Space of modular forms of level 48 and weight 22

• Label: 48.22
• Level: 48
• Weight: 22
• Dimension: 563
• Nonzero newspaces: 4
• Sturm bound: 2816
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	=	\( 22 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(2816\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(48))\).

	Total	New	Old
Modular forms	1372	571	801
Cusp forms	1316	563	753
Eisenstein series	56	8	48

Trace form

563 * q + 59047 * q^3 - 3208664 * q^4 + 20783558 * q^5 + 142760908 * q^6 + 3921368 * q^7 + 10875501588 * q^8 + 58634199111 * q^9 + 203794241504 * q^10 - 201999962220 * q^11 - 366511438088 * q^12 - 425042668434 * q^13 - 7580676743484 * q^14 - 5766503906250 * q^15 - 19346727773104 * q^16 + 1740714497002 * q^17 + 38736889598032 * q^18 + 174854315043152 * q^19 + 196422031250000 * q^20 - 18994655030156 * q^21 + 150959445555000 * q^22 - 418452746476856 * q^23 - 543163857277332 * q^24 - 2225726856549715 * q^25 - 753312645084980 * q^26 - 941848663755869 * q^27 + 5971516838613120 * q^28 + 188716292275198 * q^29 - 9861346794423140 * q^30 + 17030894945943024 * q^31 - 10070930361655680 * q^32 - 14021349681046936 * q^33 + 101761981846555272 * q^34 - 24420616782470376 * q^35 - 121573282713801328 * q^36 + 132588504477350550 * q^37 + 175187804522404712 * q^38 - 167655571739984878 * q^39 - 143311877037888824 * q^40 + 150420339888752034 * q^41 - 191070335613005844 * q^42 + 110501765390601504 * q^43 - 182643993443571464 * q^44 - 571146378416567622 * q^45 + 405098148452892032 * q^46 - 17462175811351488 * q^47 + 609215008489840416 * q^48 + 10543077933473296447 * q^49 - 1465068799295972508 * q^50 + 2623474691920519794 * q^51 + 5852564414089701872 * q^52 - 3759614744263166762 * q^53 + 2330634420068591924 * q^54 + 9648039180388601120 * q^55 - 8134614321801781632 * q^56 + 10316398651018154520 * q^57 + 9907066428017003848 * q^58 + 9676438888472473916 * q^59 - 26888744297706805864 * q^60 - 33781039210679996562 * q^61 + 37423926077749156092 * q^62 + 7893115327721582568 * q^63 - 34141024632214304192 * q^64 + 400598053845283716 * q^65 + 95956051941715322572 * q^66 + 18234570068388076592 * q^67 - 88677994614761171936 * q^68 - 30549477184661057636 * q^69 + 8411622145275193368 * q^70 + 29401064349889550264 * q^71 - 69709252294426783388 * q^72 - 137353912505976851114 * q^73 + 52823343512087181932 * q^74 - 48191100582519692491 * q^75 + 223946943242677147696 * q^76 + 179123046061605469136 * q^77 - 144661561155495490536 * q^78 - 590357105167388337584 * q^79 + 598479047524721480968 * q^80 - 1226123357243779154749 * q^81 - 788564574863045609960 * q^82 - 482217133235447500164 * q^83 + 298974331234753553944 * q^84 + 1245504822526267239644 * q^85 - 1133736219623245285424 * q^86 + 1181232655219292337258 * q^87 - 1999298059630610956480 * q^88 + 298080922501213062882 * q^89 + 1890608458027612425272 * q^90 + 318106672552773102976 * q^91 - 4114711634977220502992 * q^92 - 1458147516457987648544 * q^93 + 1081718229679723851464 * q^94 - 672420598507790817976 * q^95 - 674646009390532316792 * q^96 - 1594002130772077371050 * q^97 - 9484196106654323201240 * q^98 + 394416705631392065888 * q^99

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.22.a	\(\chi_{48}(1, \cdot)\)	48.22.a.a	1	1
		48.22.a.b	1
		48.22.a.c	1
		48.22.a.d	1
		48.22.a.e	1
		48.22.a.f	1
		48.22.a.g	2
		48.22.a.h	2
		48.22.a.i	2
		48.22.a.j	3
		48.22.a.k	3
		48.22.a.l	3
48.22.c	\(\chi_{48}(47, \cdot)\)	48.22.c.a	2	1
		48.22.c.b	12
		48.22.c.c	28
48.22.d	\(\chi_{48}(25, \cdot)\)	None	0	1
48.22.f	\(\chi_{48}(23, \cdot)\)	None	0	1
48.22.j	\(\chi_{48}(13, \cdot)\)	n/a	168	2
48.22.k	\(\chi_{48}(11, \cdot)\)	n/a	332	2

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

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)