Space of modular forms of level 7 and weight 3

• Label: 7.3
• Level: 7
• Weight: 3
• Dimension: 1
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 12
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(7))\).

	Total	New	Old
Modular forms	7	7	0
Cusp forms	1	1	0
Eisenstein series	6	6	0

Trace form

q - 3 * q^2 + 5 * q^4 - 7 * q^7 - 3 * q^8 + 9 * q^9 - 6 * q^11 + 21 * q^14 - 11 * q^16 - 27 * q^18 + 18 * q^22 + 18 * q^23 + 25 * q^25 - 35 * q^28 - 54 * q^29 + 45 * q^32 + 45 * q^36 - 38 * q^37 + 58 * q^43 - 30 * q^44 - 54 * q^46 + 49 * q^49 - 75 * q^50 - 6 * q^53 + 21 * q^56 + 162 * q^58 - 63 * q^63 - 91 * q^64 - 118 * q^67 + 114 * q^71 - 27 * q^72 + 114 * q^74 + 42 * q^77 - 94 * q^79 + 81 * q^81 - 174 * q^86 + 18 * q^88 + 90 * q^92 - 147 * q^98 - 54 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)

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
7.3.b	\(\chi_{7}(6, \cdot)\)	7.3.b.a	1	1
7.3.d	\(\chi_{7}(3, \cdot)\)	None	0	2