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

• Label: 735.2.u
• Level: $735$
• Weight: $2$
• Character orbit: 735.u
• Rep. character: $\chi_{735}(106,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $216$
• Newform subspaces: $4$
• Sturm bound: $224$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.u (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(224\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	696	216	480
Cusp forms	648	216	432
Eisenstein series	48	0	48

Trace form

\( 216 q + 4 q^{3} - 32 q^{4} + 4 q^{7} - 36 q^{9} + O(q^{10}) \)

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.u.a	$735$	$2$	735.u	49.e	$7$	$48$	$8$	$5.869$		None		$2$	$0$	\(-1\)	\(-8\)	\(8\)	\(7\)		$\mathrm{SU}(2)[C_{7}]$
735.2.u.b	$735$	$2$	735.u	49.e	$7$	$48$	$8$	$5.869$		None		$2$	$0$	\(1\)	\(-8\)	\(-8\)	\(-1\)		$\mathrm{SU}(2)[C_{7}]$
735.2.u.c	$735$	$2$	735.u	49.e	$7$	$60$	$10$	$5.869$		None		$2$	$0$	\(-1\)	\(10\)	\(10\)	\(-9\)		$\mathrm{SU}(2)[C_{7}]$
735.2.u.d	$735$	$2$	735.u	49.e	$7$	$60$	$10$	$5.869$		None		$2$	$0$	\(1\)	\(10\)	\(-10\)	\(7\)		$\mathrm{SU}(2)[C_{7}]$

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

\( S_{2}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)