Space of modular forms of level 72 and weight 4

• Label: 72.4
• Level: 72
• Weight: 4
• Dimension: 184
• Nonzero newspaces: 6
• Newform subspaces: 14
• Sturm bound: 1152
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 14 \)
Sturm bound:			\(1152\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(72))\).

	Total	New	Old
Modular forms	480	202	278
Cusp forms	384	184	200
Eisenstein series	96	18	78

Trace form

184 * q - 4 * q^2 - 3 * q^3 - 14 * q^4 - 22 * q^5 - 20 * q^6 - 42 * q^7 + 26 * q^8 + 21 * q^9 + 80 * q^10 + 107 * q^11 + 106 * q^12 + 64 * q^13 + 146 * q^14 + 24 * q^15 + 134 * q^16 - 142 * q^17 - 120 * q^18 - 186 * q^19 - 454 * q^20 + 228 * q^21 - 622 * q^22 + 246 * q^23 - 264 * q^24 + 9 * q^25 + 32 * q^26 + 288 * q^27 - 152 * q^28 - 192 * q^29 + 118 * q^30 - 32 * q^31 + 166 * q^32 - 469 * q^33 + 1382 * q^34 - 444 * q^35 - 766 * q^36 - 168 * q^37 + 394 * q^38 - 276 * q^39 + 810 * q^40 - 697 * q^41 - 118 * q^42 - 1507 * q^43 - 1038 * q^44 + 446 * q^45 - 2696 * q^46 - 1326 * q^47 - 796 * q^48 + 703 * q^49 - 3118 * q^50 + 345 * q^51 - 1562 * q^52 + 1940 * q^53 + 624 * q^54 + 1800 * q^55 + 2624 * q^56 + 1537 * q^57 + 4798 * q^58 + 4349 * q^59 + 798 * q^60 - 602 * q^61 + 4300 * q^62 + 1184 * q^63 + 1900 * q^64 - 146 * q^65 + 2500 * q^66 - 813 * q^67 - 1860 * q^68 - 3710 * q^69 - 6402 * q^70 - 6032 * q^71 + 954 * q^72 - 1410 * q^73 - 1498 * q^74 - 5879 * q^75 - 1242 * q^76 - 1260 * q^77 + 3946 * q^78 + 3796 * q^79 + 8160 * q^80 + 1937 * q^81 + 8904 * q^82 + 7372 * q^83 + 152 * q^84 + 1244 * q^85 + 146 * q^86 + 7050 * q^87 + 4430 * q^88 + 4616 * q^89 + 1870 * q^90 - 2088 * q^91 - 954 * q^92 + 3746 * q^93 - 5052 * q^94 - 5008 * q^95 - 4032 * q^96 - 561 * q^97 - 10326 * q^98 - 7458 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)

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
72.4.a	\(\chi_{72}(1, \cdot)\)	72.4.a.a	1	1
		72.4.a.b	1
		72.4.a.c	1
		72.4.a.d	1
72.4.c	\(\chi_{72}(71, \cdot)\)	None	0	1
72.4.d	\(\chi_{72}(37, \cdot)\)	72.4.d.a	2	1
		72.4.d.b	2
		72.4.d.c	4
		72.4.d.d	6
72.4.f	\(\chi_{72}(35, \cdot)\)	72.4.f.a	12	1
72.4.i	\(\chi_{72}(25, \cdot)\)	72.4.i.a	8	2
		72.4.i.b	10
72.4.l	\(\chi_{72}(11, \cdot)\)	72.4.l.a	4	2
		72.4.l.b	64
72.4.n	\(\chi_{72}(13, \cdot)\)	72.4.n.a	68	2
72.4.o	\(\chi_{72}(23, \cdot)\)	None	0	2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

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