Space of modular forms of level 432 and weight 7

• Label: 432.7
• Level: 432
• Weight: 7
• Dimension: 13752
• Nonzero newspaces: 12
• Sturm bound: 72576
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(72576\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(432))\).

	Total	New	Old
Modular forms	31524	13896	17628
Cusp forms	30684	13752	16932
Eisenstein series	840	144	696

Trace form

13752 * q - 16 * q^2 - 18 * q^3 - 28 * q^4 - 19 * q^5 - 24 * q^6 - 381 * q^7 - 16 * q^8 - 6 * q^9 - 28 * q^10 - 13 * q^11 - 24 * q^12 - 2555 * q^13 - 272 * q^14 - 18 * q^15 - 1876 * q^16 + 20479 * q^17 - 24 * q^18 - 7029 * q^19 - 47140 * q^20 - 30 * q^21 - 32788 * q^22 - 17 * q^23 - 24 * q^24 + 32080 * q^25 + 112592 * q^26 + 90558 * q^27 + 21176 * q^28 + 51389 * q^29 - 24 * q^30 - 132285 * q^31 - 132316 * q^32 - 132294 * q^33 + 145436 * q^34 - 62507 * q^35 - 24 * q^36 + 253669 * q^37 - 357604 * q^38 + 334494 * q^39 - 143164 * q^40 + 93957 * q^41 - 24 * q^42 - 728421 * q^43 + 568244 * q^44 - 462030 * q^45 + 197764 * q^46 + 125703 * q^47 - 24 * q^48 - 74174 * q^49 - 901596 * q^50 + 2169 * q^51 - 565948 * q^52 + 301088 * q^53 - 24 * q^54 + 19250 * q^55 + 3135964 * q^56 + 1169781 * q^57 + 713540 * q^58 - 2019613 * q^59 - 4750704 * q^60 - 2136683 * q^61 - 5094120 * q^62 - 30018 * q^63 + 1081052 * q^64 + 3983869 * q^65 + 6383676 * q^66 + 1500843 * q^67 + 8957500 * q^68 + 2533410 * q^69 + 2768804 * q^70 + 13 * q^71 - 2564544 * q^72 - 1364359 * q^73 - 11629816 * q^74 - 2071626 * q^75 - 9938908 * q^76 - 7378295 * q^77 - 5858604 * q^78 + 761043 * q^79 - 614716 * q^80 + 2608266 * q^81 + 377456 * q^82 + 1537187 * q^83 + 12106356 * q^84 + 5744027 * q^85 + 14175164 * q^86 + 243342 * q^87 - 3119428 * q^88 - 7549641 * q^89 - 6377316 * q^90 + 2087785 * q^91 + 5036308 * q^92 - 8617422 * q^93 + 1253844 * q^94 - 4570791 * q^95 - 24 * q^96 + 1617873 * q^97 - 5645328 * q^98 + 7045902 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(432))\)

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
432.7.b	\(\chi_{432}(55, \cdot)\)	None	0	1
432.7.e	\(\chi_{432}(161, \cdot)\)	432.7.e.a	1	1
		432.7.e.b	1
		432.7.e.c	2
		432.7.e.d	2
		432.7.e.e	2
		432.7.e.f	2
		432.7.e.g	2
		432.7.e.h	4
		432.7.e.i	4
		432.7.e.j	4
		432.7.e.k	6
		432.7.e.l	6
		432.7.e.m	12
432.7.g	\(\chi_{432}(271, \cdot)\)	432.7.g.a	2	1
		432.7.g.b	2
		432.7.g.c	4
		432.7.g.d	8
		432.7.g.e	8
		432.7.g.f	8
		432.7.g.g	8
		432.7.g.h	8
432.7.h	\(\chi_{432}(377, \cdot)\)	None	0	1
432.7.j	\(\chi_{432}(53, \cdot)\)	n/a	384	2
432.7.m	\(\chi_{432}(163, \cdot)\)	n/a	384	2
432.7.n	\(\chi_{432}(89, \cdot)\)	None	0	2
432.7.o	\(\chi_{432}(127, \cdot)\)	432.7.o.a	24	2
		432.7.o.b	24
		432.7.o.c	24
432.7.q	\(\chi_{432}(17, \cdot)\)	432.7.q.a	10	2
		432.7.q.b	12
		432.7.q.c	12
		432.7.q.d	36
432.7.t	\(\chi_{432}(199, \cdot)\)	None	0	2
432.7.w	\(\chi_{432}(19, \cdot)\)	n/a	568	4
432.7.x	\(\chi_{432}(125, \cdot)\)	n/a	568	4
432.7.z	\(\chi_{432}(7, \cdot)\)	None	0	6
432.7.ba	\(\chi_{432}(31, \cdot)\)	n/a	648	6
432.7.bc	\(\chi_{432}(65, \cdot)\)	n/a	642	6
432.7.bf	\(\chi_{432}(41, \cdot)\)	None	0	6
432.7.bh	\(\chi_{432}(43, \cdot)\)	n/a	5160	12
432.7.bi	\(\chi_{432}(5, \cdot)\)	n/a	5160	12

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(432))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(432)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 15}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 9}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 2}\)