Space of modular forms of level 167 and weight 1

• Label: 167.1
• Level: 167
• Weight: 1
• Dimension: 5
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 2324
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 167 \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(2324\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(167))\).

	Total	New	Old
Modular forms	88	88	0
Cusp forms	5	5	0
Eisenstein series	83	83	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	5	0	0	0

Trace form

5 * q - q^2 - q^3 + 4 * q^4 - 2 * q^6 - q^7 - 2 * q^8 + 4 * q^9 - q^11 - 3 * q^12 - 2 * q^14 + 3 * q^16 - 3 * q^18 - q^19 - 2 * q^21 - 2 * q^22 - 4 * q^24 + 5 * q^25 - 2 * q^27 - 3 * q^28 - q^29 - q^31 - 3 * q^32 - 2 * q^33 + q^36 - 2 * q^38 + 7 * q^42 + 8 * q^44 - q^47 + 6 * q^48 + 4 * q^49 - q^50 + 7 * q^54 - 4 * q^56 - 2 * q^57 - 2 * q^58 - q^61 + 9 * q^62 - 3 * q^63 + 2 * q^64 - 4 * q^66 + 5 * q^72 - q^75 - 3 * q^76 - 2 * q^77 + 3 * q^81 + 5 * q^84 - 2 * q^87 - 4 * q^88 - q^89 - 2 * q^93 - 2 * q^94 - 6 * q^96 - q^97 + 8 * q^98 - 3 * q^99

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(167))\)

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
167.1.b	\(\chi_{167}(166, \cdot)\)	167.1.b.a	5	1
167.1.d	\(\chi_{167}(5, \cdot)\)	None	0	82