Space of modular forms of level 462, weight 2, and Character 462.ba

• Label: 462.2.ba
• Level: $462$
• Weight: $2$
• Character orbit: 462.ba
• Rep. character: $\chi_{462}(19,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $128$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.ba (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(462, [\chi])\).

	Total	New	Old
Modular forms	832	128	704
Cusp forms	704	128	576
Eisenstein series	128	0	128

Trace form

\( 128 q - 16 q^{4} - 24 q^{5} + 20 q^{7} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(462, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
462.2.ba.a	$462$	$2$	462.ba	77.n	$30$	$64$	$8$	$3.689$		None		$2$	$0$	\(0\)	\(0\)	\(-22\)	\(4\)		$\mathrm{SU}(2)[C_{30}]$
462.2.ba.b	$462$	$2$	462.ba	77.n	$30$	$64$	$8$	$3.689$		None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(16\)		$\mathrm{SU}(2)[C_{30}]$

Decomposition of \(S_{2}^{\mathrm{old}}(462, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(462, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)