Space of modular forms of level 432 and weight 6

• Label: 432.6
• Level: 432
• Weight: 6
• Dimension: 11448
• Nonzero newspaces: 12
• Sturm bound: 62208
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(62208\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(432))\).

	Total	New	Old
Modular forms	26340	11592	14748
Cusp forms	25500	11448	14052
Eisenstein series	840	144	696

Trace form

11448 * q - 16 * q^2 - 18 * q^3 - 28 * q^4 - 21 * q^5 - 24 * q^6 + 41 * q^7 - 16 * q^8 - 6 * q^9 - 28 * q^10 - 737 * q^11 - 24 * q^12 - 151 * q^13 + 112 * q^14 - 18 * q^15 + 2412 * q^16 - 1035 * q^17 - 24 * q^18 - 2819 * q^19 - 1668 * q^20 - 30 * q^21 + 10028 * q^22 + 3167 * q^23 - 24 * q^24 + 8574 * q^25 + 1744 * q^26 - 6480 * q^27 - 16648 * q^28 - 55741 * q^29 - 24 * q^30 - 9563 * q^31 - 3836 * q^32 + 16962 * q^33 + 27612 * q^34 + 92233 * q^35 - 24 * q^36 + 31153 * q^37 + 34396 * q^38 - 3438 * q^39 + 60100 * q^40 - 63849 * q^41 - 24 * q^42 - 49223 * q^43 - 36492 * q^44 - 35430 * q^45 - 63612 * q^46 + 173819 * q^47 - 24 * q^48 + 35136 * q^49 - 63900 * q^50 - 747 * q^51 + 18244 * q^52 - 24 * q^53 - 24 * q^54 - 151550 * q^55 - 179716 * q^56 - 194853 * q^57 - 63676 * q^58 - 62669 * q^59 + 424656 * q^60 + 294057 * q^61 + 873848 * q^62 + 120912 * q^63 + 209564 * q^64 + 257537 * q^65 - 5604 * q^66 - 34739 * q^67 - 750052 * q^68 - 379134 * q^69 - 900700 * q^70 - 235427 * q^71 - 834816 * q^72 - 168519 * q^73 - 996536 * q^74 - 95820 * q^75 - 134620 * q^76 + 225609 * q^77 + 465012 * q^78 - 16559 * q^79 + 1846884 * q^80 + 742890 * q^81 + 856368 * q^82 + 534467 * q^83 + 920148 * q^84 - 14225 * q^85 + 366716 * q^86 - 113220 * q^87 - 846404 * q^88 - 1474623 * q^89 - 708612 * q^90 - 96673 * q^91 - 456556 * q^92 + 548538 * q^93 - 410412 * q^94 + 569395 * q^95 - 24 * q^96 - 92871 * q^97 - 411568 * q^98 + 551970 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(432))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
432.6.a	\(\chi_{432}(1, \cdot)\)	432.6.a.a	1	1
		432.6.a.b	1
		432.6.a.c	1
		432.6.a.d	1
		432.6.a.e	1
		432.6.a.f	1
		432.6.a.g	1
		432.6.a.h	1
		432.6.a.i	1
		432.6.a.j	1
		432.6.a.k	2
		432.6.a.l	2
		432.6.a.m	2
		432.6.a.n	2
		432.6.a.o	2
		432.6.a.p	2
		432.6.a.q	2
		432.6.a.r	2
		432.6.a.s	2
		432.6.a.t	2
		432.6.a.u	2
		432.6.a.v	2
		432.6.a.w	3
		432.6.a.x	3
432.6.c	\(\chi_{432}(431, \cdot)\)	432.6.c.a	2	1
		432.6.c.b	2
		432.6.c.c	4
		432.6.c.d	4
		432.6.c.e	8
		432.6.c.f	8
		432.6.c.g	12
432.6.d	\(\chi_{432}(217, \cdot)\)	None	0	1
432.6.f	\(\chi_{432}(215, \cdot)\)	None	0	1
432.6.i	\(\chi_{432}(145, \cdot)\)	432.6.i.a	4	2
		432.6.i.b	6
		432.6.i.c	8
		432.6.i.d	10
		432.6.i.e	14
		432.6.i.f	16
432.6.k	\(\chi_{432}(109, \cdot)\)	n/a	320	2
432.6.l	\(\chi_{432}(107, \cdot)\)	n/a	320	2
432.6.p	\(\chi_{432}(71, \cdot)\)	None	0	2
432.6.r	\(\chi_{432}(73, \cdot)\)	None	0	2
432.6.s	\(\chi_{432}(143, \cdot)\)	432.6.s.a	20	2
		432.6.s.b	20
		432.6.s.c	20
432.6.u	\(\chi_{432}(49, \cdot)\)	n/a	534	6
432.6.v	\(\chi_{432}(35, \cdot)\)	n/a	472	4
432.6.y	\(\chi_{432}(37, \cdot)\)	n/a	472	4
432.6.bb	\(\chi_{432}(25, \cdot)\)	None	0	6
432.6.bd	\(\chi_{432}(23, \cdot)\)	None	0	6
432.6.be	\(\chi_{432}(47, \cdot)\)	n/a	540	6
432.6.bg	\(\chi_{432}(13, \cdot)\)	n/a	4296	12
432.6.bj	\(\chi_{432}(11, \cdot)\)	n/a	4296	12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(432))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(432)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 15}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 2}\)