Space of modular forms of level 272, weight 12, and Character 272.b

• Label: 272.12.b
• Level: $272$
• Weight: $12$
• Character orbit: 272.b
• Rep. character: $\chi_{272}(33,\cdot)$
• Character field: $\Q$
• Dimension: $98$
• Newform subspaces: $6$
• Sturm bound: $432$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	272.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(432\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(272, [\chi])\).

	Total	New	Old
Modular forms	402	100	302
Cusp forms	390	98	292
Eisenstein series	12	2	10

Trace form

\( 98 q - 5461462 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(272, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
272.12.b.a	$272$	$12$	272.b	17.b	$2$	$8$	$8$	$208.989$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					34.12.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}-4\beta _{3}+\cdots)q^{7}+\cdots\)
272.12.b.b	$272$	$12$	272.b	17.b	$2$	$8$	$8$	$208.989$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					34.12.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}\cdot 3^{2}\cdot 17^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-2\beta _{1}-\beta _{2})q^{5}+(71\beta _{1}+\cdots)q^{7}+\cdots\)
272.12.b.c	$272$	$12$	272.b	17.b	$2$	$16$	$16$	$208.989$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					17.12.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{59}\cdot 3^{4}\cdot 17^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{7}q^{5}+(-2^{4}\beta _{1}-2\beta _{7}+\cdots)q^{7}+\cdots\)
272.12.b.d	$272$	$12$	272.b	17.b	$2$	$16$	$16$	$208.989$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					68.12.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{53}\cdot 3^{8}\cdot 17^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{8})q^{5}+(-7\beta _{1}-\beta _{9}+\cdots)q^{7}+\cdots\)
272.12.b.e	$272$	$12$	272.b	17.b	$2$	$24$	$24$	$208.989$		None					136.12.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
272.12.b.f	$272$	$12$	272.b	17.b	$2$	$26$	$26$	$208.989$		None			✓		136.12.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{12}^{\mathrm{old}}(272, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(272, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 2}\)