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

• Label: 620.2.c
• Level: $620$
• Weight: $2$
• Character orbit: 620.c
• Rep. character: $\chi_{620}(249,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 620 = 2^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	620.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	102	16	86
Cusp forms	90	16	74
Eisenstein series	12	0	12

Trace form

16 * q + 2 * q^5 - 20 * q^9 - 4 * q^11 + 10 * q^15 + 8 * q^19 - 16 * q^21 + 2 * q^25 + 8 * q^29 + 2 * q^35 + 4 * q^39 + 4 * q^41 - 30 * q^45 + 4 * q^49 - 8 * q^51 - 16 * q^55 + 20 * q^59 - 20 * q^61 - 6 * q^65 - 12 * q^69 - 24 * q^71 + 10 * q^75 - 16 * q^79 + 20 * q^81 - 6 * q^85 + 24 * q^89 + 36 * q^91 + 54 * q^95 + 56 * q^99

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.c.a	$620$	$2$	620.c	5.b	$2$	$2$	$2$	$4.951$	\(\Q(\sqrt{-1}) \)	None		✓			620.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+(-\beta-1)q^{5}+2\beta q^{7}-q^{9}+\cdots\)
620.2.c.b	$620$	$2$	620.c	5.b	$2$	$6$	$6$	$4.951$	6.0.84345856.2	None		✓			620.2.c.b	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{5})q^{7}+\cdots\)
620.2.c.c	$620$	$2$	620.c	5.b	$2$	$8$	$8$	$4.951$	8.0.\(\cdots\).1	None		✓	✓		620.2.c.c	$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{3}+\beta _{5}q^{5}+(-\beta _{2}-\beta _{7})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(620, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 2}\)