Space of modular forms of level 432 and weight 9

• Label: 432.9
• Level: 432
• Weight: 9
• Dimension: 18360
• Nonzero newspaces: 12
• Sturm bound: 93312
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(93312\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(432))\).

	Total	New	Old
Modular forms	41892	18504	23388
Cusp forms	41052	18360	22692
Eisenstein series	840	144	696

Trace form

18360 * q - 16 * q^2 - 18 * q^3 - 28 * q^4 - 19 * q^5 - 24 * q^6 - 1525 * q^7 - 16 * q^8 - 6 * q^9 - 28 * q^10 - 13 * q^11 - 24 * q^12 + 25661 * q^13 - 1040 * q^14 - 18 * q^15 + 212268 * q^16 + 82615 * q^17 - 24 * q^18 - 64661 * q^19 + 419228 * q^20 - 30 * q^21 + 909164 * q^22 - 17 * q^23 - 24 * q^24 - 1665384 * q^25 - 2051632 * q^26 + 1955502 * q^27 + 2257976 * q^28 - 3795283 * q^29 - 24 * q^30 + 662539 * q^31 - 5382556 * q^32 + 4957962 * q^33 + 2317980 * q^34 - 1562507 * q^35 - 24 * q^36 - 7541315 * q^37 - 3607396 * q^38 - 7160274 * q^39 + 15547588 * q^40 + 12380253 * q^41 - 24 * q^42 + 25906987 * q^43 - 24703948 * q^44 - 9480030 * q^45 - 11788668 * q^46 - 41428809 * q^47 - 24 * q^48 + 4997058 * q^49 + 46578084 * q^50 + 19665 * q^51 + 10529092 * q^52 + 7237424 * q^53 - 24 * q^54 + 46119250 * q^55 + 56025244 * q^56 + 6246429 * q^57 - 161014972 * q^58 - 117673933 * q^59 - 9502704 * q^60 + 102059517 * q^61 + 451447128 * q^62 + 60918702 * q^63 + 77680988 * q^64 - 31349411 * q^65 - 263573124 * q^66 - 79051541 * q^67 - 681894020 * q^68 - 216989982 * q^69 - 254096476 * q^70 + 13 * q^71 + 242185920 * q^72 + 206705145 * q^73 + 977164424 * q^74 + 150965454 * q^75 + 558027812 * q^76 + 187573609 * q^77 - 84010860 * q^78 - 202977077 * q^79 - 1666574716 * q^80 - 552226614 * q^81 - 429915408 * q^82 - 70192333 * q^83 + 24214452 * q^84 + 229276891 * q^85 + 2182587452 * q^86 + 198705006 * q^87 + 311490748 * q^88 - 256879881 * q^89 - 516560676 * q^90 - 256690711 * q^91 - 546772460 * q^92 - 173355870 * q^93 - 155259948 * q^94 + 472616913 * q^95 - 24 * q^96 - 273516927 * q^97 + 578190384 * q^98 + 190567278 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(432))\)

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
432.9.b	\(\chi_{432}(55, \cdot)\)	None	0	1
432.9.e	\(\chi_{432}(161, \cdot)\)	432.9.e.a	1	1
		432.9.e.b	1
		432.9.e.c	2
		432.9.e.d	2
		432.9.e.e	2
		432.9.e.f	2
		432.9.e.g	2
		432.9.e.h	4
		432.9.e.i	4
		432.9.e.j	6
		432.9.e.k	6
		432.9.e.l	8
		432.9.e.m	8
		432.9.e.n	16
432.9.g	\(\chi_{432}(271, \cdot)\)	432.9.g.a	2	1
		432.9.g.b	2
		432.9.g.c	8
		432.9.g.d	8
		432.9.g.e	10
		432.9.g.f	10
		432.9.g.g	12
		432.9.g.h	12
432.9.h	\(\chi_{432}(377, \cdot)\)	None	0	1
432.9.j	\(\chi_{432}(53, \cdot)\)	n/a	512	2
432.9.m	\(\chi_{432}(163, \cdot)\)	n/a	512	2
432.9.n	\(\chi_{432}(89, \cdot)\)	None	0	2
432.9.o	\(\chi_{432}(127, \cdot)\)	432.9.o.a	32	2
		432.9.o.b	32
		432.9.o.c	32
432.9.q	\(\chi_{432}(17, \cdot)\)	432.9.q.a	14	2
		432.9.q.b	16
		432.9.q.c	16
		432.9.q.d	48
432.9.t	\(\chi_{432}(199, \cdot)\)	None	0	2
432.9.w	\(\chi_{432}(19, \cdot)\)	n/a	760	4
432.9.x	\(\chi_{432}(125, \cdot)\)	n/a	760	4
432.9.z	\(\chi_{432}(7, \cdot)\)	None	0	6
432.9.ba	\(\chi_{432}(31, \cdot)\)	n/a	864	6
432.9.bc	\(\chi_{432}(65, \cdot)\)	n/a	858	6
432.9.bf	\(\chi_{432}(41, \cdot)\)	None	0	6
432.9.bh	\(\chi_{432}(43, \cdot)\)	n/a	6888	12
432.9.bi	\(\chi_{432}(5, \cdot)\)	n/a	6888	12

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

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(432))\) into lower level spaces

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