Space of modular forms of level 20 and weight 8

• Label: 20.8
• Level: 20
• Weight: 8
• Dimension: 45
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 192
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(20))\).

	Total	New	Old
Modular forms	94	53	41
Cusp forms	74	45	29
Eisenstein series	20	8	12

Trace form

45 * q - 2 * q^2 - 26 * q^3 - 35 * q^5 + 104 * q^6 + 954 * q^7 - 1004 * q^8 + 671 * q^9 - 3594 * q^10 - 2880 * q^11 + 10960 * q^12 + 2568 * q^13 + 3802 * q^15 - 44872 * q^16 + 13584 * q^17 + 60306 * q^18 - 55764 * q^19 + 89756 * q^20 - 32900 * q^21 - 191320 * q^22 + 43518 * q^23 + 249217 * q^25 + 252532 * q^26 - 159452 * q^27 - 142800 * q^28 - 446334 * q^29 - 252760 * q^30 - 100148 * q^31 + 188168 * q^32 + 551840 * q^33 + 986998 * q^35 + 231292 * q^36 + 14980 * q^37 - 406560 * q^38 - 2799124 * q^39 - 51924 * q^40 + 341138 * q^41 + 1616840 * q^42 + 2083230 * q^43 + 2566555 * q^45 - 2690616 * q^46 - 1832862 * q^47 + 549280 * q^48 - 4175253 * q^49 + 378586 * q^50 - 2308036 * q^51 - 3208564 * q^52 + 6094284 * q^53 + 5656640 * q^55 + 4064064 * q^56 - 3143464 * q^57 + 1530232 * q^58 - 9110148 * q^59 + 3280240 * q^60 - 4601290 * q^61 + 2750760 * q^62 + 7176506 * q^63 + 12375600 * q^65 - 2175120 * q^66 + 290634 * q^67 - 10060668 * q^68 - 10020092 * q^69 - 11417280 * q^70 - 2011164 * q^71 - 150012 * q^72 - 10208892 * q^73 + 2859638 * q^75 - 4045600 * q^76 + 9365280 * q^77 + 27127080 * q^78 + 11651688 * q^79 + 25379056 * q^80 + 12367749 * q^81 + 831896 * q^82 - 5962722 * q^83 - 27444652 * q^85 - 2245656 * q^86 - 3939564 * q^87 - 38612320 * q^88 + 4610214 * q^89 - 49385514 * q^90 + 8863668 * q^91 - 22809360 * q^92 + 4924984 * q^93 - 20143436 * q^95 + 49033664 * q^96 - 14554460 * q^97 + 58272326 * q^98 + 48327200 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(20))\)

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
20.8.a	\(\chi_{20}(1, \cdot)\)	20.8.a.a	1	1
		20.8.a.b	2
20.8.c	\(\chi_{20}(9, \cdot)\)	20.8.c.a	4	1
20.8.e	\(\chi_{20}(3, \cdot)\)	20.8.e.a	2	2
		20.8.e.b	36

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(20)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)