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Properties

Label 324.8.i
Level $324$
Weight $8$
Character orbit 324.i
Rep. character $\chi_{324}(37,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $126$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 324.i (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 \(M_{8}(324, [\chi])\).

Total New Old
Modular forms 2322 126 2196
Cusp forms 2214 126 2088
Eisenstein series 108 0 108

Trace form

\( 126 q + 213 q^{5} + O(q^{10}) \) \( 126 q + 213 q^{5} - 8319 q^{11} - 58956 q^{17} + 137190 q^{23} - 107991 q^{25} + 276180 q^{29} + 297981 q^{31} - 1092831 q^{35} - 1269075 q^{41} + 1080963 q^{43} - 4605705 q^{47} - 976014 q^{49} + 5087382 q^{53} - 11097924 q^{59} - 3865446 q^{61} + 22662039 q^{65} + 12074481 q^{67} + 3531612 q^{71} + 3770937 q^{73} - 6524205 q^{77} + 16415532 q^{79} + 15181065 q^{83} - 7906500 q^{85} - 20006466 q^{89} + 3315069 q^{91} - 9195990 q^{95} + 9471951 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(324, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(324, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)