Space of modular forms of level 504, weight 3, and Character 504.bw

• Label: 504.3.bw
• Level: $504$
• Weight: $3$
• Character orbit: 504.bw
• Rep. character: $\chi_{504}(325,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $156$
• Sturm bound: $288$

Defining parameters

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.bw (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(504, [\chi])\).

	Total	New	Old
Modular forms	400	164	236
Cusp forms	368	156	212
Eisenstein series	32	8	24

Trace form

156 * q - 4 * q^4 - 4 * q^7 - 12 * q^8 + 24 * q^10 - 10 * q^14 + 12 * q^16 + 6 * q^17 - 28 * q^22 + 34 * q^23 - 352 * q^25 - 14 * q^28 - 6 * q^31 - 60 * q^32 + 192 * q^38 + 42 * q^40 + 90 * q^44 + 12 * q^46 - 282 * q^47 + 12 * q^49 - 68 * q^50 + 228 * q^52 - 160 * q^56 - 122 * q^58 + 80 * q^64 + 52 * q^65 + 216 * q^70 - 120 * q^71 - 246 * q^73 + 216 * q^74 - 34 * q^79 + 624 * q^80 + 210 * q^82 - 246 * q^86 + 262 * q^88 + 150 * q^89 - 140 * q^92 - 786 * q^94 + 94 * q^95 + 204 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(504, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(504, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(504, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)