Space of modular forms of level 432 and weight 2

• Label: 432.2
• Level: 432
• Weight: 2
• Dimension: 2232
• Nonzero newspaces: 12
• Newform subspaces: 43
• Sturm bound: 20736
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 43 \)
Sturm bound:			\(20736\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(432))\).

	Total	New	Old
Modular forms	5604	2376	3228
Cusp forms	4765	2232	2533
Eisenstein series	839	144	695

Trace form

2232 * q - 16 * q^2 - 18 * q^3 - 28 * q^4 - 21 * q^5 - 24 * q^6 - 23 * q^7 - 16 * q^8 - 6 * q^9 - 28 * q^10 - 17 * q^11 - 24 * q^12 - 39 * q^13 - 8 * q^14 - 18 * q^15 - 20 * q^16 - 27 * q^17 - 24 * q^18 - 19 * q^19 + 12 * q^20 - 30 * q^21 - 4 * q^22 - q^23 - 24 * q^24 + 14 * q^25 + 16 * q^26 - 40 * q^28 + 35 * q^29 - 24 * q^30 + 5 * q^31 + 4 * q^32 - 30 * q^33 - 20 * q^34 + 73 * q^35 - 24 * q^36 + q^37 - 44 * q^38 + 18 * q^39 - 60 * q^40 + 39 * q^41 - 24 * q^42 + 41 * q^43 - 60 * q^44 - 6 * q^45 - 76 * q^46 + 59 * q^47 - 24 * q^48 - 64 * q^49 - 60 * q^50 - 27 * q^51 - 60 * q^52 - 24 * q^53 - 24 * q^54 - 30 * q^55 - 196 * q^56 - 21 * q^57 - 124 * q^58 - 29 * q^59 - 144 * q^60 - 103 * q^61 - 256 * q^62 - 48 * q^63 - 100 * q^64 - 223 * q^65 - 204 * q^66 - 67 * q^67 - 292 * q^68 - 126 * q^69 - 220 * q^70 - 131 * q^71 - 192 * q^72 - 71 * q^73 - 296 * q^74 - 60 * q^75 - 220 * q^76 - 183 * q^77 - 180 * q^78 - 79 * q^79 - 348 * q^80 - 150 * q^81 - 176 * q^82 - 109 * q^83 - 156 * q^84 - 81 * q^85 - 268 * q^86 - 36 * q^87 - 132 * q^88 - 63 * q^89 - 132 * q^90 - 81 * q^91 - 76 * q^92 - 102 * q^93 - 60 * q^94 - 173 * q^95 - 24 * q^96 - 39 * q^97 - 64 * q^98 - 126 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)

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
432.2.a	\(\chi_{432}(1, \cdot)\)	432.2.a.a	1	1
		432.2.a.b	1
		432.2.a.c	1
		432.2.a.d	1
		432.2.a.e	1
		432.2.a.f	1
		432.2.a.g	1
		432.2.a.h	1
432.2.c	\(\chi_{432}(431, \cdot)\)	432.2.c.a	2	1
		432.2.c.b	2
		432.2.c.c	4
432.2.d	\(\chi_{432}(217, \cdot)\)	None	0	1
432.2.f	\(\chi_{432}(215, \cdot)\)	None	0	1
432.2.i	\(\chi_{432}(145, \cdot)\)	432.2.i.a	2	2
		432.2.i.b	2
		432.2.i.c	2
		432.2.i.d	4
432.2.k	\(\chi_{432}(109, \cdot)\)	432.2.k.a	4	2
		432.2.k.b	4
		432.2.k.c	24
		432.2.k.d	32
432.2.l	\(\chi_{432}(107, \cdot)\)	432.2.l.a	32	2
		432.2.l.b	32
432.2.p	\(\chi_{432}(71, \cdot)\)	None	0	2
432.2.r	\(\chi_{432}(73, \cdot)\)	None	0	2
432.2.s	\(\chi_{432}(143, \cdot)\)	432.2.s.a	2	2
		432.2.s.b	2
		432.2.s.c	2
		432.2.s.d	2
		432.2.s.e	4
432.2.u	\(\chi_{432}(49, \cdot)\)	432.2.u.a	6	6
		432.2.u.b	12
		432.2.u.c	12
		432.2.u.d	18
		432.2.u.e	24
		432.2.u.f	30
432.2.v	\(\chi_{432}(35, \cdot)\)	432.2.v.a	88	4
432.2.y	\(\chi_{432}(37, \cdot)\)	432.2.y.a	4	4
		432.2.y.b	4
		432.2.y.c	4
		432.2.y.d	4
		432.2.y.e	72
432.2.bb	\(\chi_{432}(25, \cdot)\)	None	0	6
432.2.bd	\(\chi_{432}(23, \cdot)\)	None	0	6
432.2.be	\(\chi_{432}(47, \cdot)\)	432.2.be.a	36	6
		432.2.be.b	36
		432.2.be.c	36
432.2.bg	\(\chi_{432}(13, \cdot)\)	432.2.bg.a	840	12
432.2.bj	\(\chi_{432}(11, \cdot)\)	432.2.bj.a	840	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(432))\) into lower level spaces

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