Space of modular forms of level 121 and weight 2

• Label: 121.2
• Level: 121
• Weight: 2
• Dimension: 524
• Nonzero newspaces: 4
• Newform subspaces: 11
• Sturm bound: 2420
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 121 = 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(2420\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(121))\).

	Total	New	Old
Modular forms	685	665	20
Cusp forms	526	524	2
Eisenstein series	159	141	18

Trace form

524 * q - 48 * q^2 - 49 * q^3 - 52 * q^4 - 51 * q^5 - 47 * q^6 - 43 * q^7 - 40 * q^8 - 38 * q^9 - 33 * q^10 - 45 * q^11 - 73 * q^12 - 49 * q^13 - 39 * q^14 - 29 * q^15 - 16 * q^16 - 33 * q^17 - 24 * q^18 - 35 * q^19 - 17 * q^20 - 27 * q^21 - 20 * q^22 - 79 * q^23 + 5 * q^24 - 16 * q^25 + 3 * q^26 - 25 * q^27 + 9 * q^28 - 25 * q^29 + 13 * q^30 - 37 * q^31 - 8 * q^32 - 10 * q^33 - 59 * q^34 - 3 * q^35 + 44 * q^36 - 23 * q^37 + 5 * q^38 + 9 * q^39 + 35 * q^40 + 3 * q^41 + 49 * q^42 + q^43 + 20 * q^44 - 23 * q^45 + 13 * q^46 - 23 * q^47 + 61 * q^48 + 8 * q^49 + 22 * q^50 + 13 * q^51 + 27 * q^52 + 11 * q^53 + 85 * q^54 + 10 * q^55 + 15 * q^56 + 25 * q^57 + 35 * q^58 - 5 * q^59 + 117 * q^60 - 17 * q^61 + 69 * q^62 + 41 * q^63 + 88 * q^64 + 21 * q^65 + 75 * q^66 - 23 * q^67 + 79 * q^68 + 39 * q^69 + 81 * q^70 + 23 * q^71 + 140 * q^72 + 11 * q^73 + 71 * q^74 + 61 * q^75 + 85 * q^76 + 35 * q^77 + 47 * q^78 + 45 * q^79 + 139 * q^80 + 64 * q^81 + 39 * q^82 + 41 * q^83 + 161 * q^84 + 57 * q^85 + 53 * q^86 + 65 * q^87 + 110 * q^88 - 45 * q^89 + 171 * q^90 + 73 * q^91 + 117 * q^92 + 87 * q^93 + 121 * q^94 + 65 * q^95 + 213 * q^96 + 57 * q^97 + 104 * q^98 + 90 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)

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
121.2.a	\(\chi_{121}(1, \cdot)\)	121.2.a.a	1	1
		121.2.a.b	1
		121.2.a.c	1
		121.2.a.d	1
121.2.c	\(\chi_{121}(3, \cdot)\)	121.2.c.a	4	4
		121.2.c.b	4
		121.2.c.c	4
		121.2.c.d	4
		121.2.c.e	4
121.2.e	\(\chi_{121}(12, \cdot)\)	121.2.e.a	100	10
121.2.g	\(\chi_{121}(4, \cdot)\)	121.2.g.a	400	40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(121))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(121)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)