Space of modular forms of level 32 and weight 7

• Label: 32.7
• Level: 32
• Weight: 7
• Dimension: 103
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 448
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 32 = 2^{5} \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(448\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(32))\).

	Total	New	Old
Modular forms	208	113	95
Cusp forms	176	103	73
Eisenstein series	32	10	22

Trace form

103 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 40 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 1655 * q^9 + 2996 * q^10 + 1358 * q^11 - 3892 * q^12 - 4216 * q^13 - 8532 * q^14 - 8 * q^15 + 14096 * q^16 + 2934 * q^17 + 24296 * q^18 + 3934 * q^19 - 14004 * q^20 - 3396 * q^21 - 19552 * q^22 + 13116 * q^23 - 43568 * q^24 + 2059 * q^25 + 5296 * q^26 - 101504 * q^27 + 85496 * q^28 + 35592 * q^29 + 102980 * q^30 - 58904 * q^32 + 30860 * q^33 - 139248 * q^34 + 212252 * q^35 - 328464 * q^36 + 126056 * q^37 + 457684 * q^38 - 254404 * q^39 + 430952 * q^40 - 166494 * q^41 - 256504 * q^42 + 22894 * q^43 - 808764 * q^44 - 468188 * q^45 - 197284 * q^46 - 8 * q^47 + 349488 * q^48 + 382907 * q^49 + 1254548 * q^50 + 307620 * q^51 - 71644 * q^52 + 718152 * q^53 - 455840 * q^54 - 232708 * q^55 - 619736 * q^56 - 578576 * q^57 - 290272 * q^58 + 39150 * q^59 + 803000 * q^60 - 956536 * q^61 + 1415352 * q^62 - 1533928 * q^64 + 632016 * q^65 - 308980 * q^66 - 122786 * q^67 + 447632 * q^68 + 2458236 * q^69 - 676264 * q^70 - 267012 * q^71 - 1219564 * q^72 - 1322910 * q^73 - 661588 * q^74 - 400278 * q^75 + 873980 * q^76 - 2736932 * q^77 + 1480180 * q^78 - 1721864 * q^79 - 2377928 * q^80 + 3064239 * q^81 - 1407364 * q^82 + 5860478 * q^83 + 2103584 * q^84 + 3768888 * q^85 + 2146368 * q^86 - 2029892 * q^87 + 2855072 * q^88 - 3642238 * q^89 + 2497832 * q^90 - 7099204 * q^91 - 540888 * q^92 - 5896608 * q^93 - 2438936 * q^94 + 3127168 * q^96 + 4854926 * q^97 + 2073880 * q^98 + 11669854 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.7.c	\(\chi_{32}(31, \cdot)\)	32.7.c.a	2	1
		32.7.c.b	4
32.7.d	\(\chi_{32}(15, \cdot)\)	32.7.d.a	1	1
		32.7.d.b	4
32.7.f	\(\chi_{32}(7, \cdot)\)	None	0	2
32.7.h	\(\chi_{32}(3, \cdot)\)	32.7.h.a	92	4

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(32)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)