Space of modular forms of level 3132, weight 1, and Character 3132.o

• Label: 3132.1.o
• Level: $3132$
• Weight: $1$
• Character orbit: 3132.o
• Rep. character: $\chi_{3132}(1855,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $540$
• Trace bound: $2$

Defining parameters

Level:	$N$	$=$	$3132 = 2^{2} \cdot 3^{3} \cdot 29$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	3132.o (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$1044$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$2$
Sturm bound:			$540$
Trace bound:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{1}(3132, [\chi])$.

	Total	New	Old
Modular forms	60	20	40
Cusp forms	36	12	24
Eisenstein series	24	8	16

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

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	12	0	0	0

Trace form

$12 q - 6 q^{4} - 6 q^{16} - 6 q^{25} + 6 q^{29} - 6 q^{38} - 6 q^{49} + 12 q^{64} - 6 q^{65}+O(q^{100})$

Decomposition of $S_{1}^{\mathrm{new}}(3132, [\chi])$ 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3132.1.o.a	$3132$	$1$	3132.o	1044.o	$6$	$6$	$3$	$1.563$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-29})$	None					1044.1.o.a	$4$	$0$	$-3$	$0$	$0$	$0$	$3$		$q+\zeta_{18}^{6}q^{2}-\zeta_{18}^{3}q^{4}+(-\zeta_{18}^{2}-\zeta_{18}^{4}+\cdots)q^{5}+\cdots$
3132.1.o.b	$3132$	$1$	3132.o	1044.o	$6$	$6$	$3$	$1.563$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-29})$	None					1044.1.o.a	$4$	$0$	$3$	$0$	$0$	$0$	$3$		$q-\zeta_{18}^{6}q^{2}-\zeta_{18}^{3}q^{4}+(-\zeta_{18}^{2}-\zeta_{18}^{4}+\cdots)q^{5}+\cdots$

Decomposition of $S_{1}^{\mathrm{old}}(3132, [\chi])$ into lower level spaces

$S_{1}^{\mathrm{old}}(3132, [\chi]) \simeq$ $S_{1}^{\mathrm{new}}(1044, [\chi])$$^{\oplus 2}$