Space of modular forms of level 279 and weight 6

• Label: 279.6
• Level: 279
• Weight: 6
• Dimension: 11247
• Nonzero newspaces: 20
• Sturm bound: 34560
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(34560\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(279))\).

	Total	New	Old
Modular forms	14640	11507	3133
Cusp forms	14160	11247	2913
Eisenstein series	480	260	220

Trace form

11247 * q - 63 * q^2 - 36 * q^3 + 45 * q^4 - 189 * q^5 - 402 * q^6 - 21 * q^7 + 1791 * q^8 + 768 * q^9 - 183 * q^10 - 2061 * q^11 - 5508 * q^12 - 957 * q^13 - 2349 * q^14 + 4044 * q^15 + 2805 * q^16 + 10431 * q^17 + 16140 * q^18 - 927 * q^19 - 13365 * q^20 - 17400 * q^21 - 19515 * q^22 - 12648 * q^23 - 1158 * q^24 + 31316 * q^25 + 51555 * q^26 + 20244 * q^27 - 33727 * q^28 - 37455 * q^29 - 44268 * q^30 - 31647 * q^31 - 73656 * q^32 + 17580 * q^33 + 3489 * q^34 + 55173 * q^35 + 29118 * q^36 + 110142 * q^37 + 81597 * q^38 - 16500 * q^39 + 39411 * q^40 - 37866 * q^41 - 20256 * q^42 - 50194 * q^43 - 103617 * q^44 - 86136 * q^45 - 102135 * q^46 - 37269 * q^47 + 114750 * q^48 - 46881 * q^49 + 226812 * q^50 + 18732 * q^51 + 312696 * q^52 + 123681 * q^53 - 16422 * q^54 + 176013 * q^55 + 168120 * q^56 + 208536 * q^57 - 158340 * q^58 - 124035 * q^59 - 175716 * q^60 - 510750 * q^61 - 597519 * q^62 - 267168 * q^63 - 234597 * q^64 - 88587 * q^65 + 201936 * q^66 + 103917 * q^67 + 565224 * q^68 + 251904 * q^69 + 747498 * q^70 + 510711 * q^71 - 70962 * q^72 + 1311 * q^73 + 610590 * q^74 + 761034 * q^75 + 1662570 * q^76 + 214302 * q^77 - 608424 * q^78 - 476208 * q^79 - 3603501 * q^80 - 1373304 * q^81 - 1033059 * q^82 - 2187018 * q^83 - 2008128 * q^84 - 584721 * q^85 - 298503 * q^86 + 486132 * q^87 + 2019453 * q^88 + 1975014 * q^89 + 3612684 * q^90 + 1389876 * q^91 + 4295772 * q^92 + 1895082 * q^93 + 827238 * q^94 + 1758267 * q^95 + 1665444 * q^96 + 371124 * q^97 + 237771 * q^98 - 420102 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(279))\)

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
279.6.a	\(\chi_{279}(1, \cdot)\)	279.6.a.a	4	1
		279.6.a.b	5
		279.6.a.c	5
		279.6.a.d	7
		279.6.a.e	8
		279.6.a.f	8
		279.6.a.g	10
		279.6.a.h	16
279.6.c	\(\chi_{279}(278, \cdot)\)	279.6.c.a	12	1
		279.6.c.b	40
279.6.e	\(\chi_{279}(160, \cdot)\)	n/a	316	2
279.6.f	\(\chi_{279}(94, \cdot)\)	n/a	300	2
279.6.g	\(\chi_{279}(25, \cdot)\)	n/a	316	2
279.6.h	\(\chi_{279}(118, \cdot)\)	n/a	132	2
279.6.i	\(\chi_{279}(64, \cdot)\)	n/a	260	4
279.6.j	\(\chi_{279}(26, \cdot)\)	n/a	108	2
279.6.o	\(\chi_{279}(212, \cdot)\)	n/a	316	2
279.6.r	\(\chi_{279}(68, \cdot)\)	n/a	316	2
279.6.s	\(\chi_{279}(92, \cdot)\)	n/a	316	2
279.6.w	\(\chi_{279}(89, \cdot)\)	n/a	208	4
279.6.y	\(\chi_{279}(10, \cdot)\)	n/a	528	8
279.6.z	\(\chi_{279}(4, \cdot)\)	n/a	1264	8
279.6.ba	\(\chi_{279}(76, \cdot)\)	n/a	1264	8
279.6.bb	\(\chi_{279}(7, \cdot)\)	n/a	1264	8
279.6.be	\(\chi_{279}(65, \cdot)\)	n/a	1264	8
279.6.bg	\(\chi_{279}(23, \cdot)\)	n/a	1264	8
279.6.bh	\(\chi_{279}(11, \cdot)\)	n/a	1264	8
279.6.bn	\(\chi_{279}(17, \cdot)\)	n/a	432	8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(279))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(279)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 2}\)