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Properties

Label 432.6.u
Level $432$
Weight $6$
Character orbit 432.u
Rep. character $\chi_{432}(49,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $534$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 432.u (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 2196 546 1650
Cusp forms 2124 534 1590
Eisenstein series 72 12 60

Trace form

\( 534 q + 6 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{9} + O(q^{10}) \) \( 534 q + 6 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{9} + 6 q^{11} - 6 q^{13} + 6 q^{15} - 3 q^{17} + 3 q^{19} - 6 q^{21} + 6 q^{23} - 6 q^{25} - 6456 q^{27} + 11934 q^{29} + 6 q^{31} + 4248 q^{33} + 44103 q^{35} - 3 q^{37} - 3414 q^{39} - 8712 q^{41} + 6 q^{43} + 17694 q^{45} + 47544 q^{47} - 6 q^{49} - 723 q^{51} - 12 q^{53} + 12 q^{55} - 48171 q^{57} + 22884 q^{59} - 6 q^{61} + 120936 q^{63} + 35970 q^{65} + 6 q^{67} - 94782 q^{69} - 211719 q^{71} - 3 q^{73} - 95796 q^{75} + 26178 q^{77} + 6 q^{79} + 185730 q^{81} + 246936 q^{83} + 9369 q^{85} - 113196 q^{87} + 158331 q^{89} + 3 q^{91} - 6 q^{93} + 1208763 q^{95} + 174432 q^{97} + 551994 q^{99} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)