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

• Label: 432.2.bj
• Level: $432$
• Weight: $2$
• Character orbit: 432.bj
• Rep. character: $\chi_{432}(11,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $840$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.bj (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 432 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	888	888	0
Cusp forms	840	840	0
Eisenstein series	48	48	0

Trace form

840 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 24 * q^7 - 18 * q^8 - 6 * q^10 - 12 * q^11 + 6 * q^12 - 12 * q^13 - 12 * q^14 - 12 * q^16 - 36 * q^17 - 12 * q^18 - 6 * q^19 + 30 * q^20 - 12 * q^21 - 12 * q^22 - 24 * q^23 - 42 * q^24 - 12 * q^27 - 24 * q^28 - 12 * q^29 - 12 * q^30 - 12 * q^32 - 24 * q^33 - 24 * q^34 - 18 * q^35 - 12 * q^36 - 6 * q^37 - 12 * q^38 - 24 * q^39 - 12 * q^40 + 48 * q^42 - 12 * q^43 - 18 * q^44 - 12 * q^45 - 6 * q^46 - 12 * q^48 - 24 * q^49 + 144 * q^50 - 30 * q^51 - 12 * q^52 - 180 * q^54 - 48 * q^55 - 54 * q^56 - 66 * q^58 + 24 * q^59 - 72 * q^60 - 12 * q^61 - 216 * q^62 - 6 * q^64 - 24 * q^65 - 6 * q^66 - 12 * q^67 - 114 * q^68 - 12 * q^69 + 30 * q^70 - 36 * q^71 - 48 * q^72 - 96 * q^74 + 72 * q^75 - 12 * q^76 - 12 * q^77 - 90 * q^78 - 24 * q^81 - 24 * q^82 - 72 * q^83 - 192 * q^84 - 42 * q^85 - 72 * q^86 - 24 * q^87 - 12 * q^88 - 66 * q^90 - 6 * q^91 - 126 * q^92 - 12 * q^93 - 12 * q^94 + 96 * q^96 - 24 * q^97 - 18 * q^98 - 12 * q^99

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.bj.a	$432$	$2$	432.bj	432.aj	$36$	$840$	$70$	$3.450$		None		✓	✓	✓	432.2.bj.a	$4$	$0$	\(-12\)	\(-12\)	\(-12\)	\(-24\)		$\mathrm{SU}(2)[C_{36}]$