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

• Label: 546.4.bi
• Level: $546$
• Weight: $4$
• Character orbit: 546.bi
• Rep. character: $\chi_{546}(17,\cdot)$
• 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.bi (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 - 18 * q^7 + 32 * q^9 - 18 * q^13 - 120 * q^15 + 3584 * q^16 - 192 * q^18 + 252 * q^19 + 2800 * q^25 - 72 * q^28 - 220 * q^30 + 30 * q^31 + 372 * q^33 + 128 * q^36 - 300 * q^39 - 20 * q^42 + 254 * q^43 - 1438 * q^49 + 702 * q^51 - 72 * q^52 - 360 * q^54 + 720 * q^55 - 480 * q^60 - 24 * q^61 - 1188 * q^63 + 14336 * q^64 - 1200 * q^66 + 2082 * q^67 - 2628 * q^69 + 288 * q^70 - 768 * q^72 + 54 * q^73 + 1008 * q^76 - 344 * q^78 + 3902 * q^79 + 584 * q^81 + 432 * q^82 + 3816 * q^85 + 2608 * q^91 + 3600 * q^94 - 3696 * q^97

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

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