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

• Label: 546.4.ch
• Level: $546$
• Weight: $4$
• Character orbit: 546.ch
• Rep. character: $\chi_{546}(137,\cdot)$
• 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.ch (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 - 56 * q^7 - 168 * q^15 - 7168 * q^16 - 80 * q^18 + 164 * q^19 - 40 * q^21 - 552 * q^27 + 80 * q^28 - 816 * q^30 + 64 * q^31 - 888 * q^33 - 768 * q^36 + 1288 * q^37 - 1160 * q^39 + 360 * q^42 - 420 * q^43 - 160 * q^45 - 240 * q^46 - 180 * q^49 - 1328 * q^52 - 120 * q^54 - 480 * q^55 + 424 * q^57 + 48 * q^58 + 288 * q^60 + 384 * q^61 + 1856 * q^63 + 2080 * q^66 - 3316 * q^67 - 3696 * q^69 - 192 * q^70 + 832 * q^72 - 2728 * q^73 - 4048 * q^76 - 1424 * q^78 - 4416 * q^79 - 912 * q^81 + 864 * q^82 + 160 * q^84 + 8448 * q^85 + 5280 * q^87 - 3800 * q^91 - 2088 * q^93 - 2496 * q^94 - 1832 * q^97 + 3352 * 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

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