Space of modular forms of level 295, weight 1, and Character 295.d

• Label: 295.1.d
• Level: $295$
• Weight: $1$
• Character orbit: 295.d
• Rep. character: $\chi_{295}(294,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $3$
• Sturm bound: $30$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 295 = 5 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	295.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 295 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(30\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(295, [\chi])\).

	Total	New	Old
Modular forms	7	7	0
Cusp forms	5	5	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	5	0	0	0

Trace form

\( 5 q - q^{4} - 2 q^{5} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(295, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
295.1.d.a	$295$	$1$	295.d	295.d	$2$	$1$	$1$	$0.147$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-295}) \)	\(\Q(\sqrt{5}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q-q^{4}+q^{5}+q^{9}+q^{16}-2q^{19}-q^{20}+\cdots\)
295.1.d.b	$295$	$1$	295.d	295.d	$2$	$2$	$2$	$0.147$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-59}) \)	None		$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-q^{4}-\zeta_{6}q^{5}+(\zeta_{6}+\cdots)q^{7}+\cdots\)
295.1.d.c	$295$	$1$	295.d	295.d	$2$	$2$	$2$	$0.147$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-295}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\beta q^{2}+q^{4}-q^{5}+q^{9}+\beta q^{10}+\beta q^{13}+\cdots\)