Space of modular forms of level 375, weight 1, and Character 375.d

• Label: 375.1.d
• Level: $375$
• Weight: $1$
• Character orbit: 375.d
• Rep. character: $\chi_{375}(374,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $50$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	375.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(50\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(375, [\chi])\).

	Total	New	Old
Modular forms	14	4	10
Cusp forms	4	4	0
Eisenstein series	10	0	10

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

4 * q + 2 * q^4 - 2 * q^6 + 4 * q^9 - 2 * q^19 - 4 * q^24 - 2 * q^31 - 4 * q^34 + 2 * q^36 - 4 * q^46 + 4 * q^49 - 2 * q^51 - 2 * q^54 - 2 * q^61 - 2 * q^64 - 2 * q^69 - 6 * q^76 - 2 * q^79 + 4 * q^81 + 6 * q^94 + 4 * q^96

Decomposition of \(S_{1}^{\mathrm{new}}(375, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
375.1.d.a	$375$	$1$	375.d	15.d	$2$	$2$	$2$	$0.187$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-15}) \)	None	✓	✓			375.1.c.a	$2$	$0$	\(-1\)	\(2\)	\(0\)	\(0\)	$1$		\(q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
375.1.d.b	$375$	$1$	375.d	15.d	$2$	$2$	$2$	$0.187$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-15}) \)	None	✓	✓			375.1.c.a	$2$	$0$	\(1\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)