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

• Label: 272.2.b
• Level: $272$
• Weight: $2$
• Character orbit: 272.b
• Rep. character: $\chi_{272}(33,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $72$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(72\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	42	10	32
Cusp forms	30	8	22
Eisenstein series	12	2	10

Trace form

\( 8 q - 4 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
272.2.b.a	$272$	$2$	272.b	17.b	$2$	$2$	$2$	$2.172$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+\beta q^{5}-5q^{9}-\beta q^{11}+2q^{13}+\cdots\)
272.2.b.b	$272$	$2$	272.b	17.b	$2$	$2$	$2$	$2.172$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{7}-q^{9}+iq^{11}-2q^{13}+\cdots\)
272.2.b.c	$272$	$2$	272.b	17.b	$2$	$2$	$2$	$2.172$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-2\beta q^{5}-3\beta q^{7}+q^{9}-\beta q^{11}+\cdots\)
272.2.b.d	$272$	$2$	272.b	17.b	$2$	$2$	$2$	$2.172$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-\beta q^{7}+3q^{9}+2\beta q^{11}+2q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(272, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)