Space of modular forms of level 24 and weight 2

• Label: 24.2
• Level: 24
• Weight: 2
• Dimension: 5
• Nonzero newspaces: 3
• Newform subspaces: 3
• Sturm bound: 64
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(64\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(24))\).

	Total	New	Old
Modular forms	28	9	19
Cusp forms	5	5	0
Eisenstein series	23	4	19

Trace form

5 * q - 2 * q^2 - 3 * q^3 - 4 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 + 4 * q^8 - 3 * q^9 + 4 * q^10 + 4 * q^11 + 8 * q^12 - 2 * q^13 + 4 * q^14 + 6 * q^15 - 2 * q^17 - 6 * q^18 - 8 * q^20 - 8 * q^22 - 12 * q^24 - 9 * q^25 - 8 * q^26 + 9 * q^27 + 6 * q^29 - 4 * q^30 + 12 * q^31 + 8 * q^32 + 4 * q^33 + 20 * q^34 + 4 * q^36 + 6 * q^37 + 8 * q^38 - 6 * q^39 + 8 * q^40 - 2 * q^41 + 4 * q^42 - 16 * q^43 - 2 * q^45 - 8 * q^46 - 24 * q^47 - 8 * q^48 + q^49 - 2 * q^50 - 18 * q^51 + 16 * q^52 - 2 * q^53 + 6 * q^54 - 8 * q^55 - 8 * q^56 + 8 * q^57 - 12 * q^58 + 4 * q^59 - 2 * q^61 - 4 * q^62 + 4 * q^63 - 16 * q^64 + 20 * q^65 + 8 * q^66 + 24 * q^67 + 8 * q^69 - 8 * q^70 + 32 * q^71 + 12 * q^72 + 2 * q^73 + 16 * q^74 + 11 * q^75 - 24 * q^76 + 8 * q^78 + 12 * q^79 - 11 * q^81 - 36 * q^82 - 4 * q^83 - 8 * q^84 - 4 * q^85 - 8 * q^86 - 18 * q^87 + 16 * q^88 - 26 * q^89 - 4 * q^90 - 8 * q^93 + 24 * q^94 - 8 * q^95 + 24 * q^96 - 22 * q^97 + 6 * q^98 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)

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
24.2.a	\(\chi_{24}(1, \cdot)\)	24.2.a.a	1	1
24.2.c	\(\chi_{24}(23, \cdot)\)	None	0	1
24.2.d	\(\chi_{24}(13, \cdot)\)	24.2.d.a	2	1
24.2.f	\(\chi_{24}(11, \cdot)\)	24.2.f.a	2	1