Space of modular forms of level 210, weight 2, and Character 210.r

• Label: 210.2.r
• Level: $210$
• Weight: $2$
• Character orbit: 210.r
• Rep. character: $\chi_{210}(101,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(210, [\chi])\).

	Total	New	Old
Modular forms	112	24	88
Cusp forms	80	24	56
Eisenstein series	32	0	32

Trace form

\( 24 q + 12 q^{4} + 16 q^{7} + 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(210, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
210.2.r.a	$210$	$2$	210.r	21.g	$6$	$12$	$6$	$1.677$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(6\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{2}+(-\beta _{3}+\beta _{9})q^{3}-\beta _{6}q^{4}+\cdots\)
210.2.r.b	$210$	$2$	210.r	21.g	$6$	$12$	$6$	$1.677$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(-6\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{4}q^{2}-\beta _{7}q^{3}-\beta _{6}q^{4}+(-1-\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(210, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)