Space of modular forms of level 210, weight 3, and Character 210.k

• Label: 210.3.k
• Level: $210$
• Weight: $3$
• Character orbit: 210.k
• Rep. character: $\chi_{210}(83,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $64$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(210, [\chi])\).

	Total	New	Old
Modular forms	208	64	144
Cusp forms	176	64	112
Eisenstein series	32	0	32

Trace form

\( 64 q - 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(210, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
210.3.k.a	$210$	$3$	210.k	105.k	$4$	$32$	$16$	$5.722$		None		$4$	$0$	\(-32\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$
210.3.k.b	$210$	$3$	210.k	105.k	$4$	$32$	$16$	$5.722$		None		$4$	$0$	\(32\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(210, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(210, [\chi]) \cong \)