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

$54 q - 56 q^{4} + 92 q^{16} + 48 q^{22} + 38 q^{25} + 24 q^{37} + 6 q^{43} - 12 q^{46} - 104 q^{58} - 144 q^{64} + 44 q^{67} - 36 q^{79} + 44 q^{85} - 20 q^{88}+O(q^{100})$

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}$