Space of modular forms of level 84 and weight 4

• Label: 84.4
• Level: 84
• Weight: 4
• Dimension: 230
• Nonzero newspaces: 8
• Newform subspaces: 14
• Sturm bound: 1536
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 14 \)
Sturm bound:			\(1536\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(84))\).

	Total	New	Old
Modular forms	636	246	390
Cusp forms	516	230	286
Eisenstein series	120	16	104

Trace form

230 * q + 10 * q^4 + 12 * q^5 + 42 * q^6 - 56 * q^7 - 102 * q^8 - 42 * q^9 - 148 * q^10 + 96 * q^11 - 78 * q^12 + 304 * q^13 + 312 * q^14 + 180 * q^15 + 610 * q^16 - 24 * q^17 + 372 * q^18 - 184 * q^19 - 438 * q^21 - 756 * q^22 - 60 * q^23 - 930 * q^24 + 322 * q^25 - 750 * q^26 - 1062 * q^28 + 1620 * q^29 + 324 * q^30 + 8 * q^31 - 210 * q^32 + 576 * q^33 - 112 * q^34 - 816 * q^35 - 114 * q^36 - 116 * q^37 + 1494 * q^38 - 696 * q^39 + 104 * q^40 + 12 * q^41 - 948 * q^42 - 952 * q^43 + 1848 * q^44 - 1500 * q^45 + 2388 * q^46 - 684 * q^47 + 1014 * q^48 - 3922 * q^49 - 1050 * q^50 - 360 * q^51 - 2872 * q^52 - 1752 * q^53 - 2112 * q^54 - 468 * q^55 - 5022 * q^56 + 1788 * q^57 - 2320 * q^58 + 1128 * q^59 - 72 * q^60 + 6208 * q^61 + 2508 * q^63 + 694 * q^64 + 2832 * q^65 + 732 * q^66 + 3536 * q^67 + 7452 * q^68 + 1572 * q^69 + 9444 * q^70 + 1224 * q^71 + 2970 * q^72 - 2192 * q^73 + 3234 * q^74 - 2592 * q^75 - 2388 * q^76 + 468 * q^77 + 336 * q^78 - 3544 * q^79 - 5976 * q^80 - 3006 * q^81 - 7228 * q^82 - 4272 * q^83 - 1470 * q^84 - 6008 * q^85 - 6342 * q^86 - 4320 * q^87 + 3144 * q^88 + 708 * q^89 + 5148 * q^90 + 1472 * q^91 + 7644 * q^92 - 1452 * q^93 + 14292 * q^94 + 684 * q^95 + 4878 * q^96 + 3256 * q^97 + 11130 * q^98 + 9144 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(84))\)

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
84.4.a	\(\chi_{84}(1, \cdot)\)	84.4.a.a	1	1
		84.4.a.b	1
84.4.b	\(\chi_{84}(55, \cdot)\)	84.4.b.a	12	1
		84.4.b.b	12
84.4.e	\(\chi_{84}(71, \cdot)\)	84.4.e.a	36	1
84.4.f	\(\chi_{84}(41, \cdot)\)	84.4.f.a	8	1
84.4.i	\(\chi_{84}(25, \cdot)\)	84.4.i.a	4	2
		84.4.i.b	4
84.4.k	\(\chi_{84}(5, \cdot)\)	84.4.k.a	2	2
		84.4.k.b	2
		84.4.k.c	12
84.4.n	\(\chi_{84}(11, \cdot)\)	84.4.n.a	88	2
84.4.o	\(\chi_{84}(19, \cdot)\)	84.4.o.a	24	2
		84.4.o.b	24

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(84))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(84)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)