Space of modular forms of level 12, weight 3, and Character 12.c

• Label: 12.3.c
• Level: $12$
• Weight: $3$
• Character orbit: 12.c
• Rep. character: $\chi_{12}(5,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	12.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(12, [\chi])\).

	Total	New	Old
Modular forms	7	1	6
Cusp forms	1	1	0
Eisenstein series	6	0	6

Trace form

\( q - 3 q^{3} + 2 q^{7} + 9 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(12, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
12.3.c.a	$12$	$3$	12.c	3.b	$2$	$1$	$1$	$0.327$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(2\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{3}+2q^{7}+9q^{9}-22q^{13}+26q^{19}+\cdots\)