Space of modular forms of level 20 and weight 5

• Label: 20.5
• Level: 20
• Weight: 5
• Dimension: 22
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 120
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(20))\).

	Total	New	Old
Modular forms	58	26	32
Cusp forms	38	22	16
Eisenstein series	20	4	16

Trace form

22 * q + 6 * q^2 - 10 * q^3 - 36 * q^4 + 4 * q^5 + 32 * q^6 + 110 * q^7 + 216 * q^8 - 170 * q^9 - 210 * q^10 - 300 * q^11 - 200 * q^12 - 8 * q^13 - 184 * q^14 + 542 * q^15 - 592 * q^16 + 912 * q^17 + 286 * q^18 + 100 * q^20 - 2612 * q^21 + 800 * q^22 - 810 * q^23 + 3216 * q^24 + 2066 * q^25 + 324 * q^26 + 2120 * q^27 + 40 * q^28 + 1508 * q^29 - 920 * q^30 - 836 * q^31 - 2304 * q^32 - 2780 * q^33 - 4308 * q^34 - 2562 * q^35 - 9220 * q^36 - 6388 * q^37 - 3360 * q^38 + 4200 * q^40 + 10280 * q^41 + 12120 * q^42 + 3270 * q^43 + 9840 * q^44 + 3344 * q^45 + 14792 * q^46 - 2250 * q^47 + 8640 * q^48 - 5130 * q^49 - 11730 * q^50 + 1948 * q^51 - 12488 * q^52 + 4572 * q^53 - 26768 * q^54 - 6780 * q^55 - 25168 * q^56 - 10000 * q^57 - 7428 * q^58 + 11320 * q^60 + 22184 * q^61 + 25680 * q^62 + 12950 * q^63 + 33984 * q^64 - 3852 * q^65 + 38000 * q^66 - 4810 * q^67 + 2712 * q^68 - 18248 * q^69 - 10800 * q^70 - 5988 * q^71 - 36264 * q^72 - 28508 * q^73 - 42108 * q^74 - 11282 * q^75 - 36000 * q^76 + 1380 * q^77 - 14480 * q^78 + 19120 * q^80 - 1062 * q^81 + 27412 * q^82 + 19950 * q^83 + 80672 * q^84 + 36536 * q^85 + 46352 * q^86 + 24800 * q^87 + 18080 * q^88 + 60068 * q^89 - 29130 * q^90 - 11124 * q^91 - 52680 * q^92 - 22700 * q^93 - 67704 * q^94 - 15576 * q^95 - 78208 * q^96 - 7548 * q^97 - 21474 * q^98

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(20))\)

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
20.5.b	\(\chi_{20}(11, \cdot)\)	20.5.b.a	8	1
20.5.d	\(\chi_{20}(19, \cdot)\)	20.5.d.a	1	1
		20.5.d.b	1
		20.5.d.c	8
20.5.f	\(\chi_{20}(13, \cdot)\)	20.5.f.a	4	2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

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