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Properties

Label 546.4.bu
Level $546$
Weight $4$
Character orbit 546.bu
Rep. character $\chi_{546}(71,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $336$
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.bu (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
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 336 1040
Cusp forms 1312 336 976
Eisenstein series 64 0 64

Trace form

\( 336 q + O(q^{10}) \) \( 336 q - 288 q^{10} - 336 q^{13} + 168 q^{15} + 2688 q^{16} + 16 q^{18} + 96 q^{19} + 224 q^{21} + 1248 q^{27} - 816 q^{30} + 432 q^{31} - 24 q^{33} - 480 q^{34} + 768 q^{36} + 528 q^{37} + 2128 q^{39} - 664 q^{45} - 336 q^{46} + 3408 q^{54} - 624 q^{55} - 1616 q^{57} + 2160 q^{58} - 384 q^{60} + 624 q^{61} - 2128 q^{63} - 3968 q^{66} - 576 q^{67} + 360 q^{69} - 128 q^{72} + 2928 q^{73} + 14040 q^{75} + 384 q^{76} + 9040 q^{78} - 8832 q^{79} + 2160 q^{81} - 896 q^{84} + 3696 q^{85} - 1680 q^{91} - 10080 q^{93} + 480 q^{94} + 8256 q^{97} - 14432 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)