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Properties

Label 108.8.i
Level $108$
Weight $8$
Character orbit 108.i
Rep. character $\chi_{108}(13,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $126$
Sturm bound $144$

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 108.i (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(108, [\chi])\).

Total New Old
Modular forms 774 126 648
Cusp forms 738 126 612
Eisenstein series 36 0 36

Trace form

\( 126 q - 213 q^{5} - 1722 q^{9} + O(q^{10}) \) \( 126 q - 213 q^{5} - 1722 q^{9} + 8319 q^{11} - 9621 q^{15} + 58956 q^{17} - 247494 q^{21} - 137190 q^{23} - 107991 q^{25} + 258201 q^{27} - 276180 q^{29} + 297981 q^{31} + 265716 q^{33} + 1092831 q^{35} + 448239 q^{39} + 1269075 q^{41} + 1080963 q^{43} + 541449 q^{45} + 4605705 q^{47} - 976014 q^{49} - 3324933 q^{51} - 5087382 q^{53} + 1274508 q^{57} + 11097924 q^{59} - 3865446 q^{61} - 5428779 q^{63} - 22662039 q^{65} + 12074481 q^{67} + 25503111 q^{69} - 3531612 q^{71} + 3770937 q^{73} - 2819013 q^{75} + 6524205 q^{77} + 16415532 q^{79} + 309042 q^{81} - 15181065 q^{83} - 7906500 q^{85} - 12617811 q^{87} + 20006466 q^{89} + 3315069 q^{91} + 6589191 q^{93} + 9195990 q^{95} + 9471951 q^{97} - 57866049 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

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