Space of modular forms of level 42 and weight 4

• Label: 42.4
• Level: 42
• Weight: 4
• Dimension: 34
• Nonzero newspaces: 4
• Newform subspaces: 7
• Sturm bound: 384
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(384\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(42))\).

	Total	New	Old
Modular forms	168	34	134
Cusp forms	120	34	86
Eisenstein series	48	0	48

Trace form

34 * q + 4 * q^2 - 6 * q^3 - 8 * q^4 + 36 * q^5 + 24 * q^6 + 112 * q^7 + 16 * q^8 - 60 * q^9 - 48 * q^10 - 108 * q^11 - 24 * q^12 - 64 * q^13 - 32 * q^14 + 288 * q^15 - 32 * q^16 + 264 * q^17 - 132 * q^18 - 424 * q^19 - 48 * q^20 - 696 * q^21 + 48 * q^22 - 252 * q^23 - 96 * q^24 - 242 * q^25 - 304 * q^26 + 108 * q^27 - 32 * q^28 + 36 * q^29 + 600 * q^30 + 944 * q^31 + 64 * q^32 + 1386 * q^33 + 312 * q^34 + 972 * q^35 + 744 * q^36 - 1096 * q^37 - 136 * q^38 - 780 * q^39 - 192 * q^40 - 468 * q^41 - 228 * q^42 + 200 * q^43 - 432 * q^44 - 2070 * q^45 + 1008 * q^46 - 168 * q^47 + 192 * q^48 + 4330 * q^49 + 1852 * q^50 + 2394 * q^51 + 416 * q^52 + 864 * q^53 + 72 * q^54 - 1692 * q^55 - 224 * q^56 - 1728 * q^57 - 2400 * q^58 - 1152 * q^59 - 1368 * q^60 - 6604 * q^61 - 3568 * q^62 - 4530 * q^63 - 896 * q^64 - 1128 * q^65 - 2160 * q^66 - 1096 * q^67 + 1056 * q^68 + 2664 * q^69 + 816 * q^70 + 2232 * q^71 + 816 * q^72 + 5468 * q^73 + 512 * q^74 + 4476 * q^75 + 272 * q^76 + 84 * q^77 + 2664 * q^78 + 3056 * q^79 + 576 * q^80 - 36 * q^81 + 2136 * q^82 - 1992 * q^83 + 720 * q^84 - 912 * q^85 + 968 * q^86 + 2592 * q^87 - 480 * q^88 + 1284 * q^89 + 1296 * q^90 + 1784 * q^91 + 768 * q^92 + 1698 * q^93 + 1536 * q^94 + 4296 * q^95 - 384 * q^96 + 3080 * q^97 - 44 * q^98 - 468 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)

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
42.4.a	\(\chi_{42}(1, \cdot)\)	42.4.a.a	1	1
		42.4.a.b	1
42.4.d	\(\chi_{42}(41, \cdot)\)	42.4.d.a	8	1
42.4.e	\(\chi_{42}(25, \cdot)\)	42.4.e.a	2	2
		42.4.e.b	2
		42.4.e.c	4
42.4.f	\(\chi_{42}(5, \cdot)\)	42.4.f.a	16	2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(42))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(42)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)