Space of modular forms of level 48 and weight 2

• Label: 48.2
• Level: 48
• Weight: 2
• Dimension: 23
• Nonzero newspaces: 4
• Newform subspaces: 4
• Sturm bound: 256
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(256\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(48))\).

	Total	New	Old
Modular forms	92	31	61
Cusp forms	37	23	14
Eisenstein series	55	8	47

Trace form

23 * q - q^3 - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^7 - 12 * q^8 - 5 * q^9 - 8 * q^10 - 12 * q^11 - 10 * q^13 + 12 * q^14 - 10 * q^15 + 16 * q^16 + 2 * q^17 + 8 * q^18 - 16 * q^19 + 16 * q^20 + 4 * q^21 + 16 * q^22 + 8 * q^23 + 28 * q^24 + 9 * q^25 + 20 * q^26 + 11 * q^27 - 10 * q^29 + 20 * q^30 + 16 * q^31 - 8 * q^33 - 8 * q^34 + 24 * q^35 + 16 * q^36 - 34 * q^37 - 8 * q^38 + 18 * q^39 - 24 * q^40 - 6 * q^41 - 44 * q^42 - 40 * q^44 - 14 * q^45 - 48 * q^46 - 64 * q^48 - 45 * q^49 - 36 * q^50 + 34 * q^51 - 32 * q^52 + 14 * q^53 - 48 * q^54 + 32 * q^55 - 8 * q^57 + 16 * q^58 + 28 * q^59 + 8 * q^60 + 54 * q^61 - 12 * q^62 + 8 * q^63 + 64 * q^64 - 12 * q^65 + 52 * q^66 + 16 * q^67 + 32 * q^68 + 28 * q^69 + 72 * q^70 - 8 * q^71 + 36 * q^72 + 30 * q^73 + 52 * q^74 - 19 * q^75 + 64 * q^76 + 16 * q^77 + 48 * q^78 - 16 * q^79 + 8 * q^80 + 7 * q^81 + 24 * q^82 - 36 * q^83 - 8 * q^84 + 12 * q^85 - 16 * q^86 - 54 * q^87 - 32 * q^88 - 6 * q^89 - 24 * q^90 - 64 * q^91 - 16 * q^92 - 16 * q^93 - 40 * q^94 - 56 * q^95 - 56 * q^96 - 34 * q^97 - 40 * q^98 - 64 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.2.a	\(\chi_{48}(1, \cdot)\)	48.2.a.a	1	1
48.2.c	\(\chi_{48}(47, \cdot)\)	48.2.c.a	2	1
48.2.d	\(\chi_{48}(25, \cdot)\)	None	0	1
48.2.f	\(\chi_{48}(23, \cdot)\)	None	0	1
48.2.j	\(\chi_{48}(13, \cdot)\)	48.2.j.a	8	2
48.2.k	\(\chi_{48}(11, \cdot)\)	48.2.k.a	12	2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

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