Space of modular forms of level 48 and weight 3

• Label: 48.3
• Level: 48
• Weight: 3
• Dimension: 49
• Nonzero newspaces: 4
• Newform subspaces: 6
• Sturm bound: 384
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(384\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(48))\).

	Total	New	Old
Modular forms	156	59	97
Cusp forms	100	49	51
Eisenstein series	56	10	46

Trace form

49 * q - q^3 + 8 * q^4 + 12 * q^5 + 4 * q^6 + 10 * q^7 - 12 * q^8 - 11 * q^9 - 80 * q^10 + 32 * q^11 - 56 * q^12 - 34 * q^13 - 44 * q^14 - 36 * q^15 + 16 * q^16 - 12 * q^17 - 48 * q^18 - 98 * q^19 + 80 * q^20 - 26 * q^21 + 72 * q^22 - 128 * q^23 - 20 * q^24 + 33 * q^25 - 100 * q^26 + 23 * q^27 + 92 * q^29 + 156 * q^30 + 82 * q^31 + 160 * q^32 + 100 * q^33 + 232 * q^34 + 96 * q^35 + 208 * q^36 - 34 * q^37 + 168 * q^38 - 86 * q^39 + 136 * q^40 - 108 * q^41 + 220 * q^42 - 50 * q^43 + 88 * q^44 - 24 * q^45 - 64 * q^46 - 32 * q^48 + 7 * q^49 - 236 * q^50 + 128 * q^51 - 368 * q^52 - 196 * q^53 - 164 * q^54 - 192 * q^55 - 224 * q^56 - 50 * q^57 - 424 * q^58 - 128 * q^59 - 648 * q^60 - 306 * q^61 - 276 * q^62 + 90 * q^63 - 640 * q^64 - 200 * q^65 - 500 * q^66 + 318 * q^67 - 448 * q^68 + 12 * q^69 - 72 * q^70 + 512 * q^71 - 252 * q^72 + 282 * q^73 + 348 * q^74 + 459 * q^75 + 848 * q^76 + 512 * q^77 + 632 * q^78 + 370 * q^79 + 552 * q^80 - 15 * q^81 + 696 * q^82 - 160 * q^83 + 952 * q^84 + 280 * q^85 + 528 * q^86 - 96 * q^87 + 832 * q^88 + 228 * q^89 + 984 * q^90 - 28 * q^91 + 496 * q^92 - 46 * q^93 - 24 * q^94 + 8 * q^96 - 126 * q^97 - 440 * q^98 - 260 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.3.b	\(\chi_{48}(7, \cdot)\)	None	0	1
48.3.e	\(\chi_{48}(17, \cdot)\)	48.3.e.a	1	1
		48.3.e.b	2
48.3.g	\(\chi_{48}(31, \cdot)\)	48.3.g.a	2	1
48.3.h	\(\chi_{48}(41, \cdot)\)	None	0	1
48.3.i	\(\chi_{48}(5, \cdot)\)	48.3.i.a	8	2
		48.3.i.b	20
48.3.l	\(\chi_{48}(19, \cdot)\)	48.3.l.a	16	2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

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