Space of modular forms of level 32 and weight 2

• Label: 32.2
• Level: 32
• Weight: 2
• Dimension: 13
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 128
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 32 = 2^{5} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(128\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(32))\).

	Total	New	Old
Modular forms	48	23	25
Cusp forms	17	13	4
Eisenstein series	31	10	21

Trace form

13 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 6 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 7 * q^9 + 4 * q^10 - 4 * q^11 + 12 * q^12 + 2 * q^13 + 12 * q^14 + 16 * q^16 + 2 * q^17 + 16 * q^18 - 4 * q^19 + 12 * q^20 - 4 * q^21 + 8 * q^22 + 4 * q^23 - 16 * q^24 - 5 * q^25 - 24 * q^26 + 20 * q^27 - 24 * q^28 - 14 * q^29 - 36 * q^30 + 16 * q^31 - 24 * q^32 - 8 * q^33 - 16 * q^34 + 20 * q^35 - 32 * q^36 - 6 * q^37 + 4 * q^38 + 20 * q^39 + 8 * q^40 + 6 * q^41 + 16 * q^42 + 4 * q^43 + 36 * q^44 + 14 * q^45 + 28 * q^46 + 48 * q^48 - 7 * q^49 + 36 * q^50 - 8 * q^51 + 4 * q^52 + 26 * q^53 + 8 * q^54 - 36 * q^55 + 8 * q^56 - 4 * q^57 - 8 * q^58 - 36 * q^59 - 8 * q^60 + 18 * q^61 - 24 * q^62 - 48 * q^63 - 40 * q^64 - 20 * q^65 - 28 * q^66 - 44 * q^67 + 16 * q^68 + 28 * q^69 - 16 * q^70 - 36 * q^71 + 20 * q^72 - 10 * q^73 + 12 * q^74 - 16 * q^75 - 4 * q^76 + 12 * q^77 + 36 * q^78 - 8 * q^80 + 9 * q^81 - 4 * q^82 + 36 * q^83 + 16 * q^84 + 12 * q^85 - 24 * q^86 + 52 * q^87 + 6 * q^89 + 8 * q^90 + 44 * q^91 - 40 * q^92 - 16 * q^93 + 8 * q^94 + 56 * q^95 + 10 * q^97 - 24 * q^98 + 48 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.2.a	\(\chi_{32}(1, \cdot)\)	32.2.a.a	1	1
32.2.b	\(\chi_{32}(17, \cdot)\)	None	0	1
32.2.e	\(\chi_{32}(9, \cdot)\)	None	0	2
32.2.g	\(\chi_{32}(5, \cdot)\)	32.2.g.a	4	4
		32.2.g.b	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

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