Space of modular forms of level 272, weight 2, and Character 272.bd

• Label: 272.2.bd
• Level: $272$
• Weight: $2$
• Character orbit: 272.bd
• Rep. character: $\chi_{272}(3,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $272$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$272 = 2^{4} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	272.bd (of order $16$ and degree $8$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$272$
Character field:			$\Q(\zeta_{16})$
Newform subspaces:			$1$
Sturm bound:			$72$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(272, [\chi])$.

	Total	New	Old
Modular forms	304	304	0
Cusp forms	272	272	0
Eisenstein series	32	32	0

Trace form

272 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 24 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^10 - 8 * q^11 + 16 * q^12 - 8 * q^14 - 16 * q^17 - 16 * q^18 + 24 * q^19 + 24 * q^20 - 8 * q^22 - 16 * q^23 + 8 * q^24 + 8 * q^26 - 8 * q^27 - 56 * q^28 - 8 * q^29 - 72 * q^30 - 8 * q^32 - 8 * q^34 - 16 * q^35 - 72 * q^36 - 8 * q^37 + 32 * q^38 - 16 * q^39 + 112 * q^40 + 8 * q^42 - 8 * q^43 - 72 * q^44 - 8 * q^45 - 8 * q^46 - 8 * q^48 - 16 * q^49 - 80 * q^50 - 88 * q^51 - 16 * q^52 - 8 * q^53 - 8 * q^54 - 16 * q^55 - 8 * q^56 - 72 * q^58 - 8 * q^59 + 8 * q^60 - 72 * q^61 + 32 * q^62 + 48 * q^63 + 40 * q^64 - 48 * q^65 + 8 * q^66 - 8 * q^68 - 16 * q^69 - 72 * q^70 - 16 * q^71 - 112 * q^72 - 8 * q^74 - 8 * q^75 + 24 * q^76 - 8 * q^77 + 40 * q^78 - 8 * q^80 - 16 * q^81 + 88 * q^82 - 88 * q^83 - 32 * q^84 - 8 * q^85 - 96 * q^86 - 16 * q^87 - 8 * q^88 + 240 * q^90 + 48 * q^91 - 88 * q^92 - 8 * q^93 - 120 * q^94 - 112 * q^96 - 16 * q^97 + 128 * q^98 + 16 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(272, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
272.2.bd.a	$272$	$2$	272.bd	272.ad	$16$	$272$	$34$	$2.172$		None		✓	✓	✓	272.2.bd.a	$2$	$0$	$-8$	$-8$	$-8$	$-16$		$\mathrm{SU}(2)[C_{16}]$