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

• Label: 546.4.bk
• Level: $546$
• Weight: $4$
• Character orbit: 546.bk
• Rep. character: $\chi_{546}(25,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $112$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.bk (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
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	112	576
Cusp forms	656	112	544
Eisenstein series	32	0	32

Trace form

112 * q + 12 * q^3 + 224 * q^4 - 504 * q^9 - 80 * q^10 - 48 * q^12 + 92 * q^13 - 56 * q^14 - 896 * q^16 - 4 * q^17 + 112 * q^22 + 176 * q^23 + 1528 * q^25 + 152 * q^26 - 216 * q^27 + 344 * q^29 - 1112 * q^35 - 4032 * q^36 + 248 * q^38 - 546 * q^39 + 320 * q^40 + 1048 * q^43 - 384 * q^48 - 1064 * q^49 - 456 * q^51 + 184 * q^52 + 1924 * q^53 + 768 * q^55 + 32 * q^56 + 1940 * q^61 - 640 * q^62 - 7168 * q^64 + 112 * q^65 + 1056 * q^66 + 16 * q^68 + 2016 * q^69 - 624 * q^74 - 2724 * q^75 - 4600 * q^77 + 144 * q^78 - 1156 * q^79 - 4536 * q^81 - 1024 * q^82 + 1872 * q^87 + 224 * q^88 + 1440 * q^90 + 3326 * q^91 + 1408 * q^92 + 2808 * q^94 - 2424 * q^95

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

\( S_{4}^{\mathrm{old}}(546, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)