Space of modular forms of level 48 and weight 26

• Label: 48.26
• Level: 48
• Weight: 26
• Dimension: 671
• Nonzero newspaces: 4
• Sturm bound: 3328
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	=	\( 26 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(3328\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(48))\).

	Total	New	Old
Modular forms	1628	679	949
Cusp forms	1572	671	901
Eisenstein series	56	8	48

Trace form

671 * q + 531439 * q^3 + 71440552 * q^4 - 306268562 * q^5 - 5523305588 * q^6 - 63411416648 * q^7 + 223171593108 * q^8 + 8136916311459 * q^9 - 22408938559136 * q^10 + 42002332228788 * q^11 - 4457958449480 * q^12 - 142495589948410 * q^13 - 1139571992122044 * q^14 - 1297463378906250 * q^15 - 5673802170667184 * q^16 + 1186009327105202 * q^17 - 18877596795723632 * q^18 - 34322308835547856 * q^19 - 50483667968750000 * q^20 + 64078134682053412 * q^21 - 45314558139907784 * q^22 - 210628999613059192 * q^23 - 475668915229785492 * q^24 - 1474711887351062655 * q^25 + 2124873935607267020 * q^26 - 1604801042290117349 * q^27 + 2997740175355336320 * q^28 + 290777331959938790 * q^29 - 10347470579349912740 * q^30 + 10849148448203058640 * q^31 + 2739094884515808000 * q^32 + 6401265890100823832 * q^33 + 41260426890124502152 * q^34 + 22865276432669932824 * q^35 + 8143017466365710480 * q^36 + 62893538368440977006 * q^37 - 67280104521783674648 * q^38 + 49631253377802884498 * q^39 + 547917411476528901576 * q^40 + 63829338646905784362 * q^41 + 522141044792625220716 * q^42 - 197254793409605643840 * q^43 - 618755518097427318664 * q^44 - 70821741615300104862 * q^45 - 3657116543983692516096 * q^46 + 2339689137142659822720 * q^47 - 3013264732397007328224 * q^48 + 24416716085771087900091 * q^49 + 9459843554895724915812 * q^50 + 8532259221167245681410 * q^51 - 6912053143682661160592 * q^52 + 17726063573794732302974 * q^53 - 15169376444165606460364 * q^54 - 224608499625661212640 * q^55 + 30451490612476869503232 * q^56 + 28002593330262408009912 * q^57 - 6566183024011877098424 * q^58 + 38886063728638924834012 * q^59 + 15769330554893395922456 * q^60 - 100194326661148982313786 * q^61 - 65785670349702341510532 * q^62 + 13364249618591852593608 * q^63 + 260112848418357580558144 * q^64 + 74112242176077446865876 * q^65 - 250721407988534025357428 * q^66 + 462274685190180606686416 * q^67 + 583082846239535086631072 * q^68 - 674382076704784562103524 * q^69 + 290176981134652956739608 * q^70 - 305471954924433131163272 * q^71 - 187340456394177222770204 * q^72 - 1305307806958144730515410 * q^73 + 1326896444783693960665324 * q^74 - 259047671329404949535971 * q^75 - 398656711360042232271440 * q^76 - 429161818569642196640624 * q^77 - 1229510387678932137855912 * q^78 - 3078018198182256242508112 * q^79 + 5778907049821275717759368 * q^80 - 15065670705533271265369009 * q^81 - 8314574408971963301838696 * q^82 - 4548518187556328211551076 * q^83 + 12175626121261418503113880 * q^84 + 511313080135047324458604 * q^85 - 1675845412653628081467952 * q^86 - 1557962876209661305819254 * q^87 + 4240410808433170143969088 * q^88 + 3618649100407410002267562 * q^89 - 26951628466862836807186888 * q^90 + 7364539789002981332183360 * q^91 + 12306996435575049591700784 * q^92 - 15012347260112029612710896 * q^93 - 12413057613746700251574328 * q^94 - 16901937290686977585112376 * q^95 - 4666227284976050842781816 * q^96 - 34120648854336971491459474 * q^97 + 36174793225968696715471400 * q^98 + 572479458250749699225728 * q^99

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.26.a	\(\chi_{48}(1, \cdot)\)	48.26.a.a	1	1
		48.26.a.b	1
		48.26.a.c	1
		48.26.a.d	2
		48.26.a.e	2
		48.26.a.f	2
		48.26.a.g	3
		48.26.a.h	3
		48.26.a.i	3
		48.26.a.j	3
		48.26.a.k	4
48.26.c	\(\chi_{48}(47, \cdot)\)	48.26.c.a	2	1
		48.26.c.b	16
		48.26.c.c	32
48.26.d	\(\chi_{48}(25, \cdot)\)	None	0	1
48.26.f	\(\chi_{48}(23, \cdot)\)	None	0	1
48.26.j	\(\chi_{48}(13, \cdot)\)	n/a	200	2
48.26.k	\(\chi_{48}(11, \cdot)\)	n/a	396	2

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

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)