Space of modular forms of level 48 and weight 4

• Label: 48.4
• Level: 48
• Weight: 4
• Dimension: 77
• Nonzero newspaces: 4
• Newform subspaces: 7
• Sturm bound: 512
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(512\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(48))\).

	Total	New	Old
Modular forms	220	85	135
Cusp forms	164	77	87
Eisenstein series	56	8	48

Trace form

77 * q - 5 * q^3 - 24 * q^4 + 2 * q^5 + 28 * q^6 + 24 * q^7 + 84 * q^8 + 57 * q^9 + 128 * q^10 - 60 * q^11 - 104 * q^12 - 14 * q^13 - 348 * q^14 + 150 * q^15 - 304 * q^16 - 26 * q^17 + 16 * q^18 + 32 * q^19 + 80 * q^20 - 260 * q^21 + 664 * q^22 - 248 * q^23 + 108 * q^24 - 221 * q^25 - 20 * q^26 - 161 * q^27 - 640 * q^28 + 58 * q^29 - 740 * q^30 - 720 * q^31 - 960 * q^32 + 560 * q^33 - 184 * q^34 + 120 * q^35 - 496 * q^36 + 1114 * q^37 + 1256 * q^38 + 962 * q^39 + 2376 * q^40 + 414 * q^41 + 1356 * q^42 + 400 * q^43 - 200 * q^44 - 1386 * q^45 - 768 * q^46 - 576 * q^47 + 672 * q^48 - 1423 * q^49 + 708 * q^50 - 582 * q^51 + 1328 * q^52 + 1234 * q^53 + 1700 * q^54 + 1248 * q^55 + 1344 * q^56 + 2280 * q^57 + 1512 * q^58 - 628 * q^59 - 424 * q^60 - 686 * q^61 - 996 * q^62 - 216 * q^63 - 2112 * q^64 + 348 * q^65 - 2036 * q^66 - 4672 * q^67 - 1568 * q^68 - 4196 * q^69 - 6952 * q^70 - 1288 * q^71 - 4316 * q^72 - 4822 * q^73 - 2740 * q^74 + 1481 * q^75 - 2448 * q^76 + 2672 * q^77 - 3240 * q^78 + 6032 * q^79 + 712 * q^80 + 365 * q^81 + 728 * q^82 + 5868 * q^83 - 296 * q^84 + 5172 * q^85 - 1712 * q^86 + 2490 * q^87 + 4928 * q^88 - 66 * q^89 + 3320 * q^90 - 4160 * q^91 + 5296 * q^92 - 3032 * q^93 + 10888 * q^94 - 10936 * q^95 + 10888 * q^96 - 662 * q^97 + 6760 * q^98 + 656 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.4.a	\(\chi_{48}(1, \cdot)\)	48.4.a.a	1	1
		48.4.a.b	1
		48.4.a.c	1
48.4.c	\(\chi_{48}(47, \cdot)\)	48.4.c.a	2	1
		48.4.c.b	4
48.4.d	\(\chi_{48}(25, \cdot)\)	None	0	1
48.4.f	\(\chi_{48}(23, \cdot)\)	None	0	1
48.4.j	\(\chi_{48}(13, \cdot)\)	48.4.j.a	24	2
48.4.k	\(\chi_{48}(11, \cdot)\)	48.4.k.a	44	2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

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