Space of modular forms of level 2703, weight 1, and Character 2703.g

• Label: 2703.1.g
• Level: $2703$
• Weight: $1$
• Character orbit: 2703.g
• Rep. character: $\chi_{2703}(2702,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $5$
• Sturm bound: $324$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2703 = 3 \cdot 17 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2703.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2703 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(324\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2703, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	16	16	0
Eisenstein series	4	4	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q + 4 q^{4} + 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2703, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2703.1.g.a	$2703$	$1$	2703.g	2703.g	$2$	$3$	$3$	$1.349$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-2703}) \)	None	✓	✓	2703.1.g.a	$2$	$0$	\(-1\)	\(-3\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
2703.1.g.b	$2703$	$1$	2703.g	2703.g	$2$	$3$	$3$	$1.349$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-2703}) \)	None	✓	✓	2703.1.g.a	$2$	$0$	\(-1\)	\(3\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
2703.1.g.c	$2703$	$1$	2703.g	2703.g	$2$	$3$	$3$	$1.349$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-2703}) \)	None	✓	✓	2703.1.g.a	$2$	$0$	\(1\)	\(-3\)	\(0\)	\(0\)	$1$		\(q-\beta _{2}q^{2}-q^{3}+(\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
2703.1.g.d	$2703$	$1$	2703.g	2703.g	$2$	$3$	$3$	$1.349$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-2703}) \)	None	✓	✓	2703.1.g.a	$2$	$0$	\(1\)	\(3\)	\(0\)	\(0\)	$1$		\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
2703.1.g.e	$2703$	$1$	2703.g	2703.g	$2$	$4$	$4$	$1.349$	\(\Q(\zeta_{8})\)	$D_{4}$	None	\(\Q(\sqrt{901}) \)		✓	2703.1.g.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}q^{3}-q^{4}+(\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{9}+\cdots\)