Space of modular forms of level 42 and weight 12

• Label: 42.12
• Level: 42
• Weight: 12
• Dimension: 126
• Nonzero newspaces: 4
• Newform subspaces: 14
• Sturm bound: 1152
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 14 \)
Sturm bound:			\(1152\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(42))\).

	Total	New	Old
Modular forms	552	126	426
Cusp forms	504	126	378
Eisenstein series	48	0	48

Trace form

126 * q + 64 * q^2 - 2048 * q^4 - 25704 * q^5 + 31104 * q^6 - 191600 * q^7 + 65536 * q^8 - 318030 * q^9 - 123648 * q^10 - 1515888 * q^11 + 1201996 * q^13 - 335360 * q^14 - 3967092 * q^15 - 6291456 * q^16 - 2460480 * q^17 + 23977920 * q^18 - 9545720 * q^19 + 4780032 * q^20 + 26593446 * q^21 - 11623680 * q^22 + 3774564 * q^23 - 11403264 * q^24 + 113673438 * q^25 + 129449216 * q^26 + 178999296 * q^28 + 172185444 * q^29 - 949906560 * q^30 - 718340792 * q^31 + 67108864 * q^32 + 1752498216 * q^33 + 579912576 * q^34 - 254443248 * q^35 + 2100627456 * q^36 + 2980087700 * q^37 - 822336640 * q^38 - 549131880 * q^39 - 126615552 * q^40 + 4821581556 * q^41 + 1292644800 * q^42 - 5178130360 * q^43 - 1552269312 * q^44 - 973314720 * q^45 + 1180736256 * q^46 + 4236247164 * q^47 + 5344661994 * q^49 + 7115856832 * q^50 + 10171331496 * q^51 + 1411158016 * q^52 - 5146340256 * q^53 - 10759328640 * q^54 + 16250628348 * q^55 + 7451312128 * q^56 + 31140024276 * q^57 + 24213871104 * q^58 - 27171119160 * q^59 - 2160672768 * q^60 + 14305674964 * q^61 + 13034266880 * q^62 - 48413312040 * q^63 - 53687091200 * q^64 - 20497382868 * q^65 + 58691434752 * q^66 + 64304034672 * q^67 - 2519531520 * q^68 - 12681794808 * q^69 - 60354480384 * q^70 - 26178172344 * q^71 - 16813719552 * q^72 - 216424907528 * q^73 + 22378889216 * q^74 + 128608095096 * q^75 + 4194525184 * q^76 + 18416341308 * q^77 - 37906667904 * q^78 + 332486047512 * q^79 - 26952597504 * q^80 - 115975896678 * q^81 + 87889880448 * q^82 - 477078651120 * q^83 - 17187649536 * q^84 - 250895509512 * q^85 + 19561955456 * q^86 + 156207838248 * q^87 + 6091309056 * q^88 + 150006177636 * q^89 + 34601769216 * q^90 - 139296976784 * q^91 + 67291963392 * q^92 - 370849571388 * q^93 - 343892782080 * q^94 - 492139066524 * q^95 - 11676942336 * q^96 - 165507073496 * q^97 + 54426611008 * q^98 + 1044100415448 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(42))\)

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
42.12.a	\(\chi_{42}(1, \cdot)\)	42.12.a.a	1	1
		42.12.a.b	1
		42.12.a.c	1
		42.12.a.d	1
		42.12.a.e	1
		42.12.a.f	1
		42.12.a.g	2
		42.12.a.h	2
42.12.d	\(\chi_{42}(41, \cdot)\)	42.12.d.a	28	1
42.12.e	\(\chi_{42}(25, \cdot)\)	42.12.e.a	6	2
		42.12.e.b	6
		42.12.e.c	8
		42.12.e.d	8
42.12.f	\(\chi_{42}(5, \cdot)\)	42.12.f.a	60	2

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(42))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(42)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)