Space of modular forms of level 20 and weight 2

• Label: 20.2
• Level: 20
• Weight: 2
• Dimension: 3
• Nonzero newspaces: 2
• Newform subspaces: 2
• Sturm bound: 48
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(20))\).

	Total	New	Old
Modular forms	22	11	11
Cusp forms	3	3	0
Eisenstein series	19	8	11

Trace form

3 * q - 2 * q^2 - 2 * q^3 - 5 * q^5 + 2 * q^7 + 4 * q^8 + q^9 + 6 * q^10 + 2 * q^15 - 8 * q^16 - 6 * q^18 - 4 * q^19 - 4 * q^20 - 4 * q^21 + 6 * q^23 + 7 * q^25 + 4 * q^26 + 4 * q^27 + 6 * q^29 - 4 * q^31 + 8 * q^32 - 2 * q^35 + 12 * q^36 - 12 * q^37 - 4 * q^39 - 4 * q^40 - 10 * q^41 - 10 * q^43 + 5 * q^45 - 6 * q^47 - 3 * q^49 - 14 * q^50 + 12 * q^51 - 4 * q^52 + 12 * q^53 + 8 * q^57 + 8 * q^58 + 12 * q^59 + 26 * q^61 + 2 * q^63 + 2 * q^67 - 12 * q^68 - 12 * q^69 - 12 * q^71 - 12 * q^72 - 20 * q^73 - 2 * q^75 + 8 * q^79 + 16 * q^80 - 29 * q^81 + 16 * q^82 + 6 * q^83 - 12 * q^85 - 12 * q^87 - 6 * q^89 + 6 * q^90 + 4 * q^91 + 8 * q^93 + 4 * q^95 + 28 * q^97 + 14 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)

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
20.2.a	\(\chi_{20}(1, \cdot)\)	20.2.a.a	1	1
20.2.c	\(\chi_{20}(9, \cdot)\)	None	0	1
20.2.e	\(\chi_{20}(3, \cdot)\)	20.2.e.a	2	2