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

• Label: 546.4.bb
• Level: $546$
• Weight: $4$
• Character orbit: 546.bb
• Rep. character: $\chi_{546}(269,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $224$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.bb (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 273 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(448\)

Dimensions

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

	Total	New	Old
Modular forms	688	224	464
Cusp forms	656	224	432
Eisenstein series	32	0	32

Trace form

224 * q - 896 * q^4 - 38 * q^7 - 32 * q^9 + 18 * q^13 - 48 * q^15 + 3584 * q^16 + 48 * q^18 - 72 * q^19 + 40 * q^21 - 2800 * q^25 + 152 * q^28 - 52 * q^30 - 390 * q^31 - 1548 * q^33 + 128 * q^36 - 1288 * q^37 - 492 * q^39 + 908 * q^42 - 58 * q^43 - 240 * q^46 - 2206 * q^49 + 1186 * q^51 - 72 * q^52 + 720 * q^55 - 424 * q^57 - 48 * q^58 + 192 * q^60 + 24 * q^61 - 124 * q^63 - 14336 * q^64 + 1200 * q^66 + 706 * q^67 - 1068 * q^69 - 96 * q^70 - 192 * q^72 + 1818 * q^73 + 288 * q^76 - 1080 * q^78 - 830 * q^79 + 1832 * q^81 + 432 * q^82 - 160 * q^84 - 744 * q^85 - 6408 * q^91 - 1976 * q^93 + 3888 * q^94 - 48 * q^97 + 840 * 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

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