Space of modular forms of level 2900, weight 1, and Character 2900.da

• Label: 2900.1.da
• Level: $2900$
• Weight: $1$
• Character orbit: 2900.da
• Rep. character: $\chi_{2900}(127,\cdot)$
• Character field: $\Q(\zeta_{140})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $450$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2900.da (of order \(140\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2900 \)
Character field:			\(\Q(\zeta_{140})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(450\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2900, [\chi])\).

	Total	New	Old
Modular forms	240	240	0
Cusp forms	48	48	0
Eisenstein series	192	192	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	48	0	0	0

Trace form

\( 48 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2900, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2900.1.da.a	$2900$	$1$	2900.da	2900.ca	$140$	$48$	$1$	$1.447$	\(\Q(\zeta_{140})\)	$D_{140}$	\(\Q(\sqrt{-1}) \)	None		✓	2900.1.cr.a	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{140}^{8}q^{2}+\zeta_{140}^{16}q^{4}-\zeta_{140}^{39}q^{5}+\cdots\)