Space of modular forms of level 420, weight 3, and Character 420.m

• Label: 420.3.m
• Level: $420$
• Weight: $3$
• Character orbit: 420.m
• Rep. character: $\chi_{420}(251,\cdot)$
• Character field: $\Q$
• Dimension: $128$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	420.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 84 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(420, [\chi])\).

	Total	New	Old
Modular forms	200	128	72
Cusp forms	184	128	56
Eisenstein series	16	0	16

Trace form

128 * q - 16 * q^16 + 100 * q^18 + 8 * q^21 + 56 * q^22 + 640 * q^25 - 60 * q^28 - 40 * q^36 + 160 * q^37 - 232 * q^42 + 176 * q^46 + 48 * q^49 - 208 * q^58 - 140 * q^60 - 288 * q^64 + 60 * q^70 - 456 * q^72 - 660 * q^78 + 80 * q^81 + 56 * q^84 - 32 * q^88 - 320 * q^93

Decomposition of \(S_{3}^{\mathrm{new}}(420, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
420.3.m.a	$420$	$3$	420.m	84.h	$2$	$128$	$128$	$11.444$		None		✓	✓	✓	420.3.m.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(420, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(420, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)