Space of modular forms of level 825, weight 1, and Character 825.l

• Label: 825.1.l
• Level: $825$
• Weight: $1$
• Character orbit: 825.l
• Rep. character: $\chi_{825}(32,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	825.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 165 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(825, [\chi])\).

	Total	New	Old
Modular forms	36	12	24
Cusp forms	12	4	8
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	4	0	0	0

Trace form

\( 4 q + 2 q^{3} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(825, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
825.1.l.a	$825$	$1$	825.l	165.l	$4$	$2$	$1$	$0.412$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+iq^{3}+iq^{4}-q^{9}+iq^{11}-q^{12}+\cdots\)
825.1.l.b	$825$	$1$	825.l	165.l	$4$	$2$	$1$	$0.412$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+q^{3}+iq^{4}+q^{9}-iq^{11}+iq^{12}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(825, [\chi]) \cong \)