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Properties

Label 546.4.z
Level $546$
Weight $4$
Character orbit 546.z
Rep. character $\chi_{546}(131,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
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.z (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 688 192 496
Cusp forms 656 192 464
Eisenstein series 32 0 32

Trace form

\( 192 q + 384 q^{4} - 12 q^{7} + 28 q^{9} + O(q^{10}) \) \( 192 q + 384 q^{4} - 12 q^{7} + 28 q^{9} + 72 q^{10} + 336 q^{15} - 1536 q^{16} + 940 q^{21} - 48 q^{22} + 96 q^{24} - 2412 q^{25} + 48 q^{28} - 364 q^{30} - 828 q^{31} + 224 q^{36} + 384 q^{37} + 288 q^{40} + 872 q^{42} - 2688 q^{43} + 4788 q^{45} - 576 q^{46} + 756 q^{49} - 1934 q^{51} + 6176 q^{57} + 1512 q^{58} + 672 q^{60} + 216 q^{61} + 1220 q^{63} - 12288 q^{64} + 1632 q^{66} + 312 q^{70} - 4608 q^{73} - 3156 q^{75} + 924 q^{79} - 1228 q^{81} + 1184 q^{84} - 1344 q^{85} - 2676 q^{87} - 96 q^{88} - 1248 q^{91} - 3656 q^{93} + 384 q^{96} + 6888 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)