Space of modular forms of level 825, weight 3, and Character 825.ck

• Label: 825.3.ck
• Level: $825$
• Weight: $3$
• Character orbit: 825.ck
• Rep. character: $\chi_{825}(202,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $960$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	825.ck (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(825, [\chi])\).

	Total	New	Old
Modular forms	1952	960	992
Cusp forms	1888	960	928
Eisenstein series	64	0	64

Trace form

960 * q - 8 * q^5 - 8 * q^7 - 64 * q^10 + 72 * q^12 - 12 * q^13 - 48 * q^15 - 3840 * q^16 - 84 * q^17 - 40 * q^20 - 20 * q^22 - 128 * q^23 + 136 * q^25 - 144 * q^28 + 48 * q^30 - 420 * q^32 + 36 * q^33 - 52 * q^35 - 1440 * q^36 + 120 * q^37 + 56 * q^38 + 184 * q^40 + 96 * q^42 - 32 * q^43 - 32 * q^47 + 192 * q^48 + 700 * q^49 - 312 * q^50 - 304 * q^52 + 24 * q^53 - 696 * q^55 - 336 * q^57 - 512 * q^58 - 192 * q^60 - 920 * q^62 - 144 * q^63 - 104 * q^65 + 672 * q^67 + 256 * q^68 - 368 * q^70 - 464 * q^73 - 1100 * q^74 + 168 * q^75 - 88 * q^77 - 216 * q^78 + 200 * q^79 + 280 * q^80 + 2160 * q^81 - 272 * q^82 + 1256 * q^83 - 144 * q^85 + 240 * q^87 - 1236 * q^88 + 320 * q^92 - 432 * q^93 + 200 * q^94 + 248 * q^95 - 960 * q^97 + 1464 * q^98 + 300 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(825, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(825, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)