Space of modular forms of level 3312, weight 1, and Character 3312.bm

• Label: 3312.1.bm
• Level: $3312$
• Weight: $1$
• Character orbit: 3312.bm
• Rep. character: $\chi_{3312}(1057,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $576$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3312 = 2^{4} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3312.bm (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 207 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(576\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3312, [\chi])\).

	Total	New	Old
Modular forms	60	10	50
Cusp forms	36	6	30
Eisenstein series	24	4	20

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q + 3 q^{23} - 3 q^{25} + 3 q^{27} + 3 q^{39} - 3 q^{49} - 3 q^{59} - 6 q^{87} - 3 q^{93}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3312, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3312.1.bm.a	$3312$	$1$	3312.bm	207.f	$6$	$6$	$3$	$1.653$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-23}) \)	None			✓	✓	207.1.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{7}q^{3}-\zeta_{18}^{5}q^{9}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3312, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3312, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 5}\)