Space of modular forms of level 845 and weight 6

• Label: 845.6
• Level: 845
• Weight: 6
• Dimension: 127981
• Nonzero newspaces: 24
• Sturm bound: 340704
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(340704\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(845))\).

	Total	New	Old
Modular forms	142872	129207	13665
Cusp forms	141048	127981	13067
Eisenstein series	1824	1226	598

Trace form

127981 * q - 130 * q^2 - 136 * q^3 - 184 * q^4 - 263 * q^5 - 140 * q^6 - 1132 * q^7 + 2052 * q^8 + 1927 * q^9 - 468 * q^10 - 2176 * q^11 - 11564 * q^12 - 3288 * q^13 - 1188 * q^14 + 3398 * q^15 + 18212 * q^16 - 6598 * q^17 + 13166 * q^18 + 20440 * q^19 + 11174 * q^20 + 11124 * q^21 + 3052 * q^22 - 10068 * q^23 - 92100 * q^24 + 2265 * q^25 - 36372 * q^26 - 58996 * q^27 - 95644 * q^28 - 16742 * q^29 + 93994 * q^30 + 129948 * q^31 + 322084 * q^32 + 165748 * q^33 + 79104 * q^34 - 30498 * q^35 - 371728 * q^36 - 143906 * q^37 - 205972 * q^38 - 154128 * q^39 - 203842 * q^40 - 21074 * q^41 + 262788 * q^42 + 336488 * q^43 + 545524 * q^44 + 277747 * q^45 + 394940 * q^46 + 158588 * q^47 + 114556 * q^48 - 233773 * q^49 - 84880 * q^50 - 520556 * q^51 - 403148 * q^52 - 377494 * q^53 - 778700 * q^54 - 496246 * q^55 - 444228 * q^56 - 48316 * q^57 + 349928 * q^58 + 267656 * q^59 + 901174 * q^60 + 948170 * q^61 + 17628 * q^62 + 400164 * q^63 + 640308 * q^64 + 309459 * q^65 + 943580 * q^66 + 270344 * q^67 + 2003500 * q^68 + 752604 * q^69 + 72054 * q^70 + 185452 * q^71 - 1595796 * q^72 - 1064058 * q^73 - 2787752 * q^74 - 1990954 * q^75 - 2203916 * q^76 - 1166940 * q^77 - 1102332 * q^78 + 478852 * q^79 + 1196486 * q^80 + 968791 * q^81 + 1022672 * q^82 + 413136 * q^83 + 965796 * q^84 - 155142 * q^85 + 259868 * q^86 - 17500 * q^87 + 963588 * q^88 + 1619562 * q^89 + 1882088 * q^90 + 898348 * q^91 + 704772 * q^92 + 1629588 * q^93 - 1117932 * q^94 - 500546 * q^95 - 2496772 * q^96 - 909218 * q^97 - 2349218 * q^98 - 1511896 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(845))\)

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
845.6.a	\(\chi_{845}(1, \cdot)\)	845.6.a.a	1	1
		845.6.a.b	1
		845.6.a.c	3
		845.6.a.d	4
		845.6.a.e	4
		845.6.a.f	4
		845.6.a.g	6
		845.6.a.h	6
		845.6.a.i	7
		845.6.a.j	7
		845.6.a.k	12
		845.6.a.l	12
		845.6.a.m	12
		845.6.a.n	12
		845.6.a.o	24
		845.6.a.p	24
		845.6.a.q	27
		845.6.a.r	27
		845.6.a.s	33
		845.6.a.t	33
845.6.b	\(\chi_{845}(339, \cdot)\)	n/a	376	1
845.6.c	\(\chi_{845}(506, \cdot)\)	n/a	258	1
845.6.d	\(\chi_{845}(844, \cdot)\)	n/a	376	1
845.6.e	\(\chi_{845}(146, \cdot)\)	n/a	512	2
845.6.f	\(\chi_{845}(408, \cdot)\)	n/a	750	2
845.6.k	\(\chi_{845}(268, \cdot)\)	n/a	750	2
845.6.l	\(\chi_{845}(654, \cdot)\)	n/a	752	2
845.6.m	\(\chi_{845}(316, \cdot)\)	n/a	512	2
845.6.n	\(\chi_{845}(484, \cdot)\)	n/a	748	2
845.6.o	\(\chi_{845}(258, \cdot)\)	n/a	1500	4
845.6.t	\(\chi_{845}(188, \cdot)\)	n/a	1500	4
845.6.u	\(\chi_{845}(66, \cdot)\)	n/a	3624	12
845.6.v	\(\chi_{845}(64, \cdot)\)	n/a	5424	12
845.6.w	\(\chi_{845}(51, \cdot)\)	n/a	3624	12
845.6.x	\(\chi_{845}(14, \cdot)\)	n/a	5448	12
845.6.y	\(\chi_{845}(16, \cdot)\)	n/a	7296	24
845.6.z	\(\chi_{845}(8, \cdot)\)	n/a	10872	24
845.6.be	\(\chi_{845}(18, \cdot)\)	n/a	10872	24
845.6.bf	\(\chi_{845}(9, \cdot)\)	n/a	10896	24
845.6.bg	\(\chi_{845}(36, \cdot)\)	n/a	7296	24
845.6.bh	\(\chi_{845}(4, \cdot)\)	n/a	10848	24
845.6.bi	\(\chi_{845}(7, \cdot)\)	n/a	21744	48
845.6.bn	\(\chi_{845}(2, \cdot)\)	n/a	21744	48

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(845))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(845)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(845))\)\(^{\oplus 1}\)