Space of modular forms of level 432, weight 2, and Character 432.l

• Label: 432.2.l
• Level: $432$
• Weight: $2$
• Character orbit: 432.l
• Rep. character: $\chi_{432}(107,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $64$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 48 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(432, [\chi])\).

	Total	New	Old
Modular forms	156	64	92
Cusp forms	132	64	68
Eisenstein series	24	0	24

Trace form

64 * q + 4 * q^10 - 28 * q^16 - 8 * q^19 + 20 * q^22 + 12 * q^28 - 12 * q^34 - 36 * q^40 + 16 * q^43 + 16 * q^46 + 64 * q^49 - 12 * q^52 + 32 * q^55 - 48 * q^58 + 16 * q^61 + 24 * q^64 - 64 * q^67 - 72 * q^70 - 144 * q^76 - 40 * q^82 + 16 * q^85 + 12 * q^88 - 24 * q^91 - 36 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
432.2.l.a	$432$	$2$	432.l	48.k	$4$	$32$	$16$	$3.450$		None		✓			432.2.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
432.2.l.b	$432$	$2$	432.l	48.k	$4$	$32$	$16$	$3.450$		None		✓			432.2.l.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(432, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)