Space of modular forms of level 78 and weight 4

• Label: 78.4
• Level: 78
• Weight: 4
• Dimension: 124
• Nonzero newspaces: 6
• Newform subspaces: 16
• Sturm bound: 1344
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(1344\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(78))\).

	Total	New	Old
Modular forms	552	124	428
Cusp forms	456	124	332
Eisenstein series	96	0	96

Trace form

124 * q + 4 * q^2 + 6 * q^3 - 8 * q^4 - 12 * q^5 - 12 * q^6 - 112 * q^7 - 32 * q^8 - 18 * q^9 + 204 * q^10 + 216 * q^11 + 72 * q^12 + 538 * q^13 + 176 * q^14 + 180 * q^15 - 32 * q^16 - 222 * q^17 - 72 * q^18 - 1408 * q^19 - 312 * q^20 - 216 * q^21 + 48 * q^22 + 120 * q^23 - 48 * q^24 + 928 * q^25 + 76 * q^26 + 882 * q^27 + 128 * q^28 + 330 * q^29 + 744 * q^30 + 56 * q^31 + 64 * q^32 - 960 * q^33 - 504 * q^34 - 1368 * q^35 - 840 * q^36 - 1150 * q^37 + 80 * q^38 - 2130 * q^39 + 96 * q^40 - 438 * q^41 - 744 * q^42 - 568 * q^43 - 96 * q^44 + 186 * q^45 + 672 * q^46 + 936 * q^47 + 96 * q^48 + 534 * q^49 - 1232 * q^50 + 468 * q^51 - 704 * q^52 - 2484 * q^53 - 1764 * q^54 - 144 * q^55 - 448 * q^56 + 684 * q^57 + 1308 * q^58 + 3648 * q^59 + 1200 * q^60 + 2402 * q^61 + 3824 * q^62 + 8364 * q^63 + 256 * q^64 + 5130 * q^65 + 2832 * q^66 + 2288 * q^67 + 1320 * q^68 + 4524 * q^69 + 2064 * q^70 - 528 * q^71 + 336 * q^72 - 2740 * q^73 - 4756 * q^74 - 11754 * q^75 - 5632 * q^76 - 12864 * q^77 - 6060 * q^78 - 10000 * q^79 - 1248 * q^80 - 8274 * q^81 + 444 * q^82 + 3432 * q^83 + 960 * q^84 + 8718 * q^85 + 3152 * q^86 + 6420 * q^87 + 192 * q^88 + 4260 * q^89 + 2376 * q^90 + 9968 * q^91 + 2880 * q^92 + 9540 * q^93 + 8976 * q^94 + 6480 * q^95 - 192 * q^96 + 12404 * q^97 + 1284 * q^98 + 6624 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(78))\)

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
78.4.a	\(\chi_{78}(1, \cdot)\)	78.4.a.a	1	1
		78.4.a.b	1
		78.4.a.c	1
		78.4.a.d	1
		78.4.a.e	1
		78.4.a.f	1
78.4.b	\(\chi_{78}(25, \cdot)\)	78.4.b.a	2	1
		78.4.b.b	4
78.4.e	\(\chi_{78}(55, \cdot)\)	78.4.e.a	2	2
		78.4.e.b	4
		78.4.e.c	4
		78.4.e.d	6
78.4.g	\(\chi_{78}(5, \cdot)\)	78.4.g.a	28	2
78.4.i	\(\chi_{78}(43, \cdot)\)	78.4.i.a	4	2
		78.4.i.b	8
78.4.k	\(\chi_{78}(11, \cdot)\)	78.4.k.a	56	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(78))\) into lower level spaces

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