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

• Label: 210.2.t
• Level: $210$
• Weight: $2$
• Character orbit: 210.t
• Rep. character: $\chi_{210}(59,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $6$
• 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.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(11\), \(13\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	112	32	80
Cusp forms	80	32	48
Eisenstein series	32	0	32

Trace form

\( 32 q - 16 q^{4} + 6 q^{9} + O(q^{10}) \)

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.t.a	$210$	$2$	210.t	105.p	$6$	$4$	$2$	$1.677$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$1$	\(-2\)	\(-2\)	\(-6\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
210.2.t.b	$210$	$2$	210.t	105.p	$6$	$4$	$2$	$1.677$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(-2\)	\(-1\)	\(-3\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{2})q^{2}-\beta _{1}q^{3}-\beta _{2}q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots\)
210.2.t.c	$210$	$2$	210.t	105.p	$6$	$4$	$2$	$1.677$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(2\)	\(1\)	\(6\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
210.2.t.d	$210$	$2$	210.t	105.p	$6$	$4$	$2$	$1.677$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(2\)	\(2\)	\(3\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
210.2.t.e	$210$	$2$	210.t	105.p	$6$	$8$	$4$	$1.677$	8.0.3317760000.3	None		$4$	$0$	\(-4\)	\(0\)	\(12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{4}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
210.2.t.f	$210$	$2$	210.t	105.p	$6$	$8$	$4$	$1.677$	8.0.3317760000.3	None		$4$	$0$	\(4\)	\(0\)	\(-12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)

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

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