q^64 - 456156 * q^65 + 1724740 * q^66 + 494270 * q^67 + 2326892 * q^68 - 848504 * q^69 - 398578 * q^70 - 796014 * q^72 - 1204482 * q^73 - 1883202 * q^74 + 1326634 * q^75 + 1010966 * q^76 + 48168 * q^77 - 1682150 * q^78 + 396322 * q^79 + 3730896 * q^80 + 954362 * q^81 + 1833104 * q^82 + 553100 * q^83 + 4770152 * q^84 - 857748 * q^85 - 1590334 * q^86 - 1309470 * q^87 - 6555762 * q^88 - 1946698 * q^89 - 9202250 * q^90 - 1959948 * q^91 - 1371594 * q^92 - 1116448 * q^93 + 3995244 * q^94 + 1926396 * q^95 + 6478632 * q^96 + 3380376 * q^97 + 5916862 * q^98 + 3433962 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(72))\)

We only show spaces with odd 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
72.7.b	\(\chi_{72}(19, \cdot)\)	72.7.b.a	1	1
		72.7.b.b	4
		72.7.b.c	12
		72.7.b.d	12
72.7.e	\(\chi_{72}(17, \cdot)\)	72.7.e.a	2	1
		72.7.e.b	4
72.7.g	\(\chi_{72}(55, \cdot)\)	None	0	1
72.7.h	\(\chi_{72}(53, \cdot)\)	72.7.h.a	24	1
72.7.j	\(\chi_{72}(5, \cdot)\)	72.7.j.a	140	2
72.7.k	\(\chi_{72}(7, \cdot)\)	None	0	2
72.7.m	\(\chi_{72}(41, \cdot)\)	72.7.m.a	36	2
72.7.p	\(\chi_{72}(43, \cdot)\)	72.7.p.a	4	2
		72.7.p.b	136

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(72)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)