Space of modular forms of level 620, weight 2, and Character 620.k

• Label: 620.2.k
• Level: $620$
• Weight: $2$
• Character orbit: 620.k
• Rep. character: $\chi_{620}(63,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $180$
• Newform subspaces: $4$
• Sturm bound: $192$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 620 = 2^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	620.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(192\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(620, [\chi])\).

	Total	New	Old
Modular forms	200	180	20
Cusp forms	184	180	4
Eisenstein series	16	0	16

Trace form

180 * q - 6 * q^8 - 16 * q^10 - 16 * q^12 - 4 * q^13 - 20 * q^17 + 28 * q^18 - 16 * q^21 - 16 * q^22 - 20 * q^25 - 32 * q^26 - 26 * q^28 + 16 * q^30 - 32 * q^36 + 20 * q^37 - 34 * q^38 + 24 * q^40 + 16 * q^41 + 40 * q^42 + 20 * q^45 - 48 * q^46 + 8 * q^48 + 56 * q^52 + 4 * q^53 - 48 * q^56 - 32 * q^57 + 16 * q^58 - 40 * q^60 - 12 * q^65 - 16 * q^66 + 52 * q^68 + 10 * q^70 - 30 * q^72 + 52 * q^73 - 16 * q^76 + 48 * q^77 - 24 * q^78 + 40 * q^80 - 100 * q^81 - 14 * q^82 + 28 * q^85 + 8 * q^86 - 16 * q^88 - 46 * q^90 - 36 * q^92 - 40 * q^96 + 20 * q^97 - 14 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(620, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
620.2.k.a	$620$	$2$	620.k	20.e	$4$	$2$	$1$	$4.951$	\(\Q(\sqrt{-1}) \)	None		✓			620.2.k.a	$2$	$1$	\(-2\)	\(-2\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{2}+(-i-1)q^{3}+2 i q^{4}+\cdots\)
620.2.k.b	$620$	$2$	620.k	20.e	$4$	$2$	$1$	$4.951$	\(\Q(\sqrt{-1}) \)	None		✓			620.2.k.a	$2$	$0$	\(-2\)	\(2\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{2}+(i+1)q^{3}+2 i q^{4}+\cdots\)
620.2.k.c	$620$	$2$	620.k	20.e	$4$	$88$	$44$	$4.951$		None		✓			620.2.k.c	$2$	$0$	\(2\)	\(-2\)	\(-2\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$
620.2.k.d	$620$	$2$	620.k	20.e	$4$	$88$	$44$	$4.951$		None		✓			620.2.k.c	$2$	$0$	\(2\)	\(2\)	\(-2\)	\(4\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(620, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(620, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)