Space of modular forms of level 21 and weight 2

• Label: 21.2
• Level: 21
• Weight: 2
• Dimension: 5
• Nonzero newspaces: 3
• Newform subspaces: 3
• Sturm bound: 64
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(64\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(21))\).

	Total	New	Old
Modular forms	28	17	11
Cusp forms	5	5	0
Eisenstein series	23	12	11

Trace form

5 * q - 3 * q^2 - 3 * q^3 - 5 * q^4 + 3 * q^6 - 5 * q^7 + 3 * q^8 + 3 * q^9 + 6 * q^10 + 6 * q^11 + 3 * q^12 + 3 * q^14 - 6 * q^15 - q^16 - 6 * q^17 - 3 * q^18 - 6 * q^19 - 6 * q^20 - 3 * q^21 - 12 * q^22 + 3 * q^24 + 5 * q^25 + 3 * q^27 + 17 * q^28 + 6 * q^29 + 6 * q^30 + 6 * q^31 + 3 * q^32 + 6 * q^33 + 6 * q^34 - 9 * q^36 + 2 * q^37 - 6 * q^38 - 6 * q^40 - 18 * q^41 - 9 * q^42 - 4 * q^43 + 6 * q^47 - 9 * q^48 - q^49 - 3 * q^50 - 6 * q^51 - 6 * q^52 - 6 * q^53 - 3 * q^54 - 3 * q^56 + 24 * q^57 - 6 * q^58 + 24 * q^59 + 6 * q^60 + 36 * q^62 + 15 * q^63 + 7 * q^64 + 6 * q^65 - 2 * q^67 + 6 * q^68 - 18 * q^70 - 12 * q^71 + 3 * q^72 - 30 * q^73 - 12 * q^74 - 15 * q^75 - 12 * q^77 + 6 * q^78 - 2 * q^79 - 6 * q^80 - 9 * q^81 + 18 * q^82 - 3 * q^84 + 12 * q^85 - 6 * q^86 - 6 * q^87 + 12 * q^88 - 30 * q^89 - 6 * q^90 + 6 * q^91 - 24 * q^93 + 12 * q^94 - 6 * q^95 + 3 * q^96 + 6 * q^97 + 3 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)

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
21.2.a	\(\chi_{21}(1, \cdot)\)	21.2.a.a	1	1
21.2.c	\(\chi_{21}(20, \cdot)\)	None	0	1
21.2.e	\(\chi_{21}(4, \cdot)\)	21.2.e.a	2	2
21.2.g	\(\chi_{21}(5, \cdot)\)	21.2.g.a	2	2