Space of modular forms of level 84 and weight 2

• Label: 84.2
• Level: 84
• Weight: 2
• Dimension: 72
• Nonzero newspaces: 8
• Newform subspaces: 13
• Sturm bound: 768
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 13 \)
Sturm bound:			\(768\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(84))\).

	Total	New	Old
Modular forms	252	88	164
Cusp forms	133	72	61
Eisenstein series	119	16	103

Trace form

72 * q + q^3 - 6 * q^4 + 6 * q^5 - 6 * q^6 + 8 * q^7 - 6 * q^8 - 11 * q^9 - 24 * q^10 - 6 * q^11 - 18 * q^12 - 34 * q^13 - 24 * q^14 - 18 * q^15 - 30 * q^16 - 12 * q^17 - 18 * q^18 - 16 * q^19 - 35 * q^21 + 12 * q^22 - 12 * q^23 + 6 * q^24 - 42 * q^25 + 30 * q^26 - 2 * q^27 + 42 * q^28 - 36 * q^29 + 30 * q^30 - 4 * q^31 + 30 * q^32 + 3 * q^33 + 24 * q^34 + 6 * q^35 + 30 * q^36 - 14 * q^37 + 18 * q^38 + 38 * q^39 + 24 * q^40 + 24 * q^41 + 48 * q^42 + 40 * q^43 + 24 * q^44 + 39 * q^45 + 24 * q^46 + 18 * q^47 + 54 * q^48 + 18 * q^49 + 42 * q^50 + 21 * q^51 + 24 * q^52 + 24 * q^53 + 48 * q^54 + 18 * q^56 - 10 * q^57 - 12 * q^59 + 12 * q^60 - 40 * q^61 - 17 * q^63 - 42 * q^64 - 6 * q^65 - 18 * q^66 - 60 * q^67 - 36 * q^68 - 12 * q^69 - 72 * q^70 - 30 * q^72 - 58 * q^73 - 66 * q^74 + 10 * q^75 - 84 * q^76 - 120 * q^78 - 12 * q^79 - 72 * q^80 + 73 * q^81 - 84 * q^82 - 12 * q^83 - 114 * q^84 - 36 * q^85 - 66 * q^86 + 12 * q^87 - 120 * q^88 + 12 * q^89 - 120 * q^90 + 20 * q^91 - 84 * q^92 + 5 * q^93 - 24 * q^94 - 18 * q^95 - 66 * q^96 + 56 * q^97 - 42 * q^98 - 54 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)

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
84.2.a	\(\chi_{84}(1, \cdot)\)	84.2.a.a	1	1
		84.2.a.b	1
84.2.b	\(\chi_{84}(55, \cdot)\)	84.2.b.a	4	1
		84.2.b.b	4
84.2.e	\(\chi_{84}(71, \cdot)\)	84.2.e.a	12	1
84.2.f	\(\chi_{84}(41, \cdot)\)	84.2.f.a	2	1
84.2.i	\(\chi_{84}(25, \cdot)\)	84.2.i.a	2	2
84.2.k	\(\chi_{84}(5, \cdot)\)	84.2.k.a	2	2
		84.2.k.b	2
		84.2.k.c	2
84.2.n	\(\chi_{84}(11, \cdot)\)	84.2.n.a	24	2
84.2.o	\(\chi_{84}(19, \cdot)\)	84.2.o.a	8	2
		84.2.o.b	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(84))\) into lower level spaces

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