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

• Label: 525.1.u
• Level: $525$
• Weight: $1$
• Character orbit: 525.u
• Rep. character: $\chi_{525}(326,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	525.u (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	28	16	12
Cusp forms	4	4	0
Eisenstein series	24	12	12

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

\( 4 q - 2 q^{4} - 2 q^{9} - 2 q^{16} + 2 q^{19} - 2 q^{21} - 4 q^{31} + 4 q^{36} + 2 q^{39} - 2 q^{49} + 2 q^{61} + 4 q^{64} - 4 q^{76} + 2 q^{79} - 2 q^{81} + 4 q^{84} + 2 q^{91}+O(q^{100}) \)

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.u.a	$525$	$1$	525.u	21.h	$6$	$2$	$1$	$0.262$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		✓			525.1.u.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)
525.1.u.b	$525$	$1$	525.u	21.h	$6$	$2$	$1$	$0.262$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		✓			525.1.u.a	$4$	$0$	\(0\)	\(1\)	\(0\)	\(1\)	$1$		\(q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)