Space of modular forms of level 435, weight 2, and Character 435.bf

• Label: 435.2.bf
• Level: $435$
• Weight: $2$
• Character orbit: 435.bf
• Rep. character: $\chi_{435}(11,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $480$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.bf (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 87 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(435, [\chi])\).

	Total	New	Old
Modular forms	768	480	288
Cusp forms	672	480	192
Eisenstein series	96	0	96

Trace form

\( 480 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(435, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
435.2.bf.a	$435$	$2$	435.bf	87.k	$28$	$240$	$20$	$3.473$		None		✓	435.2.bf.a	$2$	$0$	\(0\)	\(-2\)	\(40\)	\(0\)		$\mathrm{SU}(2)[C_{28}]$
435.2.bf.b	$435$	$2$	435.bf	87.k	$28$	$240$	$20$	$3.473$		None		✓	435.2.bf.a	$2$	$0$	\(0\)	\(2\)	\(-40\)	\(0\)		$\mathrm{SU}(2)[C_{28}]$

Decomposition of \(S_{2}^{\mathrm{old}}(435, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(435, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)