Space of modular forms of level 1407, weight 1, and Character 1407.g

• Label: 1407.1.g
• Level: $1407$
• Weight: $1$
• Character orbit: 1407.g
• Rep. character: $\chi_{1407}(1406,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $10$
• Sturm bound: $181$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1407 = 3 \cdot 7 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1407.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1407 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(181\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1407, [\chi])\).

	Total	New	Old
Modular forms	18	18	0
Cusp forms	14	14	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	14	0	0	0

Trace form

\( 14 q + 2 q^{4} + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1407, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1407.1.g.a	$1407$	$1$	1407.g	1407.g	$2$	$1$	$1$	$0.702$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1407}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q-q^{2}-q^{3}+q^{6}-q^{7}+q^{8}+q^{9}+\cdots\)
1407.1.g.b	$1407$	$1$	1407.g	1407.g	$2$	$1$	$1$	$0.702$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1407}) \)	None	✓	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(1\)	$1$		\(q-q^{2}+q^{3}-q^{6}+q^{7}+q^{8}+q^{9}+\cdots\)
1407.1.g.c	$1407$	$1$	1407.g	1407.g	$2$	$1$	$1$	$0.702$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1407}) \)	\(\Q(\sqrt{469}) \)	✓	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$		\(q-q^{3}-q^{4}+q^{7}+q^{9}+q^{12}-2q^{13}+\cdots\)
1407.1.g.d	$1407$	$1$	1407.g	1407.g	$2$	$1$	$1$	$0.702$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1407}) \)	\(\Q(\sqrt{469}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)	$1$		\(q+q^{3}-q^{4}-q^{7}+q^{9}-q^{12}+2q^{13}+\cdots\)
1407.1.g.e	$1407$	$1$	1407.g	1407.g	$2$	$1$	$1$	$0.702$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1407}) \)	None	✓	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots\)
1407.1.g.f	$1407$	$1$	1407.g	1407.g	$2$	$1$	$1$	$0.702$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1407}) \)	None	✓	$2$	$0$	\(1\)	\(1\)	\(0\)	\(1\)	$1$		\(q+q^{2}+q^{3}+q^{6}+q^{7}-q^{8}+q^{9}+\cdots\)
1407.1.g.g	$1407$	$1$	1407.g	1407.g	$2$	$2$	$2$	$0.702$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-1407}) \)	None	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)	$1$		\(q-\beta q^{2}-q^{3}+2q^{4}+\beta q^{6}+q^{7}-\beta q^{8}+\cdots\)
1407.1.g.h	$1407$	$1$	1407.g	1407.g	$2$	$2$	$2$	$0.702$	\(\Q(\sqrt{-3}) \)	$D_{6}$	None	\(\Q(\sqrt{469}) \)		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)	$1$		\(q+\zeta_{6}^{2}q^{3}-q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{5}-q^{7}+\cdots\)
1407.1.g.i	$1407$	$1$	1407.g	1407.g	$2$	$2$	$2$	$0.702$	\(\Q(\sqrt{-3}) \)	$D_{6}$	None	\(\Q(\sqrt{469}) \)		$4$	$0$	\(0\)	\(1\)	\(0\)	\(2\)	$1$		\(q-\zeta_{6}^{2}q^{3}-q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+\cdots\)
1407.1.g.j	$1407$	$1$	1407.g	1407.g	$2$	$2$	$2$	$0.702$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-1407}) \)	None	✓	$4$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)	$1$		\(q-\beta q^{2}+q^{3}+2q^{4}-\beta q^{6}-q^{7}-\beta q^{8}+\cdots\)