Space of modular forms of level 580, weight 2, and trivial character

• Label: 580.2.a
• Level: $580$
• Weight: $2$
• Character orbit: 580.a
• Rep. character: $\chi_{580}(1,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $180$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	580.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(180\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(580))\).

	Total	New	Old
Modular forms	96	8	88
Cusp forms	85	8	77
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.

\(2\)	\(5\)	\(29\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	\(-\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(3\)
Plus space			\(+\)	\(2\)
Minus space			\(-\)	\(6\)

Trace form

8 * q + 4 * q^3 - 4 * q^7 + 8 * q^9 + 4 * q^11 - 8 * q^13 + 8 * q^17 + 12 * q^19 + 16 * q^21 - 4 * q^23 + 8 * q^25 + 16 * q^27 + 4 * q^31 + 24 * q^33 + 4 * q^35 - 8 * q^37 - 16 * q^39 + 12 * q^43 - 8 * q^45 + 4 * q^47 - 8 * q^49 - 16 * q^51 + 8 * q^53 - 8 * q^55 - 8 * q^57 + 8 * q^59 - 32 * q^61 - 20 * q^63 - 12 * q^67 - 8 * q^71 + 12 * q^73 + 4 * q^75 + 36 * q^77 - 20 * q^79 + 40 * q^81 - 12 * q^83 + 4 * q^85 + 16 * q^89 - 8 * q^91 + 16 * q^93 - 36 * q^97 + 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(580))\) 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	5	29
580.2.a.a	$580$	$2$	580.a	1.a	$1$	$1$	$1$	$4.631$	\(\Q\)	None	✓	✓	✓	✓	580.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}-2q^{11}-2q^{13}-2q^{19}+\cdots\)
580.2.a.b	$580$	$2$	580.a	1.a	$1$	$1$	$1$	$4.631$	\(\Q\)	None	✓	✓	✓	✓	580.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-3q^{9}-4q^{11}-6q^{13}+\cdots\)
580.2.a.c	$580$	$2$	580.a	1.a	$1$	$3$	$3$	$4.631$	3.3.564.1	None	✓	✓	✓	✓	580.2.a.c	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(-4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}-q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
580.2.a.d	$580$	$2$	580.a	1.a	$1$	$3$	$3$	$4.631$	3.3.148.1	None	✓	✓	✓	✓	580.2.a.d	$1$	$0$	\(0\)	\(2\)	\(3\)	\(2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+q^{5}+(1-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(580))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(580)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(290))\)\(^{\oplus 2}\)