Space of modular forms of level 22 and weight 2

• Label: 22.2
• Level: 22
• Weight: 2
• Dimension: 4
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 60
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(22))\).

	Total	New	Old
Modular forms	25	4	21
Cusp forms	6	4	2
Eisenstein series	19	0	19

Trace form

4 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 + q^6 + 2 * q^7 - q^8 + 7 * q^9 + 4 * q^10 - q^11 + 6 * q^12 - 4 * q^13 + 2 * q^14 + 6 * q^15 - q^16 + 2 * q^17 - 8 * q^18 - 5 * q^19 - 6 * q^20 - 12 * q^21 - 11 * q^22 - 4 * q^23 + q^24 + 9 * q^25 + 6 * q^26 + 5 * q^27 + 2 * q^28 + 10 * q^29 + 6 * q^30 - 2 * q^31 + 4 * q^32 + 11 * q^33 + 2 * q^34 + 12 * q^35 - 8 * q^36 - 18 * q^37 + 10 * q^38 - 6 * q^39 + 4 * q^40 - 2 * q^41 - 2 * q^42 + 6 * q^43 + 4 * q^44 - 28 * q^45 - 4 * q^46 - 8 * q^47 - 4 * q^48 + 3 * q^49 - 11 * q^50 - 7 * q^51 + 6 * q^52 - 4 * q^53 + 4 * q^55 - 8 * q^56 + 5 * q^57 + 10 * q^58 + 5 * q^59 - 4 * q^60 + 8 * q^61 - 2 * q^62 + 16 * q^63 - q^64 + 16 * q^65 + 16 * q^66 + 22 * q^67 + 2 * q^68 + 14 * q^69 - 8 * q^70 + 8 * q^71 + 7 * q^72 - 14 * q^73 - 18 * q^74 - 9 * q^75 - 10 * q^76 - 8 * q^77 - 16 * q^78 - 30 * q^79 + 4 * q^80 + 14 * q^81 - 7 * q^82 - 19 * q^83 + 8 * q^84 + 2 * q^85 + 21 * q^86 - 20 * q^87 - q^88 - 10 * q^89 + 12 * q^90 - 12 * q^91 + 6 * q^92 + 2 * q^93 + 12 * q^94 - 10 * q^95 - 4 * q^96 - 3 * q^97 - 12 * q^98 - 13 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)

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
22.2.a	\(\chi_{22}(1, \cdot)\)	None	0	1
22.2.c	\(\chi_{22}(3, \cdot)\)	22.2.c.a	4	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(22)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)