Space of modular forms of level 42 and weight 6

• Label: 42.6
• Level: 42
• Weight: 6
• Dimension: 58
• Nonzero newspaces: 4
• Newform subspaces: 12
• Sturm bound: 576
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(576\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(42))\).

	Total	New	Old
Modular forms	264	58	206
Cusp forms	216	58	158
Eisenstein series	48	0	48

Trace form

58 * q - 8 * q^2 + 32 * q^4 - 144 * q^6 - 640 * q^7 - 128 * q^8 + 570 * q^9 + 2016 * q^10 + 1008 * q^11 - 3348 * q^13 - 704 * q^14 - 5220 * q^15 - 512 * q^16 + 4080 * q^17 + 840 * q^18 - 408 * q^19 + 2112 * q^20 + 6438 * q^21 + 480 * q^22 + 2628 * q^23 - 768 * q^24 - 19886 * q^25 + 7904 * q^26 + 8512 * q^28 + 5868 * q^29 + 11760 * q^30 + 6600 * q^31 - 2048 * q^32 - 37548 * q^33 - 24432 * q^34 - 11952 * q^35 + 12768 * q^36 - 41660 * q^37 - 5200 * q^38 + 39480 * q^39 + 32256 * q^40 + 54972 * q^41 + 63720 * q^42 + 64360 * q^43 + 16128 * q^44 + 5796 * q^45 - 97440 * q^46 - 93588 * q^47 - 13034 * q^49 - 101816 * q^50 - 110232 * q^51 - 15552 * q^52 + 49248 * q^53 - 54576 * q^54 - 53316 * q^55 + 30976 * q^56 + 97428 * q^57 + 82368 * q^58 + 127656 * q^59 + 42624 * q^60 + 195132 * q^61 - 110560 * q^62 + 119040 * q^63 - 90112 * q^64 + 97692 * q^65 + 160992 * q^66 - 14224 * q^67 + 65280 * q^68 - 103464 * q^69 - 64416 * q^70 - 129528 * q^71 - 34176 * q^72 - 509856 * q^73 - 212992 * q^74 - 486936 * q^75 - 97920 * q^76 + 140484 * q^77 + 51792 * q^78 + 687800 * q^79 - 138366 * q^81 + 102864 * q^82 + 390480 * q^83 + 95136 * q^84 + 409752 * q^85 + 111440 * q^86 + 575064 * q^87 + 122112 * q^88 + 27132 * q^89 - 54432 * q^90 - 203952 * q^91 - 196224 * q^92 - 1191096 * q^93 - 386688 * q^94 - 811788 * q^95 - 12288 * q^96 - 344808 * q^97 + 133336 * q^98 - 663624 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(42))\)

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
42.6.a	\(\chi_{42}(1, \cdot)\)	42.6.a.a	1	1
		42.6.a.b	1
		42.6.a.c	1
		42.6.a.d	1
		42.6.a.e	1
		42.6.a.f	1
42.6.d	\(\chi_{42}(41, \cdot)\)	42.6.d.a	12	1
42.6.e	\(\chi_{42}(25, \cdot)\)	42.6.e.a	2	2
		42.6.e.b	2
		42.6.e.c	4
		42.6.e.d	4
42.6.f	\(\chi_{42}(5, \cdot)\)	42.6.f.a	28	2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(42))\) into lower level spaces

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