Space of modular forms of level 72 and weight 21

• Label: 72.21
• Level: 72
• Weight: 21
• Dimension: 1271
• Nonzero newspaces: 6
• Sturm bound: 6048
• Trace bound: 2

Defining parameters

Level:	$N$	=	$72 = 2^{3} \cdot 3^{2}$
Weight:	$k$	=	$21$
Nonzero newspaces:			$6$
Sturm bound:			$6048$
Trace bound:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{21}(\Gamma_1(72))$.

	Total	New	Old
Modular forms	2928	1289	1639
Cusp forms	2832	1271	1561
Eisenstein series	96	18	78

Trace form

1271 * q + 624 * q^2 - 10608 * q^3 + 1773554 * q^4 + 2097148 * q^6 + 187327246 * q^7 + 3250902426 * q^8 - 4614984444 * q^9 + 2485208888 * q^10 + 17204979084 * q^11 + 43764724066 * q^12 - 164244011776 * q^13 + 1125941212626 * q^14 + 49966873998 * q^15 + 7543044743302 * q^16 + 990389375394 * q^17 + 5071262884032 * q^18 - 3429516685570 * q^19 - 905372554422 * q^20 + 44046871197048 * q^21 + 5743863835618 * q^22 + 108084786051594 * q^23 - 185225102125368 * q^24 + 455553006559447 * q^25 + 565053227881968 * q^26 - 157950631156068 * q^27 - 344882591525976 * q^28 - 1152884208314520 * q^29 - 2102375501593274 * q^30 - 2324919620620482 * q^31 - 2106166601686986 * q^32 - 140308838709592 * q^33 - 7409565512195106 * q^34 + 2852923700343156 * q^35 - 32873664509438398 * q^36 - 8666443278779016 * q^37 + 6904548824630010 * q^38 + 13898455646458722 * q^39 - 758586945417638 * q^40 + 37751280038243310 * q^41 + 171651139491019298 * q^42 + 971087379441552 * q^43 - 258199768481253438 * q^44 + 71143601859337544 * q^45 + 100808029162326536 * q^46 - 233308649906321262 * q^47 + 92128808318770268 * q^48 - 400178081604025593 * q^49 + 130314145660259526 * q^50 + 307826743428510708 * q^51 + 64330922499280214 * q^52 - 139529007462744936 * q^54 + 2408694765810896204 * q^55 + 789918586953873168 * q^56 - 1283930417081838764 * q^57 - 1347733378972037610 * q^58 + 2432486205362121420 * q^59 + 867770889950704926 * q^60 - 2177987353783431448 * q^61 - 1658931466251292932 * q^62 - 4544240069481966994 * q^63 + 3939613611408944780 * q^64 + 3916119371583842676 * q^65 + 3296267112992954788 * q^66 - 6139921193646514816 * q^67 - 3309979436501218164 * q^68 + 6903773142328692976 * q^69 + 33859278816015114446 * q^70 - 3382928070097705566 * q^72 + 5104463845359100878 * q^73 + 49910247380625758286 * q^74 + 36079518413440432120 * q^75 - 10799967404630443018 * q^76 - 37102929004126862352 * q^77 + 80102902752137929306 * q^78 + 11283809945225014950 * q^79 + 22227068144200206000 * q^80 + 16501695225613878548 * q^81 - 139366377163736246368 * q^82 - 55952143194264537000 * q^83 + 74099554952922671816 * q^84 + 5967242750491732072 * q^85 - 75362390900074723806 * q^86 - 167474475407720941818 * q^87 + 30760182474201070606 * q^88 + 54107024905441330434 * q^89 - 67382245747501126586 * q^90 + 51808214286268572276 * q^91 - 210205889815171251498 * q^92 - 222625193756394443968 * q^93 + 80301958634910007740 * q^94 + 264973637837105927352 * q^95 - 216990945338284809960 * q^96 - 273717153426172203810 * q^97 - 379054721111273515098 * q^98 + 448906198071681035094 * q^99

Decomposition of $S_{21}^{\mathrm{new}}(\Gamma_1(72))$

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
72.21.b	$\chi_{72}(19, \cdot)$	72.21.b.a	1	1
		72.21.b.b	18
		72.21.b.c	40
		72.21.b.d	40
72.21.e	$\chi_{72}(17, \cdot)$	72.21.e.a	10	1
		72.21.e.b	10
72.21.g	$\chi_{72}(55, \cdot)$	None	0	1
72.21.h	$\chi_{72}(53, \cdot)$	72.21.h.a	80	1
72.21.j	$\chi_{72}(5, \cdot)$	n/a	476	2
72.21.k	$\chi_{72}(7, \cdot)$	None	0	2
72.21.m	$\chi_{72}(41, \cdot)$	n/a	120	2
72.21.p	$\chi_{72}(43, \cdot)$	n/a	476	2

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

Decomposition of $S_{21}^{\mathrm{old}}(\Gamma_1(72))$ into lower level spaces

$S_{21}^{\mathrm{old}}(\Gamma_1(72)) \cong$ $S_{21}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 12}$$\oplus$$S_{21}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 9}$$\oplus$$S_{21}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 8}$$\oplus$$S_{21}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 6}$$\oplus$$S_{21}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 6}$$\oplus$$S_{21}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 3}$$\oplus$$S_{21}^{\mathrm{new}}(\Gamma_1(9))$$^{\oplus 4}$$\oplus$$S_{21}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 4}$$\oplus$$S_{21}^{\mathrm{new}}(\Gamma_1(18))$$^{\oplus 3}$$\oplus$$S_{21}^{\mathrm{new}}(\Gamma_1(24))$$^{\oplus 2}$$\oplus$$S_{21}^{\mathrm{new}}(\Gamma_1(36))$$^{\oplus 2}$