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Properties

Label 342.5.bd
Level $342$
Weight $5$
Character orbit 342.bd
Rep. character $\chi_{342}(13,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $480$
Sturm bound $300$

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Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 342.bd (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(300\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(342, [\chi])\).

Total New Old
Modular forms 1464 480 984
Cusp forms 1416 480 936
Eisenstein series 48 0 48

Trace form

\( 480 q + 12 q^{3} + 48 q^{6} - 84 q^{9} + O(q^{10}) \) \( 480 q + 12 q^{3} + 48 q^{6} - 84 q^{9} - 30 q^{13} + 1146 q^{15} + 1350 q^{17} - 2880 q^{18} - 462 q^{19} - 1008 q^{22} - 1440 q^{23} + 768 q^{24} - 4140 q^{27} - 624 q^{28} - 2646 q^{29} - 6270 q^{33} - 3564 q^{35} + 672 q^{36} - 2448 q^{38} + 4512 q^{39} + 828 q^{41} - 2112 q^{43} + 4032 q^{44} - 9882 q^{45} - 4212 q^{47} - 768 q^{48} + 164640 q^{49} + 27648 q^{50} - 10710 q^{51} - 240 q^{52} - 13968 q^{53} - 5184 q^{54} + 10212 q^{57} + 11826 q^{59} + 9168 q^{60} - 10164 q^{61} + 19008 q^{62} + 28776 q^{63} + 122880 q^{64} + 79380 q^{65} + 42816 q^{66} + 15078 q^{67} + 576 q^{68} - 21762 q^{69} - 18468 q^{71} - 5376 q^{72} - 33630 q^{73} - 28320 q^{78} + 13362 q^{79} + 44484 q^{81} + 13248 q^{82} + 22608 q^{83} + 88848 q^{87} + 7344 q^{89} - 28128 q^{90} + 14208 q^{91} - 5760 q^{92} + 55920 q^{93} + 38016 q^{95} - 8460 q^{97} + 34560 q^{98} + 61698 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(342, [\chi])\) into newform subspaces

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

Decomposition of \(S_{5}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(342, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)