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

• Label: 1323.2.c
• Level: $1323$
• Weight: $2$
• Character orbit: 1323.c
• Rep. character: $\chi_{1323}(1322,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $6$
• Sturm bound: $336$
• Trace bound: $22$

Defining parameters

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(336\)
Trace bound:			\(22\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	192	54	138
Cusp forms	144	54	90
Eisenstein series	48	0	48

Trace form

\( 54 q - 56 q^{4} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1323.2.c.a	$1323$	$2$	1323.c	21.c	$2$	$2$	$2$	$10.564$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					189.2.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+2 q^{4}-4\beta q^{13}+4 q^{16}-3\beta q^{19}+\cdots\)
1323.2.c.b	$1323$	$2$	1323.c	21.c	$2$	$4$	$4$	$10.564$	\(\Q(\sqrt{-3}, \sqrt{-5})\)	None					189.2.p.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-3q^{4}-\beta _{1}q^{8}-2\beta _{1}q^{11}+\cdots\)
1323.2.c.c	$1323$	$2$	1323.c	21.c	$2$	$4$	$4$	$10.564$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					189.2.p.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{5}+2\beta _{1}q^{8}+2\beta _{2}q^{10}+\cdots\)
1323.2.c.d	$1323$	$2$	1323.c	21.c	$2$	$12$	$12$	$10.564$	12.0.\(\cdots\).1	None					189.2.p.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{2}+(-1-\beta _{6})q^{4}+\beta _{1}q^{5}+(-\beta _{8}+\cdots)q^{8}+\cdots\)
1323.2.c.e	$1323$	$2$	1323.c	21.c	$2$	$16$	$16$	$10.564$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1323.2.c.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{2}+(-1-\beta _{1}-\beta _{4})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
1323.2.c.f	$1323$	$2$	1323.c	21.c	$2$	$16$	$16$	$10.564$	16.0.\(\cdots\).5	None		✓			1323.2.c.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(-1+\beta _{13})q^{4}-\beta _{2}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1323, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)