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

• Label: 735.2.d
• Level: $735$
• Weight: $2$
• Character orbit: 735.d
• Rep. character: $\chi_{735}(589,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $6$
• Sturm bound: $224$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(224\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	128	40	88
Cusp forms	96	40	56
Eisenstein series	32	0	32

Trace form

\( 40 q - 40 q^{4} - 4 q^{5} + 4 q^{6} - 40 q^{9} + O(q^{10}) \)

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.d.a	$735$	$2$	735.d	5.b	$2$	$2$	$2$	$5.869$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}+q^{4}+(-1+2i)q^{5}+\cdots\)
735.2.d.b	$735$	$2$	735.d	5.b	$2$	$6$	$6$	$5.869$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(-1+\beta _{3}+\beta _{5})q^{4}+\cdots\)
735.2.d.c	$735$	$2$	735.d	5.b	$2$	$8$	$8$	$5.869$	8.0.309760000.3	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-\beta _{4}q^{3}+(-2+\beta _{6}-\beta _{7})q^{4}+\cdots\)
735.2.d.d	$735$	$2$	735.d	5.b	$2$	$8$	$8$	$5.869$	8.0.2058981376.2	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}-\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
735.2.d.e	$735$	$2$	735.d	5.b	$2$	$8$	$8$	$5.869$	8.0.2058981376.2	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
735.2.d.f	$735$	$2$	735.d	5.b	$2$	$8$	$8$	$5.869$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}^{4}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{3}q^{4}+(-\zeta_{24}^{2}+\cdots)q^{5}+\cdots\)

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

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