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Properties

Label 432.6.y
Level $432$
Weight $6$
Character orbit 432.y
Rep. character $\chi_{432}(37,\cdot)$
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.y (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

\( 472 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 8 q^{8} + O(q^{10}) \) \( 472 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 8 q^{8} - 8 q^{10} + 2 q^{11} - 2 q^{13} + 130 q^{14} - 2 q^{16} + 16 q^{17} - 8 q^{19} + 828 q^{20} - 2 q^{22} + 1768 q^{26} - 4104 q^{28} + 2 q^{29} - 4 q^{31} - 3818 q^{32} - 66 q^{34} + 12508 q^{35} - 8 q^{37} + 34414 q^{38} - 2 q^{40} - 2 q^{43} - 36468 q^{44} - 54016 q^{46} + 88364 q^{47} + 509008 q^{49} + 32136 q^{50} - 2 q^{52} + 8 q^{53} + 122828 q^{56} + 6496 q^{58} + 15254 q^{59} - 2 q^{61} + 258620 q^{62} + 104788 q^{64} + 4 q^{65} - 2 q^{67} - 72544 q^{68} + 33612 q^{70} - 99650 q^{74} - 50342 q^{76} + 67230 q^{77} - 4 q^{79} + 680688 q^{80} + 302300 q^{82} - 164618 q^{83} - 6252 q^{85} + 361514 q^{86} - 179546 q^{88} - 67236 q^{91} + 234416 q^{92} + 126 q^{94} - 577596 q^{95} - 4 q^{97} - 411544 q^{98} + O(q^{100}) \)

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

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