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

• Label: 1323.2.i
• Level: $1323$
• Weight: $2$
• Character orbit: 1323.i
• Rep. character: $\chi_{1323}(521,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $4$
• Sturm bound: $336$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(336\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

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 - 62 * q^4 - 3 * q^5 + 6 * q^10 - 15 * q^11 + 3 * q^13 + 46 * q^16 + 9 * q^17 + 6 * q^19 + 6 * q^20 - 8 * q^22 - 18 * q^23 - 21 * q^25 - 6 * q^26 - 6 * q^29 - 6 * q^34 + q^37 + 27 * q^38 - 24 * q^40 + 6 * q^41 - 8 * q^43 + 69 * q^44 + 16 * q^46 + 30 * q^47 - 3 * q^50 + 15 * q^52 + 36 * q^53 + q^58 - 36 * q^59 - 24 * q^62 - 28 * q^64 - 12 * q^67 - 24 * q^68 + 6 * q^73 - 129 * q^74 + 36 * q^79 + 45 * q^80 + 30 * q^83 - 21 * q^85 + 63 * q^86 + 23 * q^88 - 27 * q^89 + 84 * q^92 + 3 * q^97

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.i.a	$1323$	$2$	1323.i	63.i	$6$	$2$	$1$	$10.564$	\(\Q(\sqrt{-3}) \)	None					63.2.i.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{6})q^{2}-q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
1323.2.i.b	$1323$	$2$	1323.i	63.i	$6$	$10$	$5$	$10.564$	10.0.\(\cdots\).1	None					63.2.i.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}-\beta _{5})q^{2}+(-1-2\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
1323.2.i.c	$1323$	$2$	1323.i	63.i	$6$	$12$	$6$	$10.564$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					63.2.o.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}-\beta _{5})q^{2}+(-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
1323.2.i.d	$1323$	$2$	1323.i	63.i	$6$	$48$	$24$	$10.564$		None			✓		441.2.o.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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