Space of modular forms of level 432 and weight 4

• Label: 432.4
• Level: 432
• Weight: 4
• Dimension: 6840
• Nonzero newspaces: 12
• Sturm bound: 41472
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(41472\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(432))\).

	Total	New	Old
Modular forms	15972	6984	8988
Cusp forms	15132	6840	8292
Eisenstein series	840	144	696

Trace form

6840 * q - 16 * q^2 - 18 * q^3 - 28 * q^4 - 21 * q^5 - 24 * q^6 - 39 * q^7 - 16 * q^8 - 6 * q^9 - 28 * q^10 + 55 * q^11 - 24 * q^12 + q^13 + 16 * q^14 - 18 * q^15 + 236 * q^16 + 45 * q^17 - 24 * q^18 - 123 * q^19 - 324 * q^20 - 30 * q^21 - 532 * q^22 - 145 * q^23 - 24 * q^24 - 218 * q^25 - 560 * q^26 + 648 * q^27 - 136 * q^28 + 371 * q^29 - 24 * q^30 - 219 * q^31 + 964 * q^32 - 750 * q^33 + 668 * q^34 - 1367 * q^35 - 24 * q^36 - 839 * q^37 - 1220 * q^38 - 846 * q^39 - 316 * q^40 - 225 * q^41 - 24 * q^42 - 639 * q^43 + 1524 * q^44 + 1290 * q^45 + 1348 * q^46 - 37 * q^47 - 24 * q^48 - 128 * q^49 + 2148 * q^50 - 99 * q^51 + 836 * q^52 - 24 * q^53 - 24 * q^54 + 530 * q^55 - 7876 * q^56 - 3261 * q^57 - 9148 * q^58 + 1051 * q^59 - 7344 * q^60 - 1535 * q^61 - 6184 * q^62 - 48 * q^63 + 1052 * q^64 + 4817 * q^65 + 7356 * q^66 + 1269 * q^67 + 15068 * q^68 + 6210 * q^69 + 13220 * q^70 + 3181 * q^71 + 11904 * q^72 + 2105 * q^73 + 18184 * q^74 + 2460 * q^75 + 9764 * q^76 + 7881 * q^77 + 4500 * q^78 - 783 * q^79 - 4956 * q^80 - 1878 * q^81 - 6352 * q^82 - 3397 * q^83 - 11244 * q^84 - 5233 * q^85 - 27556 * q^86 - 3060 * q^87 - 11332 * q^88 - 12735 * q^89 - 8772 * q^90 + 3031 * q^91 + 6548 * q^92 - 7446 * q^93 + 4500 * q^94 - 365 * q^95 - 24 * q^96 - 1527 * q^97 + 7376 * q^98 + 3762 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(432))\)

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
432.4.a	\(\chi_{432}(1, \cdot)\)	432.4.a.a	1	1
		432.4.a.b	1
		432.4.a.c	1
		432.4.a.d	1
		432.4.a.e	1
		432.4.a.f	1
		432.4.a.g	1
		432.4.a.h	1
		432.4.a.i	1
		432.4.a.j	1
		432.4.a.k	1
		432.4.a.l	1
		432.4.a.m	1
		432.4.a.n	1
		432.4.a.o	2
		432.4.a.p	2
		432.4.a.q	2
		432.4.a.r	2
		432.4.a.s	2
432.4.c	\(\chi_{432}(431, \cdot)\)	432.4.c.a	2	1
		432.4.c.b	2
		432.4.c.c	2
		432.4.c.d	2
		432.4.c.e	4
		432.4.c.f	4
		432.4.c.g	4
		432.4.c.h	4
432.4.d	\(\chi_{432}(217, \cdot)\)	None	0	1
432.4.f	\(\chi_{432}(215, \cdot)\)	None	0	1
432.4.i	\(\chi_{432}(145, \cdot)\)	432.4.i.a	2	2
		432.4.i.b	4
		432.4.i.c	4
		432.4.i.d	6
		432.4.i.e	8
		432.4.i.f	10
432.4.k	\(\chi_{432}(109, \cdot)\)	n/a	192	2
432.4.l	\(\chi_{432}(107, \cdot)\)	n/a	192	2
432.4.p	\(\chi_{432}(71, \cdot)\)	None	0	2
432.4.r	\(\chi_{432}(73, \cdot)\)	None	0	2
432.4.s	\(\chi_{432}(143, \cdot)\)	432.4.s.a	2	2
		432.4.s.b	2
		432.4.s.c	10
		432.4.s.d	10
		432.4.s.e	12
432.4.u	\(\chi_{432}(49, \cdot)\)	n/a	318	6
432.4.v	\(\chi_{432}(35, \cdot)\)	n/a	280	4
432.4.y	\(\chi_{432}(37, \cdot)\)	n/a	280	4
432.4.bb	\(\chi_{432}(25, \cdot)\)	None	0	6
432.4.bd	\(\chi_{432}(23, \cdot)\)	None	0	6
432.4.be	\(\chi_{432}(47, \cdot)\)	n/a	324	6
432.4.bg	\(\chi_{432}(13, \cdot)\)	n/a	2568	12
432.4.bj	\(\chi_{432}(11, \cdot)\)	n/a	2568	12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(432))\) into lower level spaces

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