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

• Label: 504.3.bx
• Level: $504$
• Weight: $3$
• Character orbit: 504.bx
• Rep. character: $\chi_{504}(163,\cdot)$
• 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.bx (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 + 2 * q^2 - 4 * q^4 + 20 * q^8 - 18 * q^10 - 14 * q^11 + 44 * q^14 - 12 * q^16 + 2 * q^17 - 2 * q^19 - 8 * q^20 + 24 * q^22 + 348 * q^25 - 64 * q^26 - 106 * q^28 + 52 * q^32 - 12 * q^34 + 102 * q^35 + 66 * q^38 + 146 * q^40 + 8 * q^41 - 104 * q^43 - 14 * q^44 + 54 * q^46 + 12 * q^49 + 236 * q^50 - 164 * q^52 - 128 * q^56 + 30 * q^58 + 66 * q^59 + 28 * q^62 - 208 * q^64 - 48 * q^65 + 158 * q^67 + 88 * q^68 - 42 * q^70 + 78 * q^73 + 242 * q^74 + 268 * q^76 - 196 * q^80 - 90 * q^82 + 488 * q^83 + 22 * q^86 - 294 * q^88 - 46 * q^89 + 480 * q^91 - 412 * q^92 - 384 * q^94 + 408 * q^97 - 182 * 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

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