Space of modular forms of level 20 and weight 4

• Label: 20.4
• Level: 20
• Weight: 4
• Dimension: 17
• Nonzero newspaces: 3
• Newform subspaces: 4
• Sturm bound: 96
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(20))\).

	Total	New	Old
Modular forms	46	25	21
Cusp forms	26	17	9
Eisenstein series	20	8	12

Trace form

17 * q - 2 * q^2 + 4 * q^3 + 15 * q^5 + 8 * q^6 - 16 * q^7 - 44 * q^8 - 109 * q^9 - 74 * q^10 - 20 * q^11 - 80 * q^12 + 128 * q^13 + 172 * q^15 + 184 * q^16 - 116 * q^17 + 306 * q^18 - 124 * q^19 + 316 * q^20 - 56 * q^21 + 360 * q^22 + 48 * q^23 + 77 * q^25 - 460 * q^26 - 152 * q^27 - 880 * q^28 - 174 * q^29 - 1240 * q^30 - 272 * q^31 - 632 * q^32 - 160 * q^33 - 232 * q^35 + 892 * q^36 + 580 * q^37 + 1600 * q^38 + 1256 * q^39 + 1836 * q^40 + 1006 * q^41 + 1160 * q^42 - 100 * q^43 - 155 * q^45 - 1432 * q^46 + 168 * q^47 - 2720 * q^48 + 447 * q^49 - 2214 * q^50 - 1144 * q^51 - 1524 * q^52 - 1196 * q^53 - 20 * q^55 + 2048 * q^56 - 784 * q^57 + 2712 * q^58 - 308 * q^59 + 3280 * q^60 - 1526 * q^61 + 2440 * q^62 + 176 * q^63 - 2260 * q^65 - 1680 * q^66 - 1036 * q^67 - 2428 * q^68 - 872 * q^69 - 3040 * q^70 + 984 * q^71 - 2172 * q^72 + 2448 * q^73 + 2228 * q^75 + 800 * q^76 + 4080 * q^77 + 3720 * q^78 + 368 * q^79 + 2096 * q^80 + 4917 * q^81 + 536 * q^82 + 948 * q^83 + 3588 * q^85 - 2552 * q^86 - 744 * q^87 - 2400 * q^88 - 4066 * q^89 - 2154 * q^90 - 2288 * q^91 - 1840 * q^92 - 2576 * q^93 - 956 * q^95 + 1088 * q^96 - 6760 * q^97 + 326 * q^98 - 1300 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)

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
20.4.a	\(\chi_{20}(1, \cdot)\)	20.4.a.a	1	1
20.4.c	\(\chi_{20}(9, \cdot)\)	20.4.c.a	2	1
20.4.e	\(\chi_{20}(3, \cdot)\)	20.4.e.a	2	2
		20.4.e.b	12

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces

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