Space of modular forms of level 272, weight 10, and Character 272.b

• Label: 272.10.b
• Level: $272$
• Weight: $10$
• Character orbit: 272.b
• Rep. character: $\chi_{272}(33,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $6$
• Sturm bound: $360$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(360\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(272, [\chi])\).

	Total	New	Old
Modular forms	330	82	248
Cusp forms	318	80	238
Eisenstein series	12	2	10

Trace form

\( 80 q - 539500 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(272, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
272.10.b.a	$272$	$10$	272.b	17.b	$2$	$6$	$6$	$140.090$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-5\beta _{1}-\beta _{3})q^{5}+(12\beta _{1}+\cdots)q^{7}+\cdots\)
272.10.b.b	$272$	$10$	272.b	17.b	$2$	$8$	$8$	$140.090$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(8\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
272.10.b.c	$272$	$10$	272.b	17.b	$2$	$12$	$12$	$140.090$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{28}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{7})q^{5}+(\beta _{1}+\beta _{9}+\cdots)q^{7}+\cdots\)
272.10.b.d	$272$	$10$	272.b	17.b	$2$	$14$	$14$	$140.090$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{40}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{7})q^{5}+(-\beta _{1}+\beta _{8}+\cdots)q^{7}+\cdots\)
272.10.b.e	$272$	$10$	272.b	17.b	$2$	$20$	$20$	$140.090$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{90}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{9})q^{5}+(-4\beta _{1}+\beta _{10}+\cdots)q^{7}+\cdots\)
272.10.b.f	$272$	$10$	272.b	17.b	$2$	$20$	$20$	$140.090$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{90}\cdot 3^{8}\cdot 43^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{10})q^{5}+(5\beta _{1}+\beta _{11}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(272, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(272, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)