Space of modular forms of level 4000, weight 1, and Character 4000.i

• Label: 4000.1.i
• Level: $4000$
• Weight: $1$
• Character orbit: 4000.i
• Rep. character: $\chi_{4000}(57,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $0$
• Newform subspaces: $0$
• Sturm bound: $600$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 4000 = 2^{5} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	4000.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 0 \)
Sturm bound:			\(600\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(4000, [\chi])\).

	Total	New	Old
Modular forms	40	0	40
Cusp forms	0	0	0
Eisenstein series	40	0	40

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

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