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Properties

Label 546.4.bb
Level $546$
Weight $4$
Character orbit 546.bb
Rep. character $\chi_{546}(269,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $224$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 546.bb (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

\( 224 q - 896 q^{4} - 38 q^{7} - 32 q^{9} + O(q^{10}) \) \( 224 q - 896 q^{4} - 38 q^{7} - 32 q^{9} + 18 q^{13} - 48 q^{15} + 3584 q^{16} + 48 q^{18} - 72 q^{19} + 40 q^{21} - 2800 q^{25} + 152 q^{28} - 52 q^{30} - 390 q^{31} - 1548 q^{33} + 128 q^{36} - 1288 q^{37} - 492 q^{39} + 908 q^{42} - 58 q^{43} - 240 q^{46} - 2206 q^{49} + 1186 q^{51} - 72 q^{52} + 720 q^{55} - 424 q^{57} - 48 q^{58} + 192 q^{60} + 24 q^{61} - 124 q^{63} - 14336 q^{64} + 1200 q^{66} + 706 q^{67} - 1068 q^{69} - 96 q^{70} - 192 q^{72} + 1818 q^{73} + 288 q^{76} - 1080 q^{78} - 830 q^{79} + 1832 q^{81} + 432 q^{82} - 160 q^{84} - 744 q^{85} - 6408 q^{91} - 1976 q^{93} + 3888 q^{94} - 48 q^{97} + 840 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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