Space of modular forms of level 24 and weight 8

• Label: 24.8
• Level: 24
• Weight: 8
• Dimension: 43
• Nonzero newspaces: 3
• Newform subspaces: 7
• Sturm bound: 256
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(256\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(24))\).

	Total	New	Old
Modular forms	124	47	77
Cusp forms	100	43	57
Eisenstein series	24	4	20

Trace form

43 * q - 14 * q^2 + 25 * q^3 - 236 * q^4 - 446 * q^5 - 14 * q^6 + 3052 * q^7 - 428 * q^8 - 8021 * q^9 - 284 * q^10 + 3028 * q^11 - 5144 * q^12 + 5154 * q^13 + 4636 * q^14 - 24138 * q^15 - 58208 * q^16 + 35626 * q^17 + 406 * q^18 + 70768 * q^19 + 175096 * q^20 - 11664 * q^21 - 210976 * q^22 - 307680 * q^23 - 110348 * q^24 + 137921 * q^25 + 424984 * q^26 + 257725 * q^27 + 517168 * q^28 - 106902 * q^29 - 275292 * q^30 - 91940 * q^31 - 893944 * q^32 - 309628 * q^33 + 777004 * q^34 - 35616 * q^35 + 3388 * q^36 + 469002 * q^37 - 823816 * q^38 + 332586 * q^39 - 745016 * q^40 + 442714 * q^41 + 759060 * q^42 + 249280 * q^43 + 1275264 * q^44 - 325134 * q^45 - 1789848 * q^46 - 2632248 * q^47 + 332920 * q^48 - 1087081 * q^49 + 324610 * q^50 + 264422 * q^51 - 517104 * q^52 + 455554 * q^53 + 65470 * q^54 + 8823992 * q^55 + 1643704 * q^56 - 761944 * q^57 - 2993516 * q^58 - 2921612 * q^59 - 2789712 * q^60 - 5417118 * q^61 + 5767172 * q^62 + 224532 * q^63 + 3123952 * q^64 + 3499100 * q^65 - 3707128 * q^66 - 3523448 * q^67 - 3735840 * q^68 - 2845800 * q^69 + 18413048 * q^70 + 1543616 * q^71 + 3815836 * q^72 - 2225746 * q^73 - 6468800 * q^74 + 6356935 * q^75 - 9297656 * q^76 + 7828800 * q^77 - 6804360 * q^78 - 11704484 * q^79 + 14369088 * q^80 + 15456235 * q^81 - 24941852 * q^82 - 11429812 * q^83 - 14932296 * q^84 - 6864252 * q^85 + 4738312 * q^86 + 16382574 * q^87 - 4684432 * q^88 + 5133874 * q^89 + 10622124 * q^90 + 14165376 * q^91 + 11004480 * q^92 - 10069704 * q^93 - 17782296 * q^94 - 78332168 * q^95 + 9297304 * q^96 + 4154870 * q^97 + 53030538 * q^98 + 16638212 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(24))\)

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
24.8.a	\(\chi_{24}(1, \cdot)\)	24.8.a.a	1	1
		24.8.a.b	1
		24.8.a.c	1
24.8.c	\(\chi_{24}(23, \cdot)\)	None	0	1
24.8.d	\(\chi_{24}(13, \cdot)\)	24.8.d.a	14	1
24.8.f	\(\chi_{24}(11, \cdot)\)	24.8.f.a	2	1
		24.8.f.b	4
		24.8.f.c	20

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(24))\) into lower level spaces

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