Space of modular forms of level 272, weight 2, and trivial character

• Label: 272.2.a
• Level: $272$
• Weight: $2$
• Character orbit: 272.a
• Rep. character: $\chi_{272}(1,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $6$
• Sturm bound: $72$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(72\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(272))\).

	Total	New	Old
Modular forms	42	8	34
Cusp forms	31	8	23
Eisenstein series	11	0	11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(-\)	$-$	\(3\)
\(-\)	\(+\)	$-$	\(3\)
\(-\)	\(-\)	$+$	\(1\)
Plus space		\(+\)	\(2\)
Minus space		\(-\)	\(6\)

Trace form

\( 8 q + 2 q^{3} + 2 q^{7} + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(272))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	17
272.2.a.a	$272$	$2$	272.a	1.a	$1$	$1$	$1$	$2.172$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{9}-2q^{11}-6q^{13}-q^{17}+\cdots\)
272.2.a.b	$272$	$2$	272.a	1.a	$1$	$1$	$1$	$2.172$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{7}-3q^{9}-2q^{13}+q^{17}+\cdots\)
272.2.a.c	$272$	$2$	272.a	1.a	$1$	$1$	$1$	$2.172$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
272.2.a.d	$272$	$2$	272.a	1.a	$1$	$1$	$1$	$2.172$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+4q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
272.2.a.e	$272$	$2$	272.a	1.a	$1$	$2$	$2$	$2.172$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+2\beta q^{5}+(1-\beta )q^{7}+\cdots\)
272.2.a.f	$272$	$2$	272.a	1.a	$1$	$2$	$2$	$2.172$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(4\)	\(-2\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+2q^{5}+(-1-\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(272))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(272)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 2}\)