Space of modular forms of level 72 and weight 5

• Label: 72.5
• Level: 72
• Weight: 5
• Dimension: 247
• Nonzero newspaces: 6
• Newform subspaces: 11
• Sturm bound: 1440
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(1440\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(72))\).

	Total	New	Old
Modular forms	624	265	359
Cusp forms	528	247	281
Eisenstein series	96	18	78

Trace form

247 * q - 14 * q^4 + 28 * q^6 - 50 * q^7 - 102 * q^8 - 108 * q^9 - 72 * q^10 + 156 * q^11 + 226 * q^12 + 256 * q^13 + 594 * q^14 + 78 * q^15 + 134 * q^16 - 126 * q^17 - 1954 * q^19 + 1098 * q^20 + 24 * q^21 + 962 * q^22 + 714 * q^23 - 1080 * q^24 + 3367 * q^25 - 6000 * q^26 + 540 * q^27 - 3160 * q^28 + 2376 * q^29 + 4486 * q^30 - 4546 * q^31 + 5430 * q^32 - 1096 * q^33 + 574 * q^34 - 1164 * q^35 - 5566 * q^36 + 3096 * q^37 - 3750 * q^38 - 3006 * q^39 + 9562 * q^40 - 1698 * q^41 - 3742 * q^42 + 2560 * q^43 + 10434 * q^44 - 4696 * q^45 + 10696 * q^46 + 4530 * q^47 + 12764 * q^48 - 361 * q^49 - 16554 * q^50 - 15036 * q^51 - 28586 * q^52 - 19848 * q^54 - 10996 * q^55 - 17904 * q^56 - 92 * q^57 - 6634 * q^58 + 3804 * q^59 + 13086 * q^60 + 712 * q^61 + 20700 * q^62 + 33710 * q^63 + 48268 * q^64 + 14196 * q^65 - 13244 * q^66 + 20528 * q^67 + 28044 * q^68 + 5680 * q^69 + 19886 * q^70 - 4062 * q^72 + 4686 * q^73 - 40722 * q^74 - 46520 * q^75 - 65290 * q^76 - 28368 * q^77 + 4090 * q^78 - 21370 * q^79 - 33360 * q^80 - 30364 * q^81 - 34432 * q^82 - 11400 * q^83 + 19400 * q^84 - 10168 * q^85 + 51714 * q^86 + 53094 * q^87 + 73742 * q^88 + 12642 * q^89 - 15386 * q^90 + 47220 * q^91 + 73686 * q^92 + 39488 * q^93 + 65052 * q^94 + 61272 * q^95 + 42648 * q^96 - 8562 * q^97 - 15018 * q^98 + 40566 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(72))\)

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
72.5.b	\(\chi_{72}(19, \cdot)\)	72.5.b.a	1	1
		72.5.b.b	2
		72.5.b.c	8
		72.5.b.d	8
72.5.e	\(\chi_{72}(17, \cdot)\)	72.5.e.a	2	1
		72.5.e.b	2
72.5.g	\(\chi_{72}(55, \cdot)\)	None	0	1
72.5.h	\(\chi_{72}(53, \cdot)\)	72.5.h.a	16	1
72.5.j	\(\chi_{72}(5, \cdot)\)	72.5.j.a	92	2
72.5.k	\(\chi_{72}(7, \cdot)\)	None	0	2
72.5.m	\(\chi_{72}(41, \cdot)\)	72.5.m.a	24	2
72.5.p	\(\chi_{72}(43, \cdot)\)	72.5.p.a	4	2
		72.5.p.b	88

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(72)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)