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

• Label: 580.2.r
• Level: $580$
• Weight: $2$
• Character orbit: 580.r
• Rep. character: $\chi_{580}(99,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $172$
• Newform subspaces: $5$
• Sturm bound: $180$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	580.r (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 580 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(180\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	188	188	0
Cusp forms	172	172	0
Eisenstein series	16	16	0

Trace form

172 * q - 6 * q^10 - 12 * q^14 - 8 * q^16 + 12 * q^20 - 40 * q^21 - 8 * q^24 - 28 * q^25 - 12 * q^26 - 16 * q^29 + 76 * q^30 + 24 * q^36 + 18 * q^40 + 12 * q^41 - 72 * q^44 + 32 * q^45 + 12 * q^46 + 76 * q^49 + 6 * q^50 + 40 * q^54 + 28 * q^56 - 6 * q^60 - 28 * q^61 - 48 * q^65 - 108 * q^66 - 40 * q^69 - 24 * q^70 - 96 * q^74 - 28 * q^76 - 204 * q^81 + 24 * q^84 - 12 * q^85 - 20 * q^89 + 8 * q^90 + 40 * q^94

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.r.a	$580$	$2$	580.r	580.r	$4$	$2$	$1$	$4.631$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			580.2.r.a	$4$	$1$	\(-2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(i-1)q^{2}-2 i q^{4}+(2 i-1)q^{5}+\cdots\)
580.2.r.b	$580$	$2$	580.r	580.r	$4$	$2$	$1$	$4.631$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			580.2.r.a	$4$	$0$	\(2\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-i+1)q^{2}-2 i q^{4}+(2 i+1)q^{5}+\cdots\)
580.2.r.c	$580$	$2$	580.r	580.r	$4$	$4$	$2$	$4.631$	\(\Q(i, \sqrt{5})\)	\(\Q(\sqrt{-5}) \)		✓			580.2.r.c	$4$	$1$	\(-4\)	\(-4\)	\(0\)	\(-12\)	$2^{2}$	$\mathrm{U}(1)[D_{4}]$	\(q+(-1-\beta _{1})q^{2}+(-1-\beta _{1})q^{3}+2\beta _{1}q^{4}+\cdots\)
580.2.r.d	$580$	$2$	580.r	580.r	$4$	$4$	$2$	$4.631$	\(\Q(i, \sqrt{5})\)	\(\Q(\sqrt{-5}) \)		✓			580.2.r.c	$4$	$0$	\(4\)	\(4\)	\(0\)	\(12\)	$2^{2}$	$\mathrm{U}(1)[D_{4}]$	\(q+(1+\beta _{1})q^{2}+(1+\beta _{1})q^{3}+2\beta _{1}q^{4}+\cdots\)
580.2.r.e	$580$	$2$	580.r	580.r	$4$	$160$	$80$	$4.631$		None		✓	✓		580.2.r.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$