Space of modular forms of level 864, weight 4, and Character 864.p

• Label: 864.4.p
• Level: $864$
• Weight: $4$
• Character orbit: 864.p
• Rep. character: $\chi_{864}(143,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $68$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$864 = 2^{5} \cdot 3^{3}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	864.p (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$72$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$2$
Sturm bound:			$576$
Trace bound:			$1$
Distinguishing $T_p$:			$5$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(864, [\chi])$.

	Total	New	Old
Modular forms	912	76	836
Cusp forms	816	68	748
Eisenstein series	96	8	88

Trace form

$68 q - 6 q^{11} + 8 q^{19} - 652 q^{25} - 54 q^{41} + 2 q^{43} + 1076 q^{49} + 3054 q^{59} + 6 q^{65} + 2 q^{67} - 8 q^{73} + 3654 q^{83} + 1380 q^{91} - 2 q^{97}+O(q^{100})$

Decomposition of $S_{4}^{\mathrm{new}}(864, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
864.4.p.a	$864$	$4$	864.p	72.l	$6$	$4$	$2$	$50.978$	$\Q(\sqrt{-2}, \sqrt{-3})$	$\Q(\sqrt{-2})$					72.4.l.a	$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-9-5^{2}\beta _{1}-9\beta _{2})q^{11}+(-45+\cdots)q^{17}+\cdots$
864.4.p.b	$864$	$4$	864.p	72.l	$6$	$64$	$32$	$50.978$		None			✓		72.4.l.b	$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{6}]$

Decomposition of $S_{4}^{\mathrm{old}}(864, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(864, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(72, [\chi])$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(216, [\chi])$$^{\oplus 3}$$\oplus$$S_{4}^{\mathrm{new}}(288, [\chi])$$^{\oplus 2}$