Space of modular forms of level 210, weight 4, and Character 210.d

• Label: 210.4.d
• Level: $210$
• Weight: $4$
• Character orbit: 210.d
• Rep. character: $\chi_{210}(209,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	210.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(210, [\chi])\).

	Total	New	Old
Modular forms	152	48	104
Cusp forms	136	48	88
Eisenstein series	16	0	16

Trace form

\( 48 q + 192 q^{4} + 60 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(210, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
210.4.d.a	$210$	$4$	210.d	105.g	$2$	$24$	$24$	$12.390$		None		$4$	$0$	\(-48\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
210.4.d.b	$210$	$4$	210.d	105.g	$2$	$24$	$24$	$12.390$		None		$4$	$0$	\(48\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(210, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)