Space of modular forms of level 828 and weight 4

• Label: 828.4
• Level: 828
• Weight: 4
• Dimension: 26046
• Nonzero newspaces: 16
• Sturm bound: 152064
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(152064\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(828))\).

	Total	New	Old
Modular forms	57904	26426	31478
Cusp forms	56144	26046	30098
Eisenstein series	1760	380	1380

Trace form

26046 * q - 27 * q^2 + 6 * q^3 - 55 * q^4 - 102 * q^5 - 86 * q^6 - 4 * q^7 - 33 * q^8 - 178 * q^9 + 205 * q^10 - 30 * q^11 - 32 * q^12 - 210 * q^13 + 123 * q^14 + 360 * q^15 - 559 * q^16 + 326 * q^17 + 196 * q^18 + 250 * q^19 + 435 * q^20 + 404 * q^21 + 908 * q^22 + 346 * q^23 - 94 * q^24 + 134 * q^25 - 33 * q^26 - 1296 * q^27 - 795 * q^28 - 1822 * q^29 - 920 * q^30 - 614 * q^31 - 1407 * q^32 + 1910 * q^33 + 1903 * q^34 + 3350 * q^35 - 2090 * q^36 + 378 * q^37 - 1210 * q^38 + 72 * q^39 - 1853 * q^40 - 1918 * q^41 - 1508 * q^42 - 2878 * q^43 - 3344 * q^44 - 2464 * q^45 - 4587 * q^46 - 2072 * q^47 + 2698 * q^48 + 1940 * q^49 + 1996 * q^50 + 3294 * q^51 + 4813 * q^52 + 5420 * q^53 + 5998 * q^54 + 11232 * q^55 + 9554 * q^56 + 4622 * q^57 + 6244 * q^58 + 3644 * q^59 + 2560 * q^60 - 7806 * q^61 - 33 * q^62 - 7972 * q^63 + 905 * q^64 - 16242 * q^65 - 6272 * q^66 - 4594 * q^67 - 9756 * q^68 - 7580 * q^69 - 6954 * q^70 - 11190 * q^71 - 10994 * q^72 + 18 * q^73 - 14146 * q^74 - 5846 * q^75 - 7238 * q^76 + 7430 * q^77 - 5012 * q^78 + 4846 * q^79 - 4092 * q^80 + 3990 * q^81 - 749 * q^82 + 12488 * q^83 + 11656 * q^84 - 812 * q^85 + 23339 * q^86 + 2772 * q^87 + 11617 * q^88 - 5088 * q^89 + 22184 * q^90 - 3316 * q^91 + 17700 * q^92 + 3376 * q^93 + 14854 * q^94 + 1566 * q^95 + 7756 * q^96 + 3654 * q^97 + 4279 * q^98 + 3708 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(828))\)

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
828.4.a	\(\chi_{828}(1, \cdot)\)	828.4.a.a	1	1
		828.4.a.b	1
		828.4.a.c	2
		828.4.a.d	2
		828.4.a.e	3
		828.4.a.f	3
		828.4.a.g	4
		828.4.a.h	6
		828.4.a.i	6
828.4.c	\(\chi_{828}(323, \cdot)\)	n/a	132	1
828.4.e	\(\chi_{828}(91, \cdot)\)	n/a	178	1
828.4.g	\(\chi_{828}(413, \cdot)\)	828.4.g.a	24	1
828.4.i	\(\chi_{828}(277, \cdot)\)	n/a	132	2
828.4.k	\(\chi_{828}(137, \cdot)\)	n/a	144	2
828.4.m	\(\chi_{828}(367, \cdot)\)	n/a	856	2
828.4.o	\(\chi_{828}(47, \cdot)\)	n/a	792	2
828.4.q	\(\chi_{828}(73, \cdot)\)	n/a	300	10
828.4.s	\(\chi_{828}(17, \cdot)\)	n/a	240	10
828.4.u	\(\chi_{828}(19, \cdot)\)	n/a	1780	10
828.4.w	\(\chi_{828}(35, \cdot)\)	n/a	1440	10
828.4.y	\(\chi_{828}(13, \cdot)\)	n/a	1440	20
828.4.ba	\(\chi_{828}(59, \cdot)\)	n/a	8560	20
828.4.bc	\(\chi_{828}(7, \cdot)\)	n/a	8560	20
828.4.be	\(\chi_{828}(5, \cdot)\)	n/a	1440	20

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(828))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(828)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 2}\)