Space of modular forms of level 580, weight 2, and Character 580.d

• Label: 580.2.d
• Level: $580$
• Weight: $2$
• Character orbit: 580.d
• Rep. character: $\chi_{580}(521,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $180$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	580.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(180\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(580, [\chi])\).

	Total	New	Old
Modular forms	96	10	86
Cusp forms	84	10	74
Eisenstein series	12	0	12

Trace form

10 * q - 2 * q^5 - 2 * q^9 - 4 * q^13 - 16 * q^23 + 10 * q^25 + 2 * q^29 - 8 * q^35 + 10 * q^45 + 10 * q^49 - 56 * q^51 + 4 * q^53 - 8 * q^57 + 24 * q^59 - 24 * q^63 + 4 * q^65 - 16 * q^67 + 8 * q^71 - 6 * q^81 + 48 * q^83 + 16 * q^87 + 40 * q^91 - 24 * q^93

Decomposition of \(S_{2}^{\mathrm{new}}(580, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
580.2.d.a	$580$	$2$	580.d	29.b	$2$	$2$	$2$	$4.631$	\(\Q(\sqrt{-7}) \)	None		✓			580.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{5}-2q^{7}+3q^{9}-\beta q^{11}-2q^{13}+\cdots\)
580.2.d.b	$580$	$2$	580.d	29.b	$2$	$4$	$4$	$4.631$	4.0.7168.1	None		✓			580.2.d.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-q^{5}+(2+\beta _{3})q^{7}+(-3+2\beta _{3})q^{9}+\cdots\)
580.2.d.c	$580$	$2$	580.d	29.b	$2$	$4$	$4$	$4.631$	\(\Q(\sqrt{-2}, \sqrt{11})\)	None		✓			580.2.d.c	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+q^{5}+(-1+\beta _{3})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(580, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(580, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 2}\)