Space of modular forms of level 579, weight 2, and trivial character

• Label: 579.2.a
• Level: $579$
• Weight: $2$
• Character orbit: 579.a
• Rep. character: $\chi_{579}(1,\cdot)$
• Character field: $\Q$
• Dimension: $33$
• Newform subspaces: $7$
• Sturm bound: $129$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 579 = 3 \cdot 193 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	579.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(129\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(579))\).

	Total	New	Old
Modular forms	66	33	33
Cusp forms	63	33	30
Eisenstein series	3	0	3

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

\(3\)	\(193\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(5\)
\(+\)	\(-\)	\(-\)	\(11\)
\(-\)	\(+\)	\(-\)	\(13\)
\(-\)	\(-\)	\(+\)	\(4\)
Plus space		\(+\)	\(9\)
Minus space		\(-\)	\(24\)

Trace form

\( 33 q + 3 q^{2} + q^{3} + 35 q^{4} + 2 q^{5} - q^{6} + 4 q^{7} + 15 q^{8} + 33 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(579))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	193
579.2.a.a	$579$	$2$	579.a	1.a	$1$	$1$	$1$	$4.623$	\(\Q\)	None	✓	✓			579.2.a.a	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots\)
579.2.a.b	$579$	$2$	579.a	1.a	$1$	$1$	$1$	$4.623$	\(\Q\)	None	✓	✓			579.2.a.b	$1$	$0$	\(2\)	\(-1\)	\(2\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}+2q^{5}-2q^{6}+\cdots\)
579.2.a.c	$579$	$2$	579.a	1.a	$1$	$2$	$2$	$4.623$	\(\Q(\sqrt{2}) \)	None	✓	✓			579.2.a.c	$1$	$1$	\(-2\)	\(-2\)	\(-4\)	\(4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots\)
579.2.a.d	$579$	$2$	579.a	1.a	$1$	$3$	$3$	$4.623$	3.3.257.1	None	✓	✓	✓		579.2.a.d	$1$	$1$	\(0\)	\(-3\)	\(-4\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}-q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
579.2.a.e	$579$	$2$	579.a	1.a	$1$	$3$	$3$	$4.623$	\(\Q(\zeta_{18})^+\)	None	✓	✓	✓		579.2.a.e	$1$	$1$	\(0\)	\(3\)	\(-6\)	\(-9\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
579.2.a.f	$579$	$2$	579.a	1.a	$1$	$10$	$10$	$4.623$	10.10.\(\cdots\).1	None	✓	✓	✓		579.2.a.f	$1$	$0$	\(2\)	\(-10\)	\(8\)	\(-10\)		$+$	$-$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{5}q^{2}-q^{3}+(2-\beta _{4}-\beta _{6}-\beta _{9})q^{4}+\cdots\)
579.2.a.g	$579$	$2$	579.a	1.a	$1$	$13$	$13$	$4.623$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	✓	✓	✓	579.2.a.g	$1$	$0$	\(2\)	\(13\)	\(6\)	\(15\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(579))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(579)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(193))\)\(^{\oplus 2}\)