Space of modular forms of level 32 and weight 6

• Label: 32.6
• Level: 32
• Weight: 6
• Dimension: 85
• Nonzero newspaces: 3
• Newform subspaces: 6
• Sturm bound: 384
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 32 = 2^{5} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(384\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(32))\).

	Total	New	Old
Modular forms	176	95	81
Cusp forms	144	85	59
Eisenstein series	32	10	22

Trace form

85 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 34 * q^5 - 4 * q^6 - 100 * q^7 - 4 * q^8 + 281 * q^9 - 204 * q^10 - 4 * q^11 - 1588 * q^12 + 106 * q^13 + 2476 * q^14 + 416 * q^15 + 4176 * q^16 + 1810 * q^17 - 1624 * q^18 - 4 * q^19 - 7604 * q^20 - 5892 * q^21 - 12384 * q^22 - 668 * q^23 + 21456 * q^24 - 2725 * q^25 + 12976 * q^26 - 7468 * q^27 - 2184 * q^28 + 3674 * q^29 - 32316 * q^30 + 35984 * q^31 - 18584 * q^32 + 10824 * q^33 - 6256 * q^34 - 4780 * q^35 + 65584 * q^36 - 7262 * q^37 + 404 * q^38 - 80012 * q^39 - 28952 * q^40 - 35338 * q^41 - 53624 * q^42 + 32068 * q^43 + 3716 * q^44 + 64182 * q^45 + 63324 * q^46 + 54720 * q^47 + 112368 * q^48 + 67617 * q^49 - 4524 * q^50 - 19912 * q^51 + 18468 * q^52 - 125950 * q^53 + 1312 * q^54 + 24572 * q^55 - 80984 * q^56 - 135028 * q^57 - 84576 * q^58 - 28964 * q^59 - 46088 * q^60 + 204666 * q^61 + 63480 * q^62 - 5328 * q^63 - 49192 * q^64 + 93948 * q^65 - 145012 * q^66 - 61164 * q^67 - 151216 * q^68 - 271204 * q^69 - 56296 * q^70 - 62852 * q^71 + 27092 * q^72 - 80346 * q^73 + 213100 * q^74 + 205744 * q^75 + 255996 * q^76 + 180428 * q^77 + 83508 * q^78 + 247872 * q^79 - 97096 * q^80 + 299713 * q^81 + 435196 * q^82 - 329244 * q^83 + 597472 * q^84 - 118628 * q^85 + 269888 * q^86 - 590060 * q^87 - 199840 * q^88 - 259338 * q^89 - 706840 * q^90 + 200108 * q^91 - 650328 * q^92 + 151600 * q^93 - 261592 * q^94 + 837336 * q^95 - 501376 * q^96 + 260058 * q^97 - 395624 * q^98 + 338544 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.6.a	\(\chi_{32}(1, \cdot)\)	32.6.a.a	1	1
		32.6.a.b	1
		32.6.a.c	1
		32.6.a.d	2
32.6.b	\(\chi_{32}(17, \cdot)\)	32.6.b.a	4	1
32.6.e	\(\chi_{32}(9, \cdot)\)	None	0	2
32.6.g	\(\chi_{32}(5, \cdot)\)	32.6.g.a	76	4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(32)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)