Space of modular forms of level 242 and weight 4

• Label: 242.4
• Level: 242
• Weight: 4
• Dimension: 1785
• Nonzero newspaces: 4
• Newform subspaces: 39
• Sturm bound: 14520
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 39 \)
Sturm bound:			\(14520\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(242))\).

	Total	New	Old
Modular forms	5605	1785	3820
Cusp forms	5285	1785	3500
Eisenstein series	320	0	320

Trace form

1785 * q - 100 * q^6 - 40 * q^7 + 320 * q^9 + 200 * q^10 + 100 * q^11 + 160 * q^12 + 80 * q^13 - 40 * q^14 - 820 * q^15 - 620 * q^17 - 460 * q^18 + 450 * q^19 + 840 * q^21 - 780 * q^23 - 400 * q^24 - 600 * q^25 - 400 * q^26 - 150 * q^27 + 240 * q^28 + 500 * q^29 + 1560 * q^30 - 180 * q^31 + 320 * q^32 + 1265 * q^33 + 1200 * q^34 + 2020 * q^35 + 200 * q^36 + 480 * q^37 + 120 * q^38 + 320 * q^39 - 480 * q^40 - 1660 * q^41 - 4360 * q^42 - 5380 * q^43 - 1060 * q^44 - 3820 * q^45 - 720 * q^46 + 500 * q^47 + 2660 * q^49 + 1360 * q^50 + 1390 * q^51 + 1920 * q^52 - 520 * q^53 + 4320 * q^54 + 370 * q^55 + 1890 * q^57 + 3360 * q^58 + 3650 * q^59 + 960 * q^60 - 520 * q^61 - 2760 * q^62 - 3440 * q^63 - 1520 * q^65 - 2920 * q^66 - 1640 * q^67 - 2480 * q^68 - 1680 * q^70 + 6480 * q^71 + 2240 * q^72 + 1740 * q^73 + 2800 * q^74 + 10090 * q^75 + 1520 * q^76 - 630 * q^77 + 5920 * q^78 - 480 * q^79 + 1280 * q^80 - 5010 * q^81 - 3380 * q^82 - 8890 * q^83 - 3680 * q^84 - 4840 * q^85 - 4900 * q^86 - 6800 * q^87 - 560 * q^88 - 700 * q^89 - 5880 * q^90 - 7660 * q^91 + 3360 * q^92 - 12460 * q^93 + 3200 * q^94 + 4400 * q^95 + 6690 * q^97 + 8820 * q^98 + 7790 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(242))\)

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
242.4.a	\(\chi_{242}(1, \cdot)\)	242.4.a.a	1	1
		242.4.a.b	1
		242.4.a.c	1
		242.4.a.d	1
		242.4.a.e	1
		242.4.a.f	1
		242.4.a.g	1
		242.4.a.h	2
		242.4.a.i	2
		242.4.a.j	2
		242.4.a.k	2
		242.4.a.l	2
		242.4.a.m	2
		242.4.a.n	4
		242.4.a.o	4
242.4.c	\(\chi_{242}(3, \cdot)\)	242.4.c.a	4	4
		242.4.c.b	4
		242.4.c.c	4
		242.4.c.d	4
		242.4.c.e	4
		242.4.c.f	4
		242.4.c.g	4
		242.4.c.h	4
		242.4.c.i	4
		242.4.c.j	4
		242.4.c.k	4
		242.4.c.l	4
		242.4.c.m	4
		242.4.c.n	8
		242.4.c.o	8
		242.4.c.p	8
		242.4.c.q	8
		242.4.c.r	8
		242.4.c.s	8
		242.4.c.t	8
242.4.e	\(\chi_{242}(23, \cdot)\)	242.4.e.a	160	10
		242.4.e.b	170
242.4.g	\(\chi_{242}(5, \cdot)\)	242.4.g.a	640	40
		242.4.g.b	680

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(242))\) into lower level spaces

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