Space of modular forms of level 72 and weight 14

• Label: 72.14
• Level: 72
• Weight: 14
• Dimension: 826
• Nonzero newspaces: 6
• Sturm bound: 4032
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(4032\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(72))\).

	Total	New	Old
Modular forms	1920	844	1076
Cusp forms	1824	826	998
Eisenstein series	96	18	78

Trace form

826 * q - 4 * q^2 - 135 * q^3 - 8558 * q^4 + 76646 * q^5 - 16388 * q^6 + 264358 * q^7 - 978598 * q^8 - 932445 * q^9 - 78912 * q^10 - 13463761 * q^11 + 9267706 * q^12 + 16094584 * q^13 - 78342382 * q^14 + 30888456 * q^15 + 289652870 * q^16 - 158266966 * q^17 - 500213448 * q^18 - 534000898 * q^19 - 386979046 * q^20 - 73910100 * q^21 + 693030530 * q^22 - 2672056890 * q^23 + 742003416 * q^24 - 5986679879 * q^25 - 8001629296 * q^26 + 228082608 * q^27 + 17196755048 * q^28 + 2843106456 * q^29 + 13873005814 * q^30 - 4774801504 * q^31 - 824316794 * q^32 - 14956361251 * q^33 - 40183901978 * q^34 + 47997498420 * q^35 + 14602315010 * q^36 - 37601177856 * q^37 - 128866517702 * q^38 - 81611550036 * q^39 - 18753246518 * q^40 - 5159809123 * q^41 + 160739432570 * q^42 - 159914122823 * q^43 - 504002813934 * q^44 + 14563271450 * q^45 + 153492959032 * q^46 + 258976950354 * q^47 - 458029046284 * q^48 + 93803271947 * q^49 + 198998427410 * q^50 - 352299721083 * q^51 - 495251246330 * q^52 - 54867447628 * q^53 + 747326012208 * q^54 + 732147813272 * q^55 - 146205664672 * q^56 + 623258840455 * q^57 - 626766830002 * q^58 + 918465693017 * q^59 + 1949567682654 * q^60 - 874803478742 * q^61 + 100211094652 * q^62 + 4588904546240 * q^63 + 2978534816428 * q^64 + 546628558378 * q^65 + 852107746900 * q^66 - 804913089457 * q^67 + 5737077152412 * q^68 - 198208542122 * q^69 - 506304104914 * q^70 + 4954156602016 * q^71 - 3218800457046 * q^72 - 1547156188026 * q^73 + 2106823627238 * q^74 - 14750604617363 * q^75 - 739142775610 * q^76 + 2733107454588 * q^77 - 3689929822406 * q^78 - 179047275916 * q^79 + 1678149524352 * q^80 - 4689888896833 * q^81 - 13906858553464 * q^82 - 27488955878540 * q^83 - 753455861320 * q^84 + 3111359090180 * q^85 + 392808685442 * q^86 + 33421365127578 * q^87 - 3225404801842 * q^88 - 29812936222012 * q^89 - 43208099460050 * q^90 - 7353731283192 * q^91 - 13254690885210 * q^92 + 14519535506438 * q^93 - 28850462185308 * q^94 + 449750621360 * q^95 + 55481236870992 * q^96 + 12353519624829 * q^97 + 64690979584746 * q^98 - 49571340067986 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(72))\)

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
72.14.a	\(\chi_{72}(1, \cdot)\)	72.14.a.a	1	1
		72.14.a.b	1
		72.14.a.c	2
		72.14.a.d	2
		72.14.a.e	2
		72.14.a.f	2
		72.14.a.g	3
		72.14.a.h	3
72.14.c	\(\chi_{72}(71, \cdot)\)	None	0	1
72.14.d	\(\chi_{72}(37, \cdot)\)	72.14.d.a	2	1
		72.14.d.b	2
		72.14.d.c	10
		72.14.d.d	24
		72.14.d.e	26
72.14.f	\(\chi_{72}(35, \cdot)\)	72.14.f.a	52	1
72.14.i	\(\chi_{72}(25, \cdot)\)	72.14.i.a	38	2
		72.14.i.b	40
72.14.l	\(\chi_{72}(11, \cdot)\)	n/a	308	2
72.14.n	\(\chi_{72}(13, \cdot)\)	n/a	308	2
72.14.o	\(\chi_{72}(23, \cdot)\)	None	0	2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(72)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)