Space of modular forms of level 525, weight 1, and Character 525.be

• Label: 525.1.be
• Level: $525$
• Weight: $1$
• Character orbit: 525.be
• Rep. character: $\chi_{525}(68,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $80$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	525.be (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(80\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(525, [\chi])\).

	Total	New	Old
Modular forms	56	24	32
Cusp forms	8	8	0
Eisenstein series	48	16	32

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + 4 q^{16} - 4 q^{21} - 8 q^{36} - 12 q^{61} + 4 q^{81} - 4 q^{91}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(525, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
525.1.be.a	$525$	$1$	525.be	105.w	$12$	$8$	$2$	$0.262$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	525.1.be.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{5}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{11}q^{7}+\cdots\)