Space of modular forms of level 700, weight 2, and Character 700.t

• Label: 700.2.t
• Level: $700$
• Weight: $2$
• Character orbit: 700.t
• Rep. character: $\chi_{700}(199,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $136$
• Newform subspaces: $5$
• Sturm bound: $240$
• Trace bound: $12$

Defining parameters

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 140 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(240\)
Trace bound:			\(12\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(700, [\chi])\).

	Total	New	Old
Modular forms	264	152	112
Cusp forms	216	136	80
Eisenstein series	48	16	32

Trace form

\( 136 q + 2 q^{4} + 64 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(700, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
700.2.t.a	$700$	$2$	700.t	140.s	$6$	$4$	$2$	$5.590$	\(\Q(\zeta_{12})\)	None		$4$	$1$	\(-2\)	\(-6\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots\)
700.2.t.b	$700$	$2$	700.t	140.s	$6$	$4$	$2$	$5.590$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(2\)	\(6\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
700.2.t.c	$700$	$2$	700.t	140.s	$6$	$32$	$16$	$5.590$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
700.2.t.d	$700$	$2$	700.t	140.s	$6$	$32$	$16$	$5.590$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
700.2.t.e	$700$	$2$	700.t	140.s	$6$	$64$	$32$	$5.590$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(700, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)