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

• Label: 3525.1.l
• Level: $3525$
• Weight: $1$
• Character orbit: 3525.l
• Rep. character: $\chi_{3525}(1268,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• Newform subspaces: $4$
• Sturm bound: $480$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3525.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 705 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(480\)
Trace bound:			\(1\)

Dimensions

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

	Total	New	Old
Modular forms	84	68	16
Cusp forms	60	60	0
Eisenstein series	24	8	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	60	0	0	0

Trace form

\( 60 q + O(q^{10}) \)

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.l.a	$3525$	$1$	3525.l	705.l	$4$	$4$	$2$	$1.759$	\(\Q(\zeta_{8})\)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-47}) \)	\(\Q(\sqrt{705}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}q^{2}+\zeta_{8}^{3}q^{3}+3\zeta_{8}^{2}q^{4}+2q^{6}+\cdots\)
3525.1.l.b	$3525$	$1$	3525.l	705.l	$4$	$8$	$4$	$1.759$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-47}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{7}q^{3}+\zeta_{24}^{4}q^{6}+\cdots\)
3525.1.l.c	$3525$	$1$	3525.l	705.l	$4$	$16$	$8$	$1.759$	\(\Q(\zeta_{40})\)	$D_{10}$	\(\Q(\sqrt{-47}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{40}^{13}+\zeta_{40}^{17})q^{2}-\zeta_{40}^{11}q^{3}+\cdots\)
3525.1.l.d	$3525$	$1$	3525.l	705.l	$4$	$32$	$16$	$1.759$	\(\Q(\zeta_{120})\)	$D_{30}$	\(\Q(\sqrt{-47}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{120}^{41}-\zeta_{120}^{49})q^{2}+\zeta_{120}^{43}q^{3}+\cdots\)