Space of modular forms of level 20 and weight 11

• Label: 20.11
• Level: 20
• Weight: 11
• Dimension: 58
• Nonzero newspaces: 3
• Newform subspaces: 6
• Sturm bound: 264
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 11 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(264\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(20))\).

	Total	New	Old
Modular forms	130	62	68
Cusp forms	110	58	52
Eisenstein series	20	4	16

Trace form

58 * q + 22 * q^2 + 62 * q^3 - 36 * q^4 + 2450 * q^5 - 19264 * q^6 + 22286 * q^7 + 3448 * q^8 + 57520 * q^9 - 7074 * q^10 - 201700 * q^11 + 1329640 * q^12 - 39566 * q^13 - 1811224 * q^14 + 213662 * q^15 + 3722288 * q^16 - 876214 * q^17 - 3556082 * q^18 - 5470604 * q^20 + 11453812 * q^21 - 5811280 * q^22 - 4097986 * q^23 + 6545136 * q^24 + 43879442 * q^25 + 34258020 * q^26 - 4817488 * q^27 - 87415400 * q^28 - 85357072 * q^29 + 96291160 * q^30 + 23221660 * q^31 - 33171328 * q^32 + 117796780 * q^33 - 246528948 * q^34 - 55388242 * q^35 + 192889724 * q^36 - 241432630 * q^37 + 250352720 * q^38 - 467212824 * q^40 + 563589476 * q^41 - 570662040 * q^42 + 156325470 * q^43 + 1105470640 * q^44 - 483476800 * q^45 - 539220184 * q^46 - 450750018 * q^47 - 479727360 * q^48 + 692082000 * q^49 + 902891726 * q^50 + 1632585820 * q^51 - 110465096 * q^52 - 968097958 * q^53 - 96992048 * q^54 - 1301185140 * q^55 - 1804779504 * q^56 + 1408702544 * q^57 + 2075027916 * q^58 - 381215000 * q^60 - 486118204 * q^61 + 1664032240 * q^62 + 3352397678 * q^63 - 1534825536 * q^64 - 2830908830 * q^65 + 443772560 * q^66 - 6990333394 * q^67 + 3042411896 * q^68 - 6817126568 * q^69 - 5500157760 * q^70 + 9915200380 * q^71 + 1632326712 * q^72 + 10876202674 * q^73 + 12387003012 * q^74 - 10170758642 * q^75 + 3151593600 * q^76 - 19414930100 * q^77 - 19914223760 * q^78 + 8290924656 * q^80 + 30810309210 * q^81 - 3197757116 * q^82 + 16998617454 * q^83 - 9560718688 * q^84 - 26311581502 * q^85 + 13497422576 * q^86 - 36065578576 * q^87 + 2774318240 * q^88 + 12755289408 * q^89 - 7828582074 * q^90 + 52347612540 * q^91 - 27349072440 * q^92 + 14416571932 * q^93 + 21948902856 * q^94 - 23431125296 * q^95 + 8230267136 * q^96 - 88930013310 * q^97 + 38416891998 * q^98

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(20))\)

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
20.11.b	\(\chi_{20}(11, \cdot)\)	20.11.b.a	20	1
20.11.d	\(\chi_{20}(19, \cdot)\)	20.11.d.a	1	1
		20.11.d.b	1
		20.11.d.c	2
		20.11.d.d	24
20.11.f	\(\chi_{20}(13, \cdot)\)	20.11.f.a	10	2

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(20)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)