Space of modular forms of level 828, weight 3, and Character 828.t

• Label: 828.3.t
• Level: $828$
• Weight: $3$
• Character orbit: 828.t
• Rep. character: $\chi_{828}(55,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $1180$
• Sturm bound: $432$

Defining parameters

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	828.t (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 92 \)
Character field:			\(\Q(\zeta_{22})\)
Sturm bound:			\(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(828, [\chi])\).

	Total	New	Old
Modular forms	2960	1220	1740
Cusp forms	2800	1180	1620
Eisenstein series	160	40	120

Trace form

1180 * q + 7 * q^2 - 19 * q^4 + 18 * q^5 + 28 * q^8 + 19 * q^10 - 18 * q^13 + 31 * q^14 + 21 * q^16 + 18 * q^17 - 13 * q^20 - 26 * q^22 - 568 * q^25 - 32 * q^26 - 101 * q^28 - 62 * q^29 - 33 * q^32 + 269 * q^34 + 78 * q^37 - 358 * q^38 + 43 * q^40 + 34 * q^41 + 4 * q^44 - 3 * q^46 + 676 * q^49 + 280 * q^50 - 732 * q^52 - 286 * q^53 + 414 * q^56 - 187 * q^58 + 46 * q^61 - 44 * q^62 - 70 * q^64 + 94 * q^65 + 22 * q^68 - 250 * q^70 - 18 * q^73 + 292 * q^74 + 798 * q^76 - 938 * q^77 + 950 * q^80 + 1078 * q^82 - 214 * q^85 + 615 * q^86 - 215 * q^88 + 74 * q^89 + 104 * q^92 - 697 * q^94 + 198 * q^97 - 781 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(828, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(828, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(828, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 2}\)