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

• Label: 272.2.l
• Level: $272$
• Weight: $2$
• Character orbit: 272.l
• Rep. character: $\chi_{272}(69,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $64$
• Newform subspaces: $3$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	76	64	12
Cusp forms	68	64	4
Eisenstein series	8	0	8

Trace form

64 * q - 4 * q^4 - 12 * q^6 - 12 * q^8 - 12 * q^10 - 8 * q^11 + 4 * q^12 - 4 * q^14 + 20 * q^16 + 20 * q^18 - 28 * q^20 + 20 * q^22 - 32 * q^24 - 12 * q^26 + 24 * q^27 - 16 * q^29 - 24 * q^30 + 24 * q^31 - 20 * q^32 + 24 * q^35 + 32 * q^36 - 16 * q^37 + 28 * q^38 - 20 * q^40 - 24 * q^43 + 48 * q^44 - 40 * q^48 - 64 * q^49 - 36 * q^50 - 52 * q^52 + 16 * q^53 - 12 * q^54 + 68 * q^56 + 16 * q^58 - 24 * q^59 - 68 * q^62 + 40 * q^63 - 28 * q^64 + 16 * q^66 + 16 * q^67 + 24 * q^70 + 16 * q^72 + 28 * q^74 - 24 * q^75 - 28 * q^76 + 16 * q^77 + 40 * q^78 - 40 * q^79 + 44 * q^80 - 64 * q^81 - 36 * q^82 - 40 * q^83 + 88 * q^84 - 20 * q^86 - 44 * q^88 + 8 * q^90 + 8 * q^92 - 48 * q^93 - 32 * q^94 + 16 * q^95 - 40 * q^96 - 24 * q^98 + 24 * 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.l.a	$272$	$2$	272.l	16.e	$4$	$2$	$1$	$2.172$	\(\Q(\sqrt{-1}) \)	None		✓			272.2.l.a	$2$	$0$	\(-2\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{2}+(-i+1)q^{3}+2 i q^{4}+\cdots\)
272.2.l.b	$272$	$2$	272.l	16.e	$4$	$30$	$15$	$2.172$		None		✓			272.2.l.b	$2$	$0$	\(2\)	\(-2\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
272.2.l.c	$272$	$2$	272.l	16.e	$4$	$32$	$16$	$2.172$		None		✓	✓		272.2.l.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(272, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(272, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)