Space of modular forms of level 72 and weight 3

• Label: 72.3
• Level: 72
• Weight: 3
• Dimension: 119
• Nonzero newspaces: 6
• Newform subspaces: 10
• Sturm bound: 864
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(864\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(72))\).

	Total	New	Old
Modular forms	336	137	199
Cusp forms	240	119	121
Eisenstein series	96	18	78

Trace form

119 * q - 4 * q^2 - 6 * q^3 + 2 * q^4 + 4 * q^6 + 22 * q^7 + 26 * q^8 + 6 * q^9 + 8 * q^10 + 34 * q^11 - 14 * q^12 - 16 * q^13 - 78 * q^14 + 6 * q^15 - 122 * q^16 - 2 * q^17 - 96 * q^18 + 2 * q^19 - 150 * q^20 - 36 * q^21 - 38 * q^22 - 78 * q^23 - 24 * q^24 + q^25 + 24 * q^26 - 180 * q^27 + 168 * q^28 - 108 * q^29 - 74 * q^30 - 114 * q^31 + 86 * q^32 - 22 * q^33 + 102 * q^34 - 204 * q^35 + 2 * q^36 + 60 * q^37 - 110 * q^38 + 6 * q^39 - 326 * q^40 + 172 * q^41 + 194 * q^42 - 150 * q^43 + 130 * q^44 + 260 * q^45 - 40 * q^46 + 318 * q^47 + 332 * q^48 + 153 * q^49 + 530 * q^50 + 210 * q^51 + 374 * q^52 + 288 * q^54 + 404 * q^55 + 624 * q^56 - 290 * q^57 + 294 * q^58 - 62 * q^59 + 606 * q^60 - 76 * q^61 + 180 * q^62 - 490 * q^63 - 436 * q^64 - 636 * q^65 + 172 * q^66 - 94 * q^67 - 20 * q^68 - 104 * q^69 - 58 * q^70 - 78 * q^72 - 354 * q^73 + 6 * q^74 + 454 * q^75 + 182 * q^76 + 504 * q^77 - 446 * q^78 - 246 * q^79 - 624 * q^80 + 398 * q^81 + 8 * q^82 + 100 * q^83 - 952 * q^84 - 188 * q^85 - 998 * q^86 + 138 * q^87 - 626 * q^88 - 50 * q^89 - 1250 * q^90 - 780 * q^91 - 1098 * q^92 - 352 * q^93 - 828 * q^94 - 684 * q^95 - 888 * q^96 - 252 * q^97 - 1078 * q^98 - 510 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)

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
72.3.b	\(\chi_{72}(19, \cdot)\)	72.3.b.a	1	1
		72.3.b.b	4
		72.3.b.c	4
72.3.e	\(\chi_{72}(17, \cdot)\)	72.3.e.a	2	1
72.3.g	\(\chi_{72}(55, \cdot)\)	None	0	1
72.3.h	\(\chi_{72}(53, \cdot)\)	72.3.h.a	8	1
72.3.j	\(\chi_{72}(5, \cdot)\)	72.3.j.a	44	2
72.3.k	\(\chi_{72}(7, \cdot)\)	None	0	2
72.3.m	\(\chi_{72}(41, \cdot)\)	72.3.m.a	4	2
		72.3.m.b	8
72.3.p	\(\chi_{72}(43, \cdot)\)	72.3.p.a	4	2
		72.3.p.b	40

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

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