Space of modular forms of level 2601, weight 1, and Character 2601.x

• Label: 2601.1.x
• Level: $2601$
• Weight: $1$
• Character orbit: 2601.x
• Rep. character: $\chi_{2601}(40,\cdot)$
• Character field: $\Q(\zeta_{48})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $306$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2601 = 3^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2601.x (of order \(48\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 153 \)
Character field:			\(\Q(\zeta_{48})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(306\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2601, [\chi])\).

	Total	New	Old
Modular forms	320	256	64
Cusp forms	32	32	0
Eisenstein series	288	224	64

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	32	0	0

Trace form

\( 32 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2601, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2601.1.x.a	$2601$	$1$	2601.x	153.t	$48$	$32$	$2$	$1.298$	\(\Q(\zeta_{96})\)	$A_{4}$	None	None		✓	✓	✓	2601.1.x.a	$32$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{96}^{38}q^{2}-\zeta_{96}^{21}q^{3}+\zeta_{96}^{25}q^{5}+\cdots\)