Space of modular forms of level 242 and weight 2

• Label: 242.2
• Level: 242
• Weight: 2
• Dimension: 596
• Nonzero newspaces: 4
• Newform subspaces: 17
• Sturm bound: 7260
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 17 \)
Sturm bound:			\(7260\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(242))\).

	Total	New	Old
Modular forms	1975	596	1379
Cusp forms	1656	596	1060
Eisenstein series	319	0	319

Trace form

596 * q + q^2 + 4 * q^3 + q^4 + 6 * q^5 - 6 * q^6 - 12 * q^7 + q^8 - 27 * q^9 - 14 * q^10 - 10 * q^11 - 16 * q^12 - 6 * q^13 - 12 * q^14 - 36 * q^15 + q^16 - 22 * q^17 + 3 * q^18 - 10 * q^19 + 6 * q^20 - 8 * q^21 - 16 * q^23 - 6 * q^24 - 49 * q^25 - 26 * q^26 - 50 * q^27 - 12 * q^28 - 50 * q^29 - 36 * q^30 - 28 * q^31 - 9 * q^32 - 55 * q^33 - 22 * q^34 - 72 * q^35 + 3 * q^36 - 2 * q^37 - 40 * q^38 - 44 * q^39 - 14 * q^40 - 38 * q^41 - 28 * q^42 - 56 * q^43 - 15 * q^44 - 22 * q^45 - 16 * q^46 - 32 * q^47 + 4 * q^48 - 63 * q^49 - 9 * q^50 - 58 * q^51 - 26 * q^52 - 46 * q^53 - 40 * q^54 - 70 * q^55 + 8 * q^56 - 90 * q^57 - 50 * q^58 - 70 * q^59 - 16 * q^60 - 78 * q^61 - 28 * q^62 - 136 * q^63 + q^64 - 116 * q^65 - 60 * q^66 - 112 * q^67 - 22 * q^68 - 124 * q^69 - 32 * q^70 - 88 * q^71 - 27 * q^72 - 46 * q^73 - 2 * q^74 - 106 * q^75 - 80 * q^77 - 24 * q^78 - 20 * q^79 - 14 * q^80 - 149 * q^81 - 28 * q^82 - 46 * q^83 - 48 * q^84 - 112 * q^85 - 86 * q^86 - 80 * q^87 - 10 * q^88 - 70 * q^89 - 102 * q^90 - 88 * q^91 - 36 * q^92 - 132 * q^93 - 72 * q^94 - 100 * q^95 + 4 * q^96 - 92 * q^97 - 33 * q^98 - 130 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)

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
242.2.a	\(\chi_{242}(1, \cdot)\)	242.2.a.a	1	1
		242.2.a.b	1
		242.2.a.c	2
		242.2.a.d	2
		242.2.a.e	2
		242.2.a.f	2
242.2.c	\(\chi_{242}(3, \cdot)\)	242.2.c.a	4	4
		242.2.c.b	4
		242.2.c.c	4
		242.2.c.d	4
		242.2.c.e	4
		242.2.c.f	8
		242.2.c.g	8
242.2.e	\(\chi_{242}(23, \cdot)\)	242.2.e.a	50	10
		242.2.e.b	60
242.2.g	\(\chi_{242}(5, \cdot)\)	242.2.g.a	200	40
		242.2.g.b	240

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(242))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(242)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)