Space of modular forms of level 215, weight 1, and Character 215.d

• Label: 215.1.d
• Level: $215$
• Weight: $1$
• Character orbit: 215.d
• Rep. character: $\chi_{215}(214,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $22$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 215 = 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	215.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 215 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(22\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(215, [\chi])\).

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

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

\( 6 q + 4 q^{4} - 4 q^{6} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(215, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
215.1.d.a	$215$	$1$	215.d	215.d	$2$	$3$	$3$	$0.107$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-215}) \)	None	✓	✓	215.1.d.a	$2$	$0$	\(-1\)	\(-1\)	\(3\)	\(-1\)	$1$		\(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
215.1.d.b	$215$	$1$	215.d	215.d	$2$	$3$	$3$	$0.107$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-215}) \)	None	✓	✓	215.1.d.a	$2$	$0$	\(1\)	\(1\)	\(-3\)	\(1\)	$1$		\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)