Space of modular forms of level 735, weight 2, and Character 735.y

• Label: 735.2.y
• Level: $735$
• Weight: $2$
• Character orbit: 735.y
• Rep. character: $\chi_{735}(128,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $288$
• Newform subspaces: $10$
• Sturm bound: $224$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.y (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(735, [\chi])\).

	Total	New	Old
Modular forms	512	352	160
Cusp forms	384	288	96
Eisenstein series	128	64	64

Trace form

\( 288 q + 2 q^{3} + 24 q^{6} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(735, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
735.2.y.a	$735$	$2$	735.y	105.x	$12$	$8$	$2$	$5.869$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(-8\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+2\zeta_{24}^{7}q^{2}+(-1-\zeta_{24}^{3}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
735.2.y.b	$735$	$2$	735.y	105.x	$12$	$8$	$2$	$5.869$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(-4\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+2\zeta_{24}^{7}q^{2}+(-\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
735.2.y.c	$735$	$2$	735.y	105.x	$12$	$8$	$2$	$5.869$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(4\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+2\zeta_{24}^{7}q^{2}+(\zeta_{24}^{2}+\zeta_{24}^{4}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
735.2.y.d	$735$	$2$	735.y	105.x	$12$	$8$	$2$	$5.869$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(8\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+2\zeta_{24}^{7}q^{2}+(1+\zeta_{24}^{3}-\zeta_{24}^{6})q^{3}+\cdots\)
735.2.y.e	$735$	$2$	735.y	105.x	$12$	$32$	$8$	$5.869$		None		$8$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
735.2.y.f	$735$	$2$	735.y	105.x	$12$	$32$	$8$	$5.869$		None		$8$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
735.2.y.g	$735$	$2$	735.y	105.x	$12$	$48$	$12$	$5.869$		None		$8$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
735.2.y.h	$735$	$2$	735.y	105.x	$12$	$48$	$12$	$5.869$		None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
735.2.y.i	$735$	$2$	735.y	105.x	$12$	$48$	$12$	$5.869$		None		$8$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
735.2.y.j	$735$	$2$	735.y	105.x	$12$	$48$	$12$	$5.869$		None		$8$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(735, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)