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

• Label: 432.2.y
• Level: $432$
• Weight: $2$
• Character orbit: 432.y
• Rep. character: $\chi_{432}(37,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $88$
• Newform subspaces: $5$
• Sturm bound: $144$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.y (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 144 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(144\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	312	104	208
Cusp forms	264	88	176
Eisenstein series	48	16	32

Trace form

88 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 8 * q^8 - 8 * q^10 + 2 * q^11 - 2 * q^13 + 10 * q^14 - 2 * q^16 + 16 * q^17 - 8 * q^19 - 12 * q^20 - 2 * q^22 + 40 * q^26 - 24 * q^28 + 2 * q^29 - 4 * q^31 + 22 * q^32 - 6 * q^34 + 28 * q^35 - 8 * q^37 - 26 * q^38 - 2 * q^40 - 2 * q^43 - 36 * q^44 + 8 * q^46 + 44 * q^47 + 16 * q^49 + 36 * q^50 - 2 * q^52 + 8 * q^53 - 52 * q^56 - 20 * q^58 - 10 * q^59 - 2 * q^61 - 100 * q^62 - 44 * q^64 + 4 * q^65 - 2 * q^67 - 16 * q^68 + 12 * q^70 - 26 * q^74 + 10 * q^76 + 30 * q^77 - 4 * q^79 - 144 * q^80 - 52 * q^82 + 22 * q^83 - 12 * q^85 - 70 * q^86 - 26 * q^88 - 36 * q^91 + 56 * q^92 + 6 * q^94 - 60 * q^95 - 4 * q^97 - 40 * q^98

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.y.a	$432$	$2$	432.y	144.x	$12$	$4$	$1$	$3.450$	\(\Q(\zeta_{12})\)	None					144.2.x.a	$2$	$1$	\(-2\)	\(0\)	\(-2\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1-\zeta_{12}+\zeta_{12}^{2})q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{4}+\cdots\)
432.2.y.b	$432$	$2$	432.y	144.x	$12$	$4$	$1$	$3.450$	\(\Q(\zeta_{12})\)	None					144.2.x.b	$2$	$0$	\(2\)	\(0\)	\(-4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
432.2.y.c	$432$	$2$	432.y	144.x	$12$	$4$	$1$	$3.450$	\(\Q(\zeta_{12})\)	None					144.2.x.b	$2$	$0$	\(2\)	\(0\)	\(8\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
432.2.y.d	$432$	$2$	432.y	144.x	$12$	$4$	$1$	$3.450$	\(\Q(\zeta_{12})\)	None					144.2.x.a	$2$	$0$	\(4\)	\(0\)	\(4\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}^{3})q^{2}+2\zeta_{12}^{3}q^{4}+(1+\zeta_{12}+\cdots)q^{5}+\cdots\)
432.2.y.e	$432$	$2$	432.y	144.x	$12$	$72$	$18$	$3.450$		None			✓		144.2.x.e	$4$	$0$	\(-4\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

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