Space of modular forms of level 1425, weight 1, and Character 1425.o

• Label: 1425.1.o
• Level: $1425$
• Weight: $1$
• Character orbit: 1425.o
• Rep. character: $\chi_{1425}(524,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $200$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1425 = 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1425.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 285 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(200\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1425, [\chi])\).

	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

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

Decomposition of \(S_{1}^{\mathrm{new}}(1425, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1425.1.o.a	$1425$	$1$	1425.o	285.n	$6$	$4$	$2$	$0.711$	\(\Q(\zeta_{12})\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None			✓	✓	57.1.h.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1425, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1425, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)