Space of modular forms of level 828 and weight 3

• Label: 828.3
• Level: 828
• Weight: 3
• Dimension: 17302
• Nonzero newspaces: 16
• Sturm bound: 114048
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(114048\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(828))\).

	Total	New	Old
Modular forms	38896	17678	21218
Cusp forms	37136	17302	19834
Eisenstein series	1760	376	1384

Trace form

17302 * q - 35 * q^2 - 6 * q^3 - 39 * q^4 - 88 * q^5 - 26 * q^6 + 2 * q^7 + 43 * q^8 - 58 * q^9 - 51 * q^10 + 72 * q^11 + 28 * q^12 - 40 * q^13 - 33 * q^14 + 90 * q^15 - 63 * q^16 + 93 * q^17 - 68 * q^18 + 29 * q^19 - 121 * q^20 - 226 * q^21 - 74 * q^22 - 121 * q^23 - 346 * q^24 - 206 * q^25 - 361 * q^26 - 123 * q^28 - 69 * q^29 - 356 * q^30 - 85 * q^31 - 335 * q^32 + 68 * q^33 - 341 * q^34 - 220 * q^35 + 46 * q^36 - 230 * q^37 + 32 * q^38 - 114 * q^39 - 161 * q^40 - 2 * q^41 + 664 * q^42 + 4 * q^43 + 574 * q^44 - 94 * q^45 + 181 * q^46 + 250 * q^47 + 622 * q^48 + 132 * q^49 + 910 * q^50 + 54 * q^51 + 869 * q^52 - 458 * q^53 - 158 * q^54 - 598 * q^55 + 32 * q^56 - 1324 * q^57 + 154 * q^58 - 1132 * q^59 - 1196 * q^60 - 1084 * q^61 - 1113 * q^62 - 832 * q^63 - 615 * q^64 - 1409 * q^65 - 1064 * q^66 - 298 * q^67 - 742 * q^68 - 23 * q^69 - 366 * q^70 + 495 * q^71 + 334 * q^72 - 328 * q^73 + 858 * q^74 + 1672 * q^75 + 894 * q^76 + 1429 * q^77 + 1336 * q^78 + 1022 * q^79 + 2816 * q^80 + 1710 * q^81 + 963 * q^82 + 1471 * q^83 + 1240 * q^84 + 792 * q^85 + 1075 * q^86 + 126 * q^87 + 81 * q^88 + 914 * q^89 - 316 * q^90 + 604 * q^91 - 366 * q^92 + 1114 * q^93 - 862 * q^94 + 673 * q^95 - 1844 * q^96 + 1919 * q^97 - 2697 * q^98 - 342 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(828))\)

We only show spaces with odd 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
828.3.b	\(\chi_{828}(505, \cdot)\)	828.3.b.a	4	1
		828.3.b.b	8
		828.3.b.c	8
828.3.d	\(\chi_{828}(737, \cdot)\)	828.3.d.a	16	1
828.3.f	\(\chi_{828}(415, \cdot)\)	n/a	110	1
828.3.h	\(\chi_{828}(827, \cdot)\)	828.3.h.a	96	1
828.3.j	\(\chi_{828}(275, \cdot)\)	n/a	568	2
828.3.l	\(\chi_{828}(139, \cdot)\)	n/a	528	2
828.3.n	\(\chi_{828}(185, \cdot)\)	828.3.n.a	88	2
828.3.p	\(\chi_{828}(229, \cdot)\)	828.3.p.a	96	2
828.3.r	\(\chi_{828}(107, \cdot)\)	n/a	960	10
828.3.t	\(\chi_{828}(55, \cdot)\)	n/a	1180	10
828.3.v	\(\chi_{828}(197, \cdot)\)	n/a	160	10
828.3.x	\(\chi_{828}(37, \cdot)\)	n/a	200	10
828.3.z	\(\chi_{828}(61, \cdot)\)	n/a	960	20
828.3.bb	\(\chi_{828}(29, \cdot)\)	n/a	960	20
828.3.bd	\(\chi_{828}(31, \cdot)\)	n/a	5680	20
828.3.bf	\(\chi_{828}(11, \cdot)\)	n/a	5680	20

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(828))\) into lower level spaces

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