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

• Label: 546.4.o
• Level: $546$
• Weight: $4$
• Character orbit: 546.o
• Rep. character: $\chi_{546}(265,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $112$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.o (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(i)\)
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 - 28 * q^7 - 1008 * q^9 + 112 * q^11 + 80 * q^14 - 1792 * q^16 + 12 * q^21 - 224 * q^22 - 112 * q^28 - 624 * q^29 + 1040 * q^35 + 1064 * q^37 + 504 * q^39 + 448 * q^44 + 1808 * q^46 - 1472 * q^50 + 304 * q^53 - 840 * q^57 + 752 * q^58 + 252 * q^63 + 4960 * q^65 - 2736 * q^67 - 2736 * q^70 - 4832 * q^71 - 4160 * q^74 - 528 * q^78 - 3680 * q^79 + 9072 * q^81 + 48 * q^84 - 6720 * q^85 + 1568 * q^86 - 3036 * q^91 + 1408 * q^92 - 168 * q^93 + 3168 * q^98 - 1008 * 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

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