Space of modular forms of level 546, weight 4, and Character 546.bu

• Label: 546.4.bu
• Level: $546$
• Weight: $4$
• Character orbit: 546.bu
• Rep. character: $\chi_{546}(71,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $336$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.bu (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(546, [\chi])\).

	Total	New	Old
Modular forms	1376	336	1040
Cusp forms	1312	336	976
Eisenstein series	64	0	64

Trace form

336 * q - 288 * q^10 - 336 * q^13 + 168 * q^15 + 2688 * q^16 + 16 * q^18 + 96 * q^19 + 224 * q^21 + 1248 * q^27 - 816 * q^30 + 432 * q^31 - 24 * q^33 - 480 * q^34 + 768 * q^36 + 528 * q^37 + 2128 * q^39 - 664 * q^45 - 336 * q^46 + 3408 * q^54 - 624 * q^55 - 1616 * q^57 + 2160 * q^58 - 384 * q^60 + 624 * q^61 - 2128 * q^63 - 3968 * q^66 - 576 * q^67 + 360 * q^69 - 128 * q^72 + 2928 * q^73 + 14040 * q^75 + 384 * q^76 + 9040 * q^78 - 8832 * q^79 + 2160 * q^81 - 896 * q^84 + 3696 * q^85 - 1680 * q^91 - 10080 * q^93 + 480 * q^94 + 8256 * q^97 - 14432 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(546, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(546, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(546, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)