Space of modular forms of level 3525, weight 1, and Character 3525.bg

• Label: 3525.1.bg
• Level: $3525$
• Weight: $1$
• Character orbit: 3525.bg
• Rep. character: $\chi_{3525}(107,\cdot)$
• Character field: $\Q(\zeta_{92})$
• Dimension: $88$
• Newform subspaces: $1$
• Sturm bound: $480$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3525.bg (of order \(92\) and degree \(44\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 705 \)
Character field:			\(\Q(\zeta_{92})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(480\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3525, [\chi])\).

	Total	New	Old
Modular forms	616	264	352
Cusp forms	88	88	0
Eisenstein series	528	176	352

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	88	0	0	0

Trace form

\( 88 q - 8 q^{6} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3525, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3525.1.bg.a	$3525$	$1$	3525.bg	705.u	$92$	$88$	$2$	$1.759$	\(\Q(\zeta_{184})\)	$D_{46}$	\(\Q(\sqrt{-15}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{184}^{33}+\zeta_{184}^{61})q^{2}+\zeta_{184}^{19}q^{3}+\cdots\)