Space of modular forms of level 12, weight 9, and Character 12.c

• Label: 12.9.c
• Level: $12$
• Weight: $9$
• Character orbit: 12.c
• Rep. character: $\chi_{12}(5,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $18$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	12.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(18\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(12, [\chi])\).

	Total	New	Old
Modular forms	19	3	16
Cusp forms	13	3	10
Eisenstein series	6	0	6

Trace form

\( 3 q - 21 q^{3} - 2154 q^{7} + 3843 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(12, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
12.9.c.a	$12$	$9$	12.c	3.b	$2$	$1$	$1$	$4.889$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(81\)	\(0\)	\(4034\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{4}q^{3}+4034q^{7}+3^{8}q^{9}-35806q^{13}+\cdots\)
12.9.c.b	$12$	$9$	12.c	3.b	$2$	$2$	$2$	$4.889$	\(\Q(\sqrt{-110}) \)	None		$2$	$0$	\(0\)	\(-102\)	\(0\)	\(-6188\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-51+\beta )q^{3}-18\beta q^{5}-3094q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)