Space of modular forms of level 272, weight 10, and trivial character

• Label: 272.10.a
• Level: $272$
• Weight: $10$
• Character orbit: 272.a
• Rep. character: $\chi_{272}(1,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $12$
• Sturm bound: $360$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	272.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(360\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(272))\).

	Total	New	Old
Modular forms	330	72	258
Cusp forms	318	72	246
Eisenstein series	12	0	12

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
\(+\)	\(+\)	$+$	\(17\)
\(+\)	\(-\)	$-$	\(19\)
\(-\)	\(+\)	$-$	\(19\)
\(-\)	\(-\)	$+$	\(17\)
Plus space		\(+\)	\(34\)
Minus space		\(-\)	\(38\)

Trace form

\( 72 q + 162 q^{3} - 2750 q^{7} + 472392 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(272))\) 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
272.10.a.a	$272$	$10$	272.a	1.a	$1$	$2$	$2$	$140.090$	\(\Q(\sqrt{43}) \)	None	✓	$1$	$1$	\(0\)	\(-64\)	\(-2788\)	\(728\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-2^{5}+\beta )q^{3}+(-1394-30\beta )q^{5}+\cdots\)
272.10.a.b	$272$	$10$	272.a	1.a	$1$	$3$	$3$	$140.090$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-84\)	\(-1304\)	\(-690\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-28+\beta _{1})q^{3}+(-435-3\beta _{1}-\beta _{2})q^{5}+\cdots\)
272.10.a.c	$272$	$10$	272.a	1.a	$1$	$3$	$3$	$140.090$	3.3.3262740.1	None	✓	$1$	$1$	\(0\)	\(-84\)	\(1314\)	\(-6912\)		$-$	$-$	$+$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-28+\beta _{2})q^{3}+(438+13\beta _{1}-4\beta _{2})q^{5}+\cdots\)
272.10.a.d	$272$	$10$	272.a	1.a	$1$	$4$	$4$	$140.090$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-226\)	\(-1656\)	\(-2654\)		$-$	$+$	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-57-\beta _{1})q^{3}+(-412+4\beta _{1}-3\beta _{2}+\cdots)q^{5}+\cdots\)
272.10.a.e	$272$	$10$	272.a	1.a	$1$	$5$	$5$	$140.090$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(236\)	\(-1138\)	\(-3712\)		$-$	$-$	$+$	$2^{11}\cdot 3$	$\mathrm{SU}(2)$	\(q+(47-\beta _{1})q^{3}+(-227+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
272.10.a.f	$272$	$10$	272.a	1.a	$1$	$5$	$5$	$140.090$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(236\)	\(1480\)	\(13202\)		$-$	$+$	$-$	$2^{6}\cdot 3$	$\mathrm{SU}(2)$	\(q+(47-\beta _{3})q^{3}+(295-2\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
272.10.a.g	$272$	$10$	272.a	1.a	$1$	$7$	$7$	$140.090$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-88\)	\(1362\)	\(-9388\)		$-$	$-$	$+$	$2^{19}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+(-13+\beta _{1})q^{3}+(195-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
272.10.a.h	$272$	$10$	272.a	1.a	$1$	$7$	$7$	$140.090$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(74\)	\(1480\)	\(-5132\)		$-$	$+$	$-$	$2^{17}\cdot 3$	$\mathrm{SU}(2)$	\(q+(11-\beta _{1})q^{3}+(212-\beta _{1}-\beta _{4})q^{5}+\cdots\)
272.10.a.i	$272$	$10$	272.a	1.a	$1$	$8$	$8$	$140.090$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-152\)	\(176\)	\(-48\)		$+$	$+$	$+$	$2^{21}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+(-19+\beta _{1})q^{3}+(22+\beta _{2})q^{5}+(-6+\cdots)q^{7}+\cdots\)
272.10.a.j	$272$	$10$	272.a	1.a	$1$	$9$	$9$	$140.090$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-10\)	\(-176\)	\(5952\)		$+$	$+$	$+$	$2^{28}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(-19-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
272.10.a.k	$272$	$10$	272.a	1.a	$1$	$9$	$9$	$140.090$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(314\)	\(-1426\)	\(10754\)		$+$	$-$	$-$	$2^{30}\cdot 3$	$\mathrm{SU}(2)$	\(q+(35+\beta _{1})q^{3}+(-158+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
272.10.a.l	$272$	$10$	272.a	1.a	$1$	$10$	$10$	$140.090$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(10\)	\(2676\)	\(-4850\)		$+$	$-$	$-$	$2^{38}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(268+\beta _{2})q^{5}+(-485+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(272))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(272)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 2}\)