Space of modular forms of level 32 and weight 12

• Label: 32.12
• Level: 32
• Weight: 12
• Dimension: 193
• Nonzero newspaces: 3
• Newform subspaces: 7
• Sturm bound: 768
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 32 = 2^{5} \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(768\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(32))\).

	Total	New	Old
Modular forms	368	203	165
Cusp forms	336	193	143
Eisenstein series	32	10	22

Trace form

193 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 2638 * q^5 - 4 * q^6 + 33612 * q^7 - 4 * q^8 - 30103 * q^9 + 1074996 * q^10 - 4 * q^11 - 937012 * q^12 + 2841686 * q^13 - 836180 * q^14 - 3391792 * q^15 - 4037424 * q^16 + 3146602 * q^17 + 27162536 * q^18 - 4 * q^19 - 59950004 * q^20 - 25262340 * q^21 + 122555936 * q^22 + 58837300 * q^23 - 334731312 * q^24 - 33236469 * q^25 + 217620016 * q^26 + 133635188 * q^27 - 358859144 * q^28 + 288459782 * q^29 + 522810948 * q^30 - 1129135024 * q^31 + 378885736 * q^32 + 652026048 * q^33 - 903806832 * q^34 + 1064775860 * q^35 - 1742651216 * q^36 + 191689870 * q^37 + 4762268180 * q^38 - 148500668 * q^39 - 6076605976 * q^40 - 742509154 * q^41 + 2725941256 * q^42 - 2884696668 * q^43 + 3351027716 * q^44 - 1064396670 * q^45 - 4548769956 * q^46 + 560226528 * q^47 - 9307187088 * q^48 + 2137610269 * q^49 + 20902534356 * q^50 - 223733992 * q^51 - 4545755100 * q^52 + 4586350478 * q^53 - 5073222368 * q^54 + 13490021484 * q^55 - 8499230552 * q^56 + 8123399972 * q^57 + 4427412000 * q^58 - 22992780452 * q^59 - 18895397768 * q^60 - 19024119002 * q^61 + 7502301048 * q^62 + 54181086336 * q^63 + 14171170136 * q^64 - 13381292844 * q^65 + 19818223628 * q^66 - 50706890124 * q^67 - 25843435312 * q^68 + 7142122460 * q^69 - 68590230760 * q^70 + 55447362220 * q^71 + 85943700308 * q^72 + 19332464494 * q^73 + 119430394348 * q^74 - 56217569072 * q^75 - 93226214404 * q^76 + 22168238060 * q^77 - 171984085068 * q^78 - 57291670496 * q^79 - 75713213512 * q^80 + 77597796757 * q^81 - 135013459204 * q^82 + 11370505476 * q^83 + 533304923488 * q^84 + 29451624788 * q^85 + 283641279680 * q^86 + 23716294180 * q^87 - 298570656032 * q^88 - 50163950370 * q^89 - 807228839320 * q^90 + 209413389548 * q^91 + 218404393128 * q^92 + 107197578256 * q^93 + 353726807208 * q^94 - 565366635384 * q^95 + 692713936256 * q^96 - 43416697134 * q^97 - 52777082216 * q^98 + 378702509904 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.12.a	\(\chi_{32}(1, \cdot)\)	32.12.a.a	1	1
		32.12.a.b	2
		32.12.a.c	2
		32.12.a.d	3
		32.12.a.e	3
32.12.b	\(\chi_{32}(17, \cdot)\)	32.12.b.a	10	1
32.12.e	\(\chi_{32}(9, \cdot)\)	None	0	2
32.12.g	\(\chi_{32}(5, \cdot)\)	32.12.g.a	172	4

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(32)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)