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Properties

Label 546.4.u
Level $546$
Weight $4$
Character orbit 546.u
Rep. character $\chi_{546}(185,\cdot)$
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.u (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

\( 224 q + 448 q^{4} - 56 q^{7} + 64 q^{9} + O(q^{10}) \) \( 224 q + 448 q^{4} - 56 q^{7} + 64 q^{9} - 18 q^{13} - 48 q^{15} - 1792 q^{16} + 48 q^{18} + 40 q^{21} - 2800 q^{25} - 376 q^{28} + 104 q^{30} - 390 q^{31} + 128 q^{36} + 644 q^{37} + 318 q^{39} - 256 q^{42} - 58 q^{43} + 120 q^{46} - 1108 q^{49} + 1186 q^{51} - 672 q^{52} + 180 q^{54} - 720 q^{55} - 424 q^{57} + 96 q^{58} + 192 q^{60} - 1948 q^{63} - 14336 q^{64} + 1200 q^{66} - 1412 q^{67} + 1068 q^{69} - 96 q^{70} + 384 q^{72} + 1818 q^{73} - 9192 q^{75} - 288 q^{76} - 1080 q^{78} - 830 q^{79} - 3664 q^{81} - 160 q^{84} - 744 q^{85} - 312 q^{87} + 5106 q^{91} + 988 q^{93} + 48 q^{97} + 840 q^{99} + O(q^{100}) \)

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

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