Space of modular forms of level 100 and weight 1

• Label: 100.1
• Level: 100
• Weight: 1
• Dimension: 4
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 600
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(600\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(100))\).

	Total	New	Old
Modular forms	74	25	49
Cusp forms	4	4	0
Eisenstein series	70	21	49

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

4 * q - q^2 - q^4 - q^5 - q^8 - q^9 - q^10 - 2 * q^13 - q^16 - 2 * q^17 + 4 * q^18 + 4 * q^20 - q^25 - 2 * q^26 - 2 * q^29 + 4 * q^32 + 3 * q^34 - q^36 + 3 * q^37 - q^40 - 2 * q^41 - q^45 + 4 * q^49 - q^50 - 2 * q^52 + 3 * q^53 - 2 * q^58 - 2 * q^61 - q^64 + 3 * q^65 - 2 * q^68 - q^72 - 2 * q^73 - 2 * q^74 - q^80 - q^81 - 2 * q^82 + 3 * q^85 + 3 * q^89 - q^90 - 2 * q^97 - q^98

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)

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
100.1.b	\(\chi_{100}(51, \cdot)\)	None	0	1
100.1.d	\(\chi_{100}(99, \cdot)\)	None	0	1
100.1.f	\(\chi_{100}(57, \cdot)\)	None	0	2
100.1.h	\(\chi_{100}(19, \cdot)\)	None	0	4
100.1.j	\(\chi_{100}(11, \cdot)\)	100.1.j.a	4	4
100.1.k	\(\chi_{100}(13, \cdot)\)	None	0	8