Space of modular forms of level 78 and weight 3

• Label: 78.3
• Level: 78
• Weight: 3
• Dimension: 84
• Nonzero newspaces: 6
• Newform subspaces: 11
• Sturm bound: 1008
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(1008\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(78))\).

	Total	New	Old
Modular forms	384	84	300
Cusp forms	288	84	204
Eisenstein series	96	0	96

Trace form

84 * q + 40 * q^7 + 24 * q^8 + 12 * q^9 + 60 * q^10 + 24 * q^11 - 48 * q^13 - 48 * q^14 - 72 * q^15 - 32 * q^16 - 72 * q^17 - 36 * q^18 - 80 * q^19 - 48 * q^20 + 60 * q^21 + 48 * q^23 - 72 * q^27 - 120 * q^29 - 192 * q^30 - 144 * q^31 - 372 * q^33 - 240 * q^35 - 48 * q^36 - 72 * q^37 + 96 * q^39 + 60 * q^41 + 144 * q^42 + 256 * q^43 + 456 * q^45 + 96 * q^47 + 16 * q^49 + 84 * q^50 + 624 * q^51 + 72 * q^52 + 480 * q^53 + 360 * q^54 + 456 * q^55 + 192 * q^56 + 396 * q^57 + 324 * q^58 + 168 * q^59 + 96 * q^60 - 156 * q^61 + 144 * q^62 - 300 * q^63 - 180 * q^65 - 96 * q^66 - 416 * q^67 - 24 * q^68 - 708 * q^69 - 432 * q^70 - 336 * q^71 - 192 * q^72 - 512 * q^73 - 156 * q^74 - 360 * q^75 + 160 * q^76 - 216 * q^78 + 336 * q^79 - 96 * q^80 - 180 * q^81 + 660 * q^82 + 504 * q^83 + 168 * q^84 + 828 * q^85 + 192 * q^86 + 696 * q^87 + 432 * q^89 - 104 * q^91 - 96 * q^92 + 660 * q^93 - 480 * q^94 - 480 * q^95 - 1320 * q^97 - 384 * q^98 - 612 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(78))\)

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
78.3.c	\(\chi_{78}(53, \cdot)\)	78.3.c.a	8	1
78.3.d	\(\chi_{78}(77, \cdot)\)	78.3.d.a	4	1
		78.3.d.b	4
78.3.f	\(\chi_{78}(31, \cdot)\)	78.3.f.a	4	2
		78.3.f.b	8
78.3.h	\(\chi_{78}(29, \cdot)\)	78.3.h.a	8	2
		78.3.h.b	12
78.3.j	\(\chi_{78}(17, \cdot)\)	78.3.j.a	20	2
78.3.l	\(\chi_{78}(7, \cdot)\)	78.3.l.a	4	4
		78.3.l.b	4
		78.3.l.c	8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(78))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(78)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)