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Properties

Label 432.6.v
Level $432$
Weight $6$
Character orbit 432.v
Rep. character $\chi_{432}(35,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $472$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 432.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(432, [\chi])\).

Total New Old
Modular forms 1464 488 976
Cusp forms 1416 472 944
Eisenstein series 48 16 32

Trace form

\( 472 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} + O(q^{10}) \) \( 472 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} - 2472 q^{20} - 2 q^{22} + 12 q^{23} + 4088 q^{28} + 6 q^{29} + 6 q^{32} + 62 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} + 53744 q^{46} - 509016 q^{49} - 96012 q^{50} - 2 q^{52} - 16 q^{55} - 100836 q^{56} - 6500 q^{58} - 45750 q^{59} - 2 q^{61} + 104788 q^{64} + 12 q^{65} - 2 q^{67} - 229920 q^{68} - 33616 q^{70} - 298950 q^{74} + 50338 q^{76} + 6 q^{77} + 302556 q^{82} + 493866 q^{83} + 6248 q^{85} + 1746 q^{86} + 179542 q^{88} + 67220 q^{91} - 690948 q^{92} + 126 q^{94} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)