Space of modular forms of level 270, weight 3, and Character 270.n

• Label: 270.3.n
• Level: $270$
• Weight: $3$
• Character orbit: 270.n
• Rep. character: $\chi_{270}(29,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $216$
• Newform subspaces: $1$
• Sturm bound: $162$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$270 = 2 \cdot 3^{3} \cdot 5$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	270.n (of order $18$ and degree $6$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$135$
Character field:			$\Q(\zeta_{18})$
Newform subspaces:			$1$
Sturm bound:			$162$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{3}(270, [\chi])$.

	Total	New	Old
Modular forms	672	216	456
Cusp forms	624	216	408
Eisenstein series	48	0	48

Trace form

216 * q - 18 * q^5 + 12 * q^6 + 12 * q^9 - 36 * q^11 + 36 * q^14 + 18 * q^15 - 72 * q^20 + 360 * q^21 + 18 * q^25 - 36 * q^29 + 144 * q^30 + 180 * q^31 + 486 * q^35 - 192 * q^36 + 348 * q^39 - 72 * q^41 + 258 * q^45 - 72 * q^49 - 288 * q^50 - 312 * q^51 - 360 * q^54 - 72 * q^56 - 612 * q^59 - 36 * q^60 - 144 * q^61 - 864 * q^64 - 234 * q^65 + 336 * q^69 + 288 * q^74 + 642 * q^75 + 72 * q^79 + 636 * q^81 - 216 * q^84 + 432 * q^86 - 1620 * q^89 - 240 * q^90 - 504 * q^94 + 108 * q^95 - 1008 * q^99

Decomposition of $S_{3}^{\mathrm{new}}(270, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
270.3.n.a	$270$	$3$	270.n	135.n	$18$	$216$	$36$	$7.357$		None		✓	✓	✓	270.3.n.a	$4$	$0$	$0$	$0$	$-18$	$0$		$\mathrm{SU}(2)[C_{18}]$

Decomposition of $S_{3}^{\mathrm{old}}(270, [\chi])$ into lower level spaces

$S_{3}^{\mathrm{old}}(270, [\chi]) \simeq$ $S_{3}^{\mathrm{new}}(135, [\chi])$$^{\oplus 2}$