Space of modular forms of level 84 and weight 3

• Label: 84.3
• Level: 84
• Weight: 3
• Dimension: 150
• Nonzero newspaces: 8
• Newform subspaces: 18
• Sturm bound: 1152
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1152\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(84))\).

	Total	New	Old
Modular forms	444	174	270
Cusp forms	324	150	174
Eisenstein series	120	24	96

Trace form

150 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 + 2 * q^5 - 12 * q^6 + 6 * q^7 - 2 * q^8 + 15 * q^9 + 40 * q^10 + 54 * q^11 + 36 * q^12 + 50 * q^13 + 6 * q^15 - 46 * q^16 - 88 * q^17 - 90 * q^18 - 92 * q^19 - 268 * q^20 + 3 * q^21 - 264 * q^22 + 48 * q^23 - 84 * q^24 + 40 * q^25 - 22 * q^26 - 72 * q^27 - 6 * q^28 - 52 * q^29 + 6 * q^30 - 8 * q^31 + 214 * q^32 - 177 * q^33 + 292 * q^34 - 78 * q^35 - 126 * q^36 - 482 * q^37 + 54 * q^38 - 180 * q^39 + 208 * q^40 - 232 * q^41 - 54 * q^42 + 12 * q^43 - 168 * q^44 + 87 * q^45 - 84 * q^46 + 66 * q^47 - 96 * q^48 + 12 * q^49 - 294 * q^50 + 315 * q^51 - 56 * q^52 + 332 * q^53 + 198 * q^54 + 504 * q^55 + 354 * q^56 + 642 * q^57 + 568 * q^58 + 372 * q^59 + 504 * q^60 + 212 * q^61 + 708 * q^62 - 105 * q^63 + 470 * q^64 + 82 * q^65 + 522 * q^66 - 376 * q^67 + 536 * q^68 - 570 * q^69 + 216 * q^70 - 168 * q^71 + 594 * q^72 - 214 * q^73 - 226 * q^74 - 462 * q^75 - 216 * q^76 - 600 * q^77 + 72 * q^78 - 508 * q^79 - 352 * q^80 - 33 * q^81 - 128 * q^82 + 60 * q^84 + 284 * q^85 + 390 * q^86 + 468 * q^87 + 204 * q^88 - 4 * q^89 + 24 * q^90 + 484 * q^91 - 48 * q^92 + 513 * q^93 - 936 * q^94 + 330 * q^95 - 756 * q^96 - 712 * q^97 - 530 * q^98 + 102 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(84))\)

We only show spaces with odd 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
84.3.c	\(\chi_{84}(29, \cdot)\)	84.3.c.a	4	1
84.3.d	\(\chi_{84}(13, \cdot)\)	84.3.d.a	2	1
84.3.g	\(\chi_{84}(43, \cdot)\)	84.3.g.a	12	1
84.3.h	\(\chi_{84}(83, \cdot)\)	84.3.h.a	1	1
		84.3.h.b	1
		84.3.h.c	1
		84.3.h.d	1
		84.3.h.e	24
84.3.j	\(\chi_{84}(47, \cdot)\)	84.3.j.a	56	2
84.3.l	\(\chi_{84}(67, \cdot)\)	84.3.l.a	2	2
		84.3.l.b	2
		84.3.l.c	14
		84.3.l.d	14
84.3.m	\(\chi_{84}(61, \cdot)\)	84.3.m.a	2	2
		84.3.m.b	4
84.3.p	\(\chi_{84}(53, \cdot)\)	84.3.p.a	2	2
		84.3.p.b	4
		84.3.p.c	4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(84))\) into lower level spaces

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