Space of modular forms of level 24 and weight 4

• Label: 24.4
• Level: 24
• Weight: 4
• Dimension: 17
• Nonzero newspaces: 3
• Newform subspaces: 4
• Sturm bound: 128
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(128\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(24))\).

	Total	New	Old
Modular forms	60	21	39
Cusp forms	36	17	19
Eisenstein series	24	4	20

Trace form

17 * q + 2 * q^2 + q^3 + 20 * q^4 + 14 * q^5 - 14 * q^6 + 4 * q^7 - 76 * q^8 - 47 * q^9 + 36 * q^10 - 28 * q^11 - 56 * q^12 - 74 * q^13 - 100 * q^14 - 18 * q^15 - 96 * q^16 + 134 * q^17 + 166 * q^18 + 64 * q^19 + 56 * q^20 - 72 * q^21 + 448 * q^22 + 336 * q^23 + 532 * q^24 + 11 * q^25 + 56 * q^26 - 107 * q^27 + 176 * q^28 - 138 * q^29 - 252 * q^30 - 556 * q^31 - 248 * q^32 - 148 * q^33 - 1332 * q^34 - 336 * q^35 - 1028 * q^36 + 30 * q^37 - 776 * q^38 + 90 * q^39 - 1016 * q^40 + 518 * q^41 + 756 * q^42 + 432 * q^43 + 1152 * q^44 + 126 * q^45 + 1768 * q^46 - 168 * q^47 + 2296 * q^48 + 621 * q^49 + 1970 * q^50 + 998 * q^51 + 1744 * q^52 - 130 * q^53 - 2114 * q^54 + 632 * q^55 - 1864 * q^56 + 224 * q^57 - 2476 * q^58 + 596 * q^59 - 3792 * q^60 - 218 * q^61 - 2108 * q^62 - 468 * q^63 - 1552 * q^64 - 2780 * q^65 + 1352 * q^66 - 2072 * q^67 + 2976 * q^68 + 24 * q^69 + 5048 * q^70 - 848 * q^71 + 3964 * q^72 + 170 * q^73 + 1568 * q^74 - 1745 * q^75 + 1864 * q^76 + 672 * q^77 - 2088 * q^78 - 76 * q^79 - 2112 * q^80 + 721 * q^81 - 5372 * q^82 - 1508 * q^83 - 6216 * q^84 + 1148 * q^85 - 760 * q^86 + 630 * q^87 - 2576 * q^88 - 466 * q^89 + 3564 * q^90 + 4944 * q^91 + 1728 * q^92 + 240 * q^93 + 6888 * q^94 + 6392 * q^95 + 6424 * q^96 - 1630 * q^97 + 3354 * q^98 + 3860 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)

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
24.4.a	\(\chi_{24}(1, \cdot)\)	24.4.a.a	1	1
24.4.c	\(\chi_{24}(23, \cdot)\)	None	0	1
24.4.d	\(\chi_{24}(13, \cdot)\)	24.4.d.a	6	1
24.4.f	\(\chi_{24}(11, \cdot)\)	24.4.f.a	2	1
		24.4.f.b	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(24))\) into lower level spaces

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