Space of modular forms of level 724, weight 2, and trivial character

• Label: 724.2.a
• Level: $724$
• Weight: $2$
• Character orbit: 724.a
• Rep. character: $\chi_{724}(1,\cdot)$
• Character field: $\Q$
• Dimension: $15$
• Newform subspaces: $3$
• Sturm bound: $182$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 724 = 2^{2} \cdot 181 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	724.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(182\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(724))\).

	Total	New	Old
Modular forms	94	15	79
Cusp forms	89	15	74
Eisenstein series	5	0	5

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

\(2\)	\(181\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(21\)	\(0\)	\(21\)		\(20\)	\(0\)	\(20\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(26\)	\(0\)	\(26\)		\(24\)	\(0\)	\(24\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(26\)	\(10\)	\(16\)		\(25\)	\(10\)	\(15\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(21\)	\(5\)	\(16\)		\(20\)	\(5\)	\(15\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(42\)	\(5\)	\(37\)		\(40\)	\(5\)	\(35\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(52\)	\(10\)	\(42\)		\(49\)	\(10\)	\(39\)		\(3\)	\(0\)	\(3\)

Trace form

15 * q - 2 * q^3 + 2 * q^5 - 2 * q^7 + 17 * q^9 + 4 * q^13 + 4 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 + 2 * q^23 + 13 * q^25 - 8 * q^27 + 18 * q^29 - 8 * q^31 + 14 * q^33 - 4 * q^35 - 4 * q^37 + 12 * q^39 + 6 * q^41 + 18 * q^43 + 22 * q^45 + 20 * q^47 + 25 * q^49 + 20 * q^53 - 20 * q^55 - 20 * q^57 + 4 * q^59 - 2 * q^61 + 18 * q^63 + 20 * q^65 - 18 * q^67 - 6 * q^69 + 14 * q^71 - 2 * q^73 - 18 * q^75 - 12 * q^77 + 31 * q^81 - 16 * q^83 + 24 * q^85 - 6 * q^87 - 10 * q^89 - 12 * q^91 - 46 * q^93 + 36 * q^95 - 14 * q^97 - 66 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(724))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	181
724.2.a.a	$724$	$2$	724.a	1.a	$1$	$2$	$2$	$5.781$	\(\Q(\sqrt{13}) \)	None	✓	✓			724.2.a.a	$1$	$0$	\(0\)	\(4\)	\(5\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+(3-\beta )q^{5}+(-2+\beta )q^{7}+q^{9}+\cdots\)
724.2.a.b	$724$	$2$	724.a	1.a	$1$	$5$	$5$	$5.781$	5.5.65657.1	None	✓	✓	✓	✓	724.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-5\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
724.2.a.c	$724$	$2$	724.a	1.a	$1$	$8$	$8$	$5.781$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓		724.2.a.c	$1$	$0$	\(0\)	\(-5\)	\(2\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-\beta _{6}q^{5}+(1-\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(724))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(724)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(181))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(362))\)\(^{\oplus 2}\)