Space of modular forms of level 32 and weight 4

• Label: 32.4
• Level: 32
• Weight: 4
• Dimension: 49
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 256
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 32 = 2^{5} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(256\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(32))\).

	Total	New	Old
Modular forms	112	59	53
Cusp forms	80	49	31
Eisenstein series	32	10	22

Trace form

49 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 2 * q^5 - 4 * q^6 + 12 * q^7 - 4 * q^8 + 41 * q^9 + 116 * q^10 - 4 * q^11 - 52 * q^12 - 122 * q^13 - 212 * q^14 - 112 * q^15 - 304 * q^16 - 182 * q^17 - 184 * q^18 - 4 * q^19 + 76 * q^20 + 252 * q^21 + 192 * q^22 + 628 * q^23 - 48 * q^24 + 331 * q^25 + 16 * q^26 - 268 * q^27 + 376 * q^28 - 202 * q^29 + 1188 * q^30 - 1200 * q^31 + 616 * q^32 - 480 * q^33 + 528 * q^34 - 460 * q^35 + 1456 * q^36 + 830 * q^37 + 980 * q^38 + 1156 * q^39 - 536 * q^40 + 446 * q^41 - 2264 * q^42 + 804 * q^43 - 2044 * q^44 - 1230 * q^45 - 1444 * q^46 - 672 * q^47 - 2448 * q^48 - 1075 * q^49 - 3564 * q^50 - 1384 * q^51 - 2524 * q^52 + 446 * q^53 - 1088 * q^54 + 44 * q^55 + 1192 * q^56 + 1028 * q^57 + 3200 * q^58 + 1372 * q^59 + 5752 * q^60 - 938 * q^61 + 3384 * q^62 + 2496 * q^63 + 4952 * q^64 + 1716 * q^65 + 5996 * q^66 + 2036 * q^67 + 2768 * q^68 - 292 * q^69 + 1400 * q^70 + 364 * q^71 - 1708 * q^72 - 754 * q^73 - 3476 * q^74 - 1712 * q^75 - 5124 * q^76 + 620 * q^77 - 11916 * q^78 + 928 * q^79 - 10312 * q^80 - 1499 * q^81 - 6404 * q^82 + 2436 * q^83 - 6560 * q^84 - 972 * q^85 - 928 * q^86 - 2972 * q^87 + 1248 * q^88 - 1794 * q^89 + 7400 * q^90 - 3604 * q^91 + 10152 * q^92 + 5008 * q^93 + 12840 * q^94 - 5304 * q^95 + 17792 * q^96 + 2354 * q^97 + 11224 * q^98 - 5424 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.4.a	\(\chi_{32}(1, \cdot)\)	32.4.a.a	1	1
		32.4.a.b	1
		32.4.a.c	1
32.4.b	\(\chi_{32}(17, \cdot)\)	32.4.b.a	2	1
32.4.e	\(\chi_{32}(9, \cdot)\)	None	0	2
32.4.g	\(\chi_{32}(5, \cdot)\)	32.4.g.a	44	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

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