Space of modular forms of level 1323, weight 1, and Character 1323.b

• Label: 1323.1.b
• Level: $1323$
• Weight: $1$
• Character orbit: 1323.b
• Rep. character: $\chi_{1323}(1079,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $168$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1323.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(168\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1323, [\chi])\).

	Total	New	Old
Modular forms	30	2	28
Cusp forms	6	2	4
Eisenstein series	24	0	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(1323, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1323.1.b.a	$1323$	$1$	1323.b	3.b	$2$	$1$	$1$	$0.660$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{4}-q^{13}+q^{16}+2q^{19}+q^{25}+\cdots\)
1323.1.b.b	$1323$	$1$	1323.b	3.b	$2$	$1$	$1$	$0.660$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{4}+q^{13}+q^{16}-2q^{19}+q^{25}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)