Space of modular forms of level 135, weight 1, and Character 135.d

• Label: 135.1.d
• Level: $135$
• Weight: $1$
• Character orbit: 135.d
• Rep. character: $\chi_{135}(134,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $18$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	135.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(18\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(135, [\chi])\).

	Total	New	Old
Modular forms	8	2	6
Cusp forms	2	2	0
Eisenstein series	6	0	6

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

\( 2 q - 2 q^{10} - 2 q^{16} - 2 q^{19} + 2 q^{25} - 2 q^{31} + 2 q^{34} + 2 q^{40} + 2 q^{46} + 2 q^{49} - 2 q^{61} + 2 q^{64} - 2 q^{79} - 2 q^{85} - 4 q^{94}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(135, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
135.1.d.a	$135$	$1$	135.d	15.d	$2$	$1$	$1$	$0.067$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-15}) \)	None	✓	✓			135.1.d.a	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)	$1$		\(q-q^{2}+q^{5}+q^{8}-q^{10}-q^{16}-q^{17}+\cdots\)
135.1.d.b	$135$	$1$	135.d	15.d	$2$	$1$	$1$	$0.067$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-15}) \)	None	✓	✓			135.1.d.a	$2$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+q^{2}-q^{5}-q^{8}-q^{10}-q^{16}+q^{17}+\cdots\)