Space of modular forms of level 32 and weight 9

• Label: 32.9
• Level: 32
• Weight: 9
• Dimension: 139
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 576
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 32 = 2^{5} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(576\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(32))\).

	Total	New	Old
Modular forms	272	149	123
Cusp forms	240	139	101
Eisenstein series	32	10	22

Trace form

139 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 332 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 2759 * q^9 + 34996 * q^10 - 19778 * q^11 - 45364 * q^12 + 79948 * q^13 + 145580 * q^14 - 8 * q^15 - 278384 * q^16 - 182114 * q^17 - 131224 * q^18 + 167550 * q^19 + 689996 * q^20 - 98052 * q^21 + 6048 * q^22 + 845564 * q^23 - 310832 * q^24 + 673851 * q^25 + 1682096 * q^26 - 63488 * q^27 - 1807624 * q^28 - 1196212 * q^29 - 3968188 * q^30 + 2420456 * q^32 + 1564436 * q^33 + 4139280 * q^34 - 4404868 * q^35 - 2364816 * q^36 + 1262156 * q^37 - 4553644 * q^38 + 7650044 * q^39 - 14971800 * q^40 - 4292646 * q^41 + 17019656 * q^42 + 2595390 * q^43 + 13377860 * q^44 + 6951880 * q^45 + 11790684 * q^46 - 8 * q^47 - 21819984 * q^48 - 15927473 * q^49 - 49149676 * q^50 - 28917372 * q^51 - 33503196 * q^52 - 12186676 * q^53 + 82403296 * q^54 + 46326780 * q^55 + 87708200 * q^56 + 34860184 * q^57 - 37235424 * q^58 - 46004162 * q^59 - 167711176 * q^60 + 47775564 * q^61 + 23721528 * q^62 + 27135128 * q^64 + 16926232 * q^65 + 226680332 * q^66 + 59474558 * q^67 - 491760 * q^68 - 87107076 * q^69 - 167238952 * q^70 - 79832068 * q^71 - 184202092 * q^72 + 1939162 * q^73 + 28015148 * q^74 + 85394490 * q^75 + 201789948 * q^76 + 43691132 * q^77 + 473461108 * q^78 + 144406520 * q^79 - 447998920 * q^80 - 157734165 * q^81 - 231632004 * q^82 - 315240962 * q^83 + 263072 * q^84 - 34200288 * q^85 + 268005440 * q^86 - 149712644 * q^87 + 220344096 * q^88 + 132054618 * q^89 + 51924392 * q^90 + 624372476 * q^91 - 622977496 * q^92 + 118704768 * q^93 - 100742552 * q^94 + 101686144 * q^96 - 291759082 * q^97 + 721239576 * q^98 - 1075195778 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.9.c	\(\chi_{32}(31, \cdot)\)	32.9.c.a	4	1
		32.9.c.b	4
32.9.d	\(\chi_{32}(15, \cdot)\)	32.9.d.a	1	1
		32.9.d.b	6
32.9.f	\(\chi_{32}(7, \cdot)\)	None	0	2
32.9.h	\(\chi_{32}(3, \cdot)\)	32.9.h.a	124	4

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(32)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)