Space of modular forms of level 20 and weight 3

• Label: 20.3
• Level: 20
• Weight: 3
• Dimension: 10
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 72
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(72\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(20))\).

	Total	New	Old
Modular forms	34	14	20
Cusp forms	14	10	4
Eisenstein series	20	4	16

Trace form

10 * q - 2 * q^2 + 2 * q^3 - 4 * q^4 - 10 * q^5 - 16 * q^6 - 14 * q^7 - 8 * q^8 - 8 * q^9 + 6 * q^10 + 20 * q^11 + 40 * q^12 + 2 * q^13 + 56 * q^14 + 2 * q^15 + 48 * q^16 - 22 * q^17 + 22 * q^18 - 44 * q^20 - 20 * q^21 - 80 * q^22 - 46 * q^23 - 144 * q^24 + 42 * q^25 - 108 * q^26 + 32 * q^27 - 40 * q^28 + 32 * q^29 + 40 * q^30 - 28 * q^31 + 128 * q^32 + 100 * q^33 + 156 * q^34 + 98 * q^35 + 92 * q^36 + 82 * q^37 + 80 * q^38 - 24 * q^40 - 52 * q^41 - 120 * q^42 - 30 * q^43 - 80 * q^44 - 220 * q^45 - 136 * q^46 - 78 * q^47 - 168 * q^49 + 86 * q^50 + 4 * q^51 + 56 * q^52 - 190 * q^53 + 112 * q^54 - 60 * q^55 + 144 * q^56 - 16 * q^57 - 36 * q^58 + 40 * q^60 + 140 * q^61 - 80 * q^62 + 98 * q^63 - 64 * q^64 + 250 * q^65 + 80 * q^66 - 14 * q^67 - 136 * q^68 + 472 * q^69 - 80 * q^70 + 196 * q^71 - 72 * q^72 + 362 * q^73 - 204 * q^74 - 62 * q^75 + 100 * q^77 - 80 * q^78 - 144 * q^80 - 366 * q^81 + 116 * q^82 - 126 * q^83 + 32 * q^84 - 302 * q^85 + 224 * q^86 - 16 * q^87 + 160 * q^88 - 528 * q^89 - 114 * q^90 - 252 * q^91 - 120 * q^92 - 428 * q^93 - 104 * q^94 + 64 * q^95 - 256 * q^96 - 198 * q^97 + 102 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)

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
20.3.b	\(\chi_{20}(11, \cdot)\)	20.3.b.a	4	1
20.3.d	\(\chi_{20}(19, \cdot)\)	20.3.d.a	1	1
		20.3.d.b	1
		20.3.d.c	2
20.3.f	\(\chi_{20}(13, \cdot)\)	20.3.f.a	2	2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(20)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)