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

• Label: 546.4.u
• Level: $546$
• Weight: $4$
• Character orbit: 546.u
• Rep. character: $\chi_{546}(185,\cdot)$
• 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.u (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 + 448 * q^4 - 56 * q^7 + 64 * q^9 - 18 * q^13 - 48 * q^15 - 1792 * q^16 + 48 * q^18 + 40 * q^21 - 2800 * q^25 - 376 * q^28 + 104 * q^30 - 390 * q^31 + 128 * q^36 + 644 * q^37 + 318 * q^39 - 256 * q^42 - 58 * q^43 + 120 * q^46 - 1108 * q^49 + 1186 * q^51 - 672 * q^52 + 180 * q^54 - 720 * q^55 - 424 * q^57 + 96 * q^58 + 192 * q^60 - 1948 * q^63 - 14336 * q^64 + 1200 * q^66 - 1412 * q^67 + 1068 * q^69 - 96 * q^70 + 384 * q^72 + 1818 * q^73 - 9192 * q^75 - 288 * q^76 - 1080 * q^78 - 830 * q^79 - 3664 * q^81 - 160 * q^84 - 744 * q^85 - 312 * q^87 + 5106 * q^91 + 988 * q^93 + 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

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