Space of modular forms of level 242 and weight 3

• Label: 242.3
• Level: 242
• Weight: 3
• Dimension: 1190
• Nonzero newspaces: 4
• Newform subspaces: 13
• Sturm bound: 10890
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 13 \)
Sturm bound:			\(10890\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(242))\).

	Total	New	Old
Modular forms	3790	1190	2600
Cusp forms	3470	1190	2280
Eisenstein series	320	0	320

Trace form

1190 * q + 40 * q^6 + 60 * q^7 + 40 * q^9 - 10 * q^11 - 40 * q^12 - 60 * q^13 - 80 * q^14 - 80 * q^15 - 60 * q^17 - 80 * q^18 + 60 * q^19 + 140 * q^23 + 80 * q^24 + 120 * q^25 + 240 * q^26 + 120 * q^27 + 80 * q^28 + 20 * q^29 + 120 * q^30 - 160 * q^31 - 80 * q^34 - 140 * q^35 - 40 * q^36 - 200 * q^37 - 360 * q^38 - 260 * q^39 - 160 * q^40 - 500 * q^41 - 160 * q^42 + 40 * q^44 + 240 * q^45 + 320 * q^46 + 340 * q^47 + 380 * q^49 + 160 * q^50 + 60 * q^51 + 80 * q^52 + 540 * q^53 + 40 * q^55 + 260 * q^57 - 320 * q^58 + 120 * q^59 - 240 * q^60 - 100 * q^61 - 40 * q^62 + 40 * q^63 + 160 * q^66 - 580 * q^67 - 120 * q^68 - 220 * q^69 + 40 * q^70 - 80 * q^71 + 160 * q^72 + 140 * q^73 + 80 * q^74 - 540 * q^75 - 410 * q^77 - 160 * q^78 - 740 * q^79 - 80 * q^80 - 580 * q^81 + 240 * q^82 + 300 * q^83 + 240 * q^84 + 660 * q^85 + 240 * q^86 - 120 * q^88 + 340 * q^89 - 320 * q^90 + 300 * q^91 + 360 * q^92 + 200 * q^93 + 40 * q^94 + 660 * q^95 + 520 * q^97 + 420 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(242))\)

We only show spaces with odd 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
242.3.b	\(\chi_{242}(241, \cdot)\)	242.3.b.a	2	1
		242.3.b.b	4
		242.3.b.c	4
		242.3.b.d	8
242.3.d	\(\chi_{242}(161, \cdot)\)	242.3.d.a	8	4
		242.3.d.b	8
		242.3.d.c	8
		242.3.d.d	8
		242.3.d.e	8
		242.3.d.f	16
		242.3.d.g	16
242.3.f	\(\chi_{242}(21, \cdot)\)	242.3.f.a	220	10
242.3.h	\(\chi_{242}(7, \cdot)\)	242.3.h.a	880	40

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(242))\) into lower level spaces

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