Space of modular forms of level 48 and weight 8

• Label: 48.8
• Level: 48
• Weight: 8
• Dimension: 185
• Nonzero newspaces: 4
• Newform subspaces: 12
• Sturm bound: 1024
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1024\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(48))\).

	Total	New	Old
Modular forms	476	193	283
Cusp forms	420	185	235
Eisenstein series	56	8	48

Trace form

185 * q - 29 * q^3 + 360 * q^4 - 278 * q^5 + 172 * q^6 - 328 * q^7 + 2004 * q^8 + 1749 * q^9 - 25952 * q^10 - 3612 * q^11 + 27352 * q^12 + 3018 * q^13 - 44028 * q^14 + 33750 * q^15 - 52784 * q^16 + 1454 * q^17 + 41584 * q^18 - 183040 * q^19 + 82000 * q^20 - 7892 * q^21 - 99784 * q^22 + 230984 * q^23 - 276372 * q^24 - 121801 * q^25 + 363980 * q^26 + 218359 * q^27 + 129920 * q^28 - 8734 * q^29 - 165380 * q^30 - 348464 * q^31 - 571200 * q^32 - 249376 * q^33 - 1188984 * q^34 + 82680 * q^35 + 829712 * q^36 - 194574 * q^37 + 1921576 * q^38 + 347906 * q^39 + 840776 * q^40 + 33702 * q^41 - 3120084 * q^42 - 646352 * q^43 + 1417400 * q^44 + 601854 * q^45 - 1954496 * q^46 + 97920 * q^47 + 903072 * q^48 + 2951533 * q^49 + 2069988 * q^50 - 422646 * q^51 - 4600400 * q^52 - 3045958 * q^53 + 282548 * q^54 + 1936608 * q^55 + 9766848 * q^56 + 4241544 * q^57 + 3314376 * q^58 + 3139756 * q^59 - 5474344 * q^60 - 8654870 * q^61 - 14719044 * q^62 - 2233656 * q^63 + 76992 * q^64 + 463788 * q^65 - 421076 * q^66 + 20314336 * q^67 + 9981536 * q^68 + 6422812 * q^69 + 14142488 * q^70 - 9291464 * q^71 - 823388 * q^72 + 3579010 * q^73 + 18583468 * q^74 - 6654319 * q^75 - 15895824 * q^76 - 19878608 * q^77 - 31906248 * q^78 + 18725040 * q^79 - 26364088 * q^80 - 18019975 * q^81 - 13930664 * q^82 + 3459852 * q^83 - 5064872 * q^84 - 7384508 * q^85 + 32307920 * q^86 - 38674854 * q^87 + 96492352 * q^88 + 17795334 * q^89 + 28364600 * q^90 + 199424 * q^91 - 16335952 * q^92 - 24594728 * q^93 - 117047480 * q^94 + 59742664 * q^95 - 60505976 * q^96 - 46238590 * q^97 - 8969560 * q^98 - 7334224 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.8.a	\(\chi_{48}(1, \cdot)\)	48.8.a.a	1	1
		48.8.a.b	1
		48.8.a.c	1
		48.8.a.d	1
		48.8.a.e	1
		48.8.a.f	1
		48.8.a.g	1
48.8.c	\(\chi_{48}(47, \cdot)\)	48.8.c.a	2	1
		48.8.c.b	4
		48.8.c.c	8
48.8.d	\(\chi_{48}(25, \cdot)\)	None	0	1
48.8.f	\(\chi_{48}(23, \cdot)\)	None	0	1
48.8.j	\(\chi_{48}(13, \cdot)\)	48.8.j.a	56	2
48.8.k	\(\chi_{48}(11, \cdot)\)	48.8.k.a	108	2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

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