Space of modular forms of level 432 and weight 5

• Label: 432.5
• Level: 432
• Weight: 5
• Dimension: 9144
• Nonzero newspaces: 12
• Sturm bound: 51840
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(51840\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(432))\).

	Total	New	Old
Modular forms	21156	9288	11868
Cusp forms	20316	9144	11172
Eisenstein series	840	144	696

Trace form

9144 * q - 16 * q^2 - 18 * q^3 - 28 * q^4 - 19 * q^5 - 24 * q^6 - 5 * q^7 - 16 * q^8 - 6 * q^9 - 28 * q^10 - 13 * q^11 - 24 * q^12 + 141 * q^13 - 80 * q^14 - 18 * q^15 - 980 * q^16 - 185 * q^17 - 24 * q^18 - 85 * q^19 + 2588 * q^20 - 30 * q^21 + 1004 * q^22 - 17 * q^23 - 24 * q^24 - 2104 * q^25 - 4144 * q^26 - 1458 * q^27 - 3784 * q^28 + 3149 * q^29 - 24 * q^30 + 4091 * q^31 + 3044 * q^32 + 2922 * q^33 + 4636 * q^34 - 2507 * q^35 - 24 * q^36 - 5555 * q^37 + 1244 * q^38 - 8946 * q^39 - 6972 * q^40 - 9939 * q^41 - 24 * q^42 + 7307 * q^43 - 10444 * q^44 + 2370 * q^45 - 2812 * q^46 + 21591 * q^47 - 24 * q^48 + 2498 * q^49 + 14244 * q^50 + 225 * q^51 + 12612 * q^52 - 10096 * q^53 - 24 * q^54 - 18030 * q^55 + 59164 * q^56 + 27789 * q^57 + 42308 * q^58 + 18707 * q^59 + 1296 * q^60 - 8083 * q^61 - 103272 * q^62 - 14898 * q^63 - 39844 * q^64 - 81251 * q^65 - 96324 * q^66 - 4501 * q^67 - 100100 * q^68 - 25758 * q^69 - 26716 * q^70 + 13 * q^71 + 24000 * q^72 + 4345 * q^73 + 116744 * q^74 + 22494 * q^75 + 121892 * q^76 + 92329 * q^77 + 116820 * q^78 + 34907 * q^79 + 244484 * q^80 + 59466 * q^81 + 36592 * q^82 + 5267 * q^83 - 1740 * q^84 - 2469 * q^85 - 201604 * q^86 - 23634 * q^87 - 158532 * q^88 - 42633 * q^89 - 78756 * q^90 - 20247 * q^91 - 40940 * q^92 + 10050 * q^93 - 9132 * q^94 - 33567 * q^95 - 24 * q^96 + 19233 * q^97 + 28464 * q^98 - 115794 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(432))\)

We only show spaces with odd 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
432.5.b	\(\chi_{432}(55, \cdot)\)	None	0	1
432.5.e	\(\chi_{432}(161, \cdot)\)	432.5.e.a	1	1
		432.5.e.b	1
		432.5.e.c	2
		432.5.e.d	2
		432.5.e.e	2
		432.5.e.f	2
		432.5.e.g	2
		432.5.e.h	4
		432.5.e.i	4
		432.5.e.j	4
		432.5.e.k	8
432.5.g	\(\chi_{432}(271, \cdot)\)	432.5.g.a	2	1
		432.5.g.b	2
		432.5.g.c	4
		432.5.g.d	4
		432.5.g.e	4
		432.5.g.f	4
		432.5.g.g	6
		432.5.g.h	6
432.5.h	\(\chi_{432}(377, \cdot)\)	None	0	1
432.5.j	\(\chi_{432}(53, \cdot)\)	n/a	256	2
432.5.m	\(\chi_{432}(163, \cdot)\)	n/a	256	2
432.5.n	\(\chi_{432}(89, \cdot)\)	None	0	2
432.5.o	\(\chi_{432}(127, \cdot)\)	432.5.o.a	16	2
		432.5.o.b	16
		432.5.o.c	16
432.5.q	\(\chi_{432}(17, \cdot)\)	432.5.q.a	6	2
		432.5.q.b	8
		432.5.q.c	8
		432.5.q.d	24
432.5.t	\(\chi_{432}(199, \cdot)\)	None	0	2
432.5.w	\(\chi_{432}(19, \cdot)\)	n/a	376	4
432.5.x	\(\chi_{432}(125, \cdot)\)	n/a	376	4
432.5.z	\(\chi_{432}(7, \cdot)\)	None	0	6
432.5.ba	\(\chi_{432}(31, \cdot)\)	n/a	432	6
432.5.bc	\(\chi_{432}(65, \cdot)\)	n/a	426	6
432.5.bf	\(\chi_{432}(41, \cdot)\)	None	0	6
432.5.bh	\(\chi_{432}(43, \cdot)\)	n/a	3432	12
432.5.bi	\(\chi_{432}(5, \cdot)\)	n/a	3432	12

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(432))\) into lower level spaces

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