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

• Label: 2601.1.p
• Level: $2601$
• Weight: $1$
• Character orbit: 2601.p
• Rep. character: $\chi_{2601}(802,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $306$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2601 = 3^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2601.p (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(306\)
Trace bound:			\(1\)

Dimensions

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

	Total	New	Old
Modular forms	312	80	232
Cusp forms	24	24	0
Eisenstein series	288	56	232

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2601.1.p.a	$2601$	$1$	2601.p	17.e	$16$	$8$	$1$	$1.298$	\(\Q(\zeta_{16})\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-51}) \)	\(\Q(\sqrt{17}) \)		$32$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{16}^{6}q^{4}-\zeta_{16}^{2}q^{13}-\zeta_{16}^{4}q^{16}+\cdots\)
2601.1.p.b	$2601$	$1$	2601.p	17.e	$16$	$16$	$2$	$1.298$	16.0.\(\cdots\).2	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$32$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\beta _{12}q^{4}+\beta _{3}q^{7}+\beta _{4}q^{13}-\beta _{8}q^{16}+\cdots\)