Space of modular forms of level 32 and weight 16

• Label: 32.16
• Level: 32
• Weight: 16
• Dimension: 265
• Nonzero newspaces: 3
• Sturm bound: 1024
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 32 = 2^{5} \)
Weight:	\( k \)	=	\( 16 \)
Nonzero newspaces:			\( 3 \)
Sturm bound:			\(1024\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(32))\).

	Total	New	Old
Modular forms	496	275	221
Cusp forms	464	265	199
Eisenstein series	32	10	22

Trace form

265 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 136758 * q^5 - 4 * q^6 + 1647084 * q^7 - 4 * q^8 + 21973001 * q^9 - 58125004 * q^10 - 4 * q^11 - 576983092 * q^12 + 120424702 * q^13 + 724400556 * q^14 - 712135312 * q^15 + 1646188496 * q^16 + 5166732410 * q^17 - 8513684824 * q^18 - 4 * q^19 + 21351249996 * q^20 - 9134904324 * q^21 - 27559175136 * q^22 + 65788542868 * q^23 + 88692916176 * q^24 + 10777898731 * q^25 + 30752852016 * q^26 - 254883575500 * q^27 - 109888046984 * q^28 - 90077046866 * q^29 + 174163970628 * q^30 - 554544599856 * q^31 + 166159286376 * q^32 - 193492788720 * q^33 - 787181016432 * q^34 - 729080762380 * q^35 + 3129580501936 * q^36 - 317507747338 * q^37 - 7083478923500 * q^38 + 4559000030116 * q^39 + 8684597398504 * q^40 - 3723462625650 * q^41 - 17038673277944 * q^42 - 288421539612 * q^43 + 13030399553796 * q^44 + 13406997565290 * q^45 - 6258058711204 * q^46 - 12527998446432 * q^47 - 14332262782608 * q^48 + 33475384564037 * q^49 + 46526667368916 * q^50 - 19478774607016 * q^51 + 14666588948516 * q^52 - 37120075918282 * q^53 - 75091122605024 * q^54 - 6320940354676 * q^55 + 112477170718376 * q^56 + 3249221268404 * q^57 - 66198330597856 * q^58 - 56894451017124 * q^59 - 30476024277128 * q^60 + 70879674395086 * q^61 - 89374826236296 * q^62 + 121416863452896 * q^63 + 1544484974168 * q^64 + 103621877137636 * q^65 - 314748144713716 * q^66 - 211689401031244 * q^67 - 4588648698416 * q^68 - 87485505595300 * q^69 + 644126855169560 * q^70 + 312427002131532 * q^71 - 873355802788780 * q^72 - 182588445016930 * q^73 - 86990457176340 * q^74 + 276446486716048 * q^75 + 1108325964927996 * q^76 - 76183609245012 * q^77 - 940978451436876 * q^78 + 294370273271392 * q^79 - 620821063170632 * q^80 + 94125160143949 * q^81 + 2023664503174396 * q^82 + 302821103836356 * q^83 - 757049450837408 * q^84 + 261780347994468 * q^85 - 546938702869824 * q^86 - 3677894670110204 * q^87 + 802678086579168 * q^88 + 1416417267964110 * q^89 + 1152030600819560 * q^90 + 2535925148261996 * q^91 - 2087656433709400 * q^92 - 3206066380102064 * q^93 + 3102735042217896 * q^94 - 3618057647320024 * q^95 + 4441188475723136 * q^96 - 1666933524528478 * q^97 - 6453159723911016 * q^98 + 6055458652625808 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.16.a	\(\chi_{32}(1, \cdot)\)	32.16.a.a	1	1
		32.16.a.b	2
		32.16.a.c	4
		32.16.a.d	4
		32.16.a.e	4
32.16.b	\(\chi_{32}(17, \cdot)\)	32.16.b.a	14	1
32.16.e	\(\chi_{32}(9, \cdot)\)	None	0	2
32.16.g	\(\chi_{32}(5, \cdot)\)	n/a	236	4

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

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

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