Space of modular forms of level 9 and weight 3

• Label: 9.3
• Level: 9
• Weight: 3
• Dimension: 2
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 18
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 9 = 3^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(18\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(9))\).

	Total	New	Old
Modular forms	10	6	4
Cusp forms	2	2	0
Eisenstein series	8	4	4

Trace form

2 * q - 3 * q^2 - 3 * q^3 - q^4 + 6 * q^5 + 9 * q^6 - 2 * q^7 - 9 * q^9 - 12 * q^10 - 3 * q^11 + 6 * q^12 + 4 * q^13 + 6 * q^14 + 11 * q^16 + 22 * q^19 - 6 * q^20 - 6 * q^21 + 3 * q^22 - 48 * q^23 - 45 * q^24 - 13 * q^25 + 54 * q^27 + 4 * q^28 + 78 * q^29 + 18 * q^30 - 32 * q^31 + 27 * q^32 + 9 * q^33 - 27 * q^34 - 9 * q^36 - 68 * q^37 - 33 * q^38 - 24 * q^39 + 30 * q^40 - 21 * q^41 + 61 * q^43 - 54 * q^45 + 96 * q^46 - 84 * q^47 + 33 * q^48 + 45 * q^49 + 39 * q^50 + 81 * q^51 + 4 * q^52 - 81 * q^54 - 12 * q^55 - 30 * q^56 - 33 * q^57 - 78 * q^58 + 87 * q^59 + 18 * q^60 - 56 * q^61 + 36 * q^63 - 142 * q^64 + 24 * q^65 - 18 * q^66 + 31 * q^67 - 27 * q^68 + 12 * q^70 + 135 * q^72 + 130 * q^73 + 102 * q^74 - 39 * q^75 - 11 * q^76 + 6 * q^77 + 36 * q^78 - 38 * q^79 - 81 * q^81 + 42 * q^82 - 84 * q^83 - 6 * q^84 - 54 * q^85 - 183 * q^86 - 234 * q^87 + 15 * q^88 + 54 * q^90 - 16 * q^91 + 48 * q^92 + 192 * q^93 + 84 * q^94 + 66 * q^95 + 115 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)

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
9.3.b	\(\chi_{9}(8, \cdot)\)	None	0	1
9.3.d	\(\chi_{9}(2, \cdot)\)	9.3.d.a	2	2