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

• Label: 546.4.bv
• Level: $546$
• Weight: $4$
• Character orbit: 546.bv
• Rep. character: $\chi_{546}(317,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $448$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 273 \)
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	448	928
Cusp forms	1312	448	864
Eisenstein series	64	0	64

Trace form

448 * q + 148 * q^7 + 336 * q^15 + 3584 * q^16 - 128 * q^18 + 668 * q^19 - 40 * q^21 - 552 * q^27 + 224 * q^28 - 356 * q^31 - 888 * q^33 + 1540 * q^37 + 304 * q^39 + 1152 * q^42 - 160 * q^45 - 240 * q^46 + 16 * q^52 - 120 * q^54 + 960 * q^55 - 848 * q^57 + 48 * q^58 - 672 * q^60 + 384 * q^61 + 6020 * q^63 - 4160 * q^66 + 884 * q^67 - 192 * q^70 - 512 * q^72 - 2836 * q^73 - 5344 * q^76 + 2848 * q^78 + 6816 * q^79 + 7200 * q^81 - 320 * q^84 + 2400 * q^85 - 2016 * q^87 + 6364 * q^91 + 264 * q^93 + 4992 * q^94 + 2704 * q^97 - 6704 * 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

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