Space of modular forms of level 1323, weight 2, and Character 1323.o

• Label: 1323.2.o
• Level: $1323$
• Weight: $2$
• Character orbit: 1323.o
• Rep. character: $\chi_{1323}(440,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $5$
• Sturm bound: $336$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(336\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1323, [\chi])\).

	Total	New	Old
Modular forms	384	88	296
Cusp forms	288	72	216
Eisenstein series	96	16	80

Trace form

\( 72 q - 6 q^{2} + 34 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1323.2.o.a	$1323$	$2$	1323.o	63.o	$6$	$2$	$1$	$10.564$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-3\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
1323.2.o.b	$1323$	$2$	1323.o	63.o	$6$	$2$	$1$	$10.564$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-3\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
1323.2.o.c	$1323$	$2$	1323.o	63.o	$6$	$10$	$5$	$10.564$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(1+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)
1323.2.o.d	$1323$	$2$	1323.o	63.o	$6$	$10$	$5$	$10.564$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(1+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)
1323.2.o.e	$1323$	$2$	1323.o	63.o	$6$	$48$	$24$	$10.564$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces

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