Space of modular forms of level 12 and weight 3

• Label: 12.3
• Level: 12
• Weight: 3
• Dimension: 3
• Nonzero newspaces: 2
• Newform subspaces: 2
• Sturm bound: 24
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(12))\).

	Total	New	Old
Modular forms	13	3	10
Cusp forms	3	3	0
Eisenstein series	10	0	10

Trace form

3 * q - 2 * q^2 - 3 * q^3 - 4 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 + 16 * q^8 + 3 * q^9 + 4 * q^10 - 12 * q^12 - 18 * q^13 - 24 * q^14 - 16 * q^16 + 20 * q^17 + 6 * q^18 + 26 * q^19 + 8 * q^20 + 18 * q^21 + 24 * q^22 - 17 * q^25 - 4 * q^26 - 27 * q^27 + 48 * q^28 - 52 * q^29 - 12 * q^30 - 46 * q^31 - 32 * q^32 - 24 * q^33 - 20 * q^34 + 12 * q^36 + 78 * q^37 + 72 * q^38 + 66 * q^39 - 32 * q^40 + 116 * q^41 - 24 * q^42 - 22 * q^43 - 48 * q^44 + 12 * q^45 - 96 * q^46 + 48 * q^48 - 43 * q^49 + 42 * q^50 - 8 * q^52 - 148 * q^53 - 18 * q^54 - 150 * q^57 + 52 * q^58 + 24 * q^60 + 126 * q^61 + 24 * q^62 + 18 * q^63 + 128 * q^64 - 8 * q^65 + 24 * q^66 + 122 * q^67 - 40 * q^68 + 96 * q^69 + 48 * q^70 - 48 * q^72 - 138 * q^73 - 52 * q^74 - 75 * q^75 - 144 * q^76 + 96 * q^77 + 12 * q^78 - 142 * q^79 + 32 * q^80 + 99 * q^81 - 116 * q^82 - 48 * q^84 - 40 * q^85 - 168 * q^86 + 164 * q^89 - 12 * q^90 - 44 * q^91 + 192 * q^92 + 114 * q^93 + 240 * q^94 - 96 * q^96 + 6 * q^97 - 2 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)

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
12.3.c	\(\chi_{12}(5, \cdot)\)	12.3.c.a	1	1
12.3.d	\(\chi_{12}(7, \cdot)\)	12.3.d.a	2	1