Space of modular forms of level 675, weight 1, and Character 675.d

• Label: 675.1.d
• Level: $675$
• Weight: $1$
• Character orbit: 675.d
• Rep. character: $\chi_{675}(674,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $90$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	675.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(90\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(675, [\chi])\).

	Total	New	Old
Modular forms	24	2	22
Cusp forms	6	2	4
Eisenstein series	18	0	18

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q - 2 q^{4} + 2 q^{16} + 2 q^{19} - 2 q^{31} - 2 q^{61} - 2 q^{64} - 2 q^{76} + 2 q^{79} - 4 q^{91}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(675, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
675.1.d.a	$675$	$1$	675.d	15.d	$2$	$2$	$2$	$0.337$	\(\Q(\sqrt{-1}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	675.1.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{4}-i q^{7}-2 i q^{13}+q^{16}+q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(675, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)