Space of modular forms of level 20 and weight 9

• Label: 20.9
• Level: 20
• Weight: 9
• Dimension: 46
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 216
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(216\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(20))\).

	Total	New	Old
Modular forms	106	50	56
Cusp forms	86	46	40
Eisenstein series	20	4	16

Trace form

46 * q + 6 * q^2 - 70 * q^3 - 292 * q^4 + 724 * q^5 + 2720 * q^6 - 2030 * q^7 - 14184 * q^8 + 562 * q^9 + 4590 * q^10 - 420 * q^11 - 64040 * q^12 + 84572 * q^13 + 138824 * q^14 - 48478 * q^15 - 9552 * q^16 + 71172 * q^17 - 616994 * q^18 + 488260 * q^20 + 326068 * q^21 - 389120 * q^22 - 663270 * q^23 - 1287216 * q^24 + 1537386 * q^25 + 596676 * q^26 + 1576040 * q^27 + 1288520 * q^28 + 3466316 * q^29 - 3297080 * q^30 - 3178492 * q^31 - 4379904 * q^32 - 6465620 * q^33 + 8136492 * q^34 + 2571618 * q^35 - 3237892 * q^36 + 14353552 * q^37 - 3087360 * q^38 - 560280 * q^40 - 22531576 * q^41 - 4067400 * q^42 - 10342710 * q^43 + 19588080 * q^44 + 26139524 * q^45 - 654520 * q^46 + 19232250 * q^47 - 2696640 * q^48 - 25225998 * q^49 + 4383630 * q^50 - 47126684 * q^51 + 6679352 * q^52 - 21868608 * q^53 - 13863632 * q^54 + 21483180 * q^55 + 14835440 * q^56 + 100176080 * q^57 + 52156572 * q^58 - 46919720 * q^60 - 113927608 * q^61 + 1290000 * q^62 - 77441350 * q^63 + 6212288 * q^64 + 36903528 * q^65 + 51260720 * q^66 + 100675930 * q^67 + 16095192 * q^68 + 52534648 * q^69 + 1774000 * q^70 - 99290076 * q^71 - 42242664 * q^72 - 31621288 * q^73 - 119096508 * q^74 + 76524178 * q^75 - 52428000 * q^76 - 22797780 * q^77 - 104032400 * q^78 + 127478320 * q^80 + 174217170 * q^81 + 83921012 * q^82 - 10450350 * q^83 + 15568928 * q^84 + 13516156 * q^85 - 87919600 * q^86 + 164801600 * q^87 + 44728480 * q^88 - 1955764 * q^89 - 198194250 * q^90 - 130681068 * q^91 - 13876200 * q^92 + 55380220 * q^93 + 170290504 * q^94 + 84367944 * q^95 - 755889280 * q^96 - 7719528 * q^97 - 285387714 * q^98

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(20))\)

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
20.9.b	\(\chi_{20}(11, \cdot)\)	20.9.b.a	16	1
20.9.d	\(\chi_{20}(19, \cdot)\)	20.9.d.a	1	1
		20.9.d.b	1
		20.9.d.c	20
20.9.f	\(\chi_{20}(13, \cdot)\)	20.9.f.a	8	2

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(20)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)