Space of modular forms of level 1215, weight 1, and Character 1215.d

• Label: 1215.1.d
• Level: $1215$
• Weight: $1$
• Character orbit: 1215.d
• Rep. character: $\chi_{1215}(1214,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $162$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1215 = 3^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1215.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(162\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1215, [\chi])\).

	Total	New	Old
Modular forms	30	6	24
Cusp forms	12	6	6
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	6	0	0	0

Trace form

\( 6 q + 6 q^{4} + 6 q^{16} + 6 q^{25} - 6 q^{34} - 6 q^{40} - 6 q^{46} + 6 q^{49} - 6 q^{76}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1215, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1215.1.d.a	$1215$	$1$	1215.d	15.d	$2$	$3$	$3$	$0.606$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-15}) \)	None	✓	✓			1215.1.d.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$		\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{8}+\cdots\)
1215.1.d.b	$1215$	$1$	1215.d	15.d	$2$	$3$	$3$	$0.606$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-15}) \)	None	✓	✓			1215.1.d.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$		\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1-\beta _{1}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1215, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1215, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 3}\)