Space of modular forms of level 867 and weight 4

• Label: 867.4
• Level: 867
• Weight: 4
• Dimension: 61624
• Nonzero newspaces: 10
• Sturm bound: 221952
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 10 \)
Sturm bound:			\(221952\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(867))\).

	Total	New	Old
Modular forms	84032	62360	21672
Cusp forms	82432	61624	20808
Eisenstein series	1600	736	864

Trace form

61624 * q - 120 * q^3 - 240 * q^4 - 120 * q^6 - 240 * q^7 - 120 * q^9 - 656 * q^10 - 448 * q^11 - 312 * q^12 - 112 * q^13 + 640 * q^14 + 552 * q^15 + 1520 * q^16 + 256 * q^17 + 664 * q^18 + 80 * q^19 + 448 * q^20 - 312 * q^21 - 1136 * q^22 - 832 * q^23 - 3864 * q^24 - 5152 * q^25 - 4128 * q^26 - 120 * q^27 + 336 * q^28 + 1040 * q^29 + 2568 * q^30 + 3216 * q^31 + 4960 * q^32 + 1976 * q^33 + 3968 * q^34 + 3968 * q^35 + 616 * q^36 + 2448 * q^37 + 2080 * q^38 + 2696 * q^39 - 2544 * q^40 - 1840 * q^41 - 1752 * q^42 - 5712 * q^43 - 9856 * q^44 - 2984 * q^45 - 8112 * q^46 - 7592 * q^48 - 240 * q^49 - 1728 * q^51 - 464 * q^52 - 6864 * q^53 - 13576 * q^54 - 11632 * q^55 - 10400 * q^56 - 5576 * q^57 - 5392 * q^58 - 640 * q^59 + 7288 * q^60 + 4560 * q^61 + 8288 * q^62 + 13992 * q^63 + 8272 * q^64 + 14640 * q^65 + 16568 * q^66 + 8304 * q^67 + 7280 * q^68 + 7256 * q^69 + 4848 * q^70 + 768 * q^71 + 7224 * q^72 + 960 * q^73 + 1056 * q^74 + 1608 * q^75 + 1712 * q^76 - 832 * q^77 - 3688 * q^78 - 1648 * q^79 + 544 * q^80 - 13000 * q^81 - 1904 * q^82 - 14272 * q^83 + 15992 * q^84 + 2072 * q^85 + 10496 * q^86 + 17832 * q^87 + 27408 * q^88 + 6144 * q^89 + 6184 * q^90 + 7824 * q^91 + 8960 * q^92 - 3064 * q^93 - 1776 * q^94 - 3328 * q^95 - 31304 * q^96 - 9456 * q^97 - 14112 * q^98 - 26216 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(867))\)

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
867.4.a	\(\chi_{867}(1, \cdot)\)	867.4.a.a	1	1
		867.4.a.b	1
		867.4.a.c	1
		867.4.a.d	1
		867.4.a.e	1
		867.4.a.f	1
		867.4.a.g	1
		867.4.a.h	2
		867.4.a.i	2
		867.4.a.j	2
		867.4.a.k	3
		867.4.a.l	4
		867.4.a.m	4
		867.4.a.n	4
		867.4.a.o	4
		867.4.a.p	8
		867.4.a.q	8
		867.4.a.r	9
		867.4.a.s	9
		867.4.a.t	15
		867.4.a.u	15
		867.4.a.v	20
		867.4.a.w	20
867.4.d	\(\chi_{867}(577, \cdot)\)	n/a	136	1
867.4.e	\(\chi_{867}(616, \cdot)\)	n/a	272	2
867.4.h	\(\chi_{867}(688, \cdot)\)	n/a	536	4
867.4.i	\(\chi_{867}(65, \cdot)\)	n/a	2048	8
867.4.k	\(\chi_{867}(52, \cdot)\)	n/a	2432	16
867.4.l	\(\chi_{867}(16, \cdot)\)	n/a	2432	16
867.4.p	\(\chi_{867}(4, \cdot)\)	n/a	4864	32
867.4.q	\(\chi_{867}(19, \cdot)\)	n/a	9856	64
867.4.t	\(\chi_{867}(5, \cdot)\)	n/a	38912	128

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(867))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(867)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 1}\)