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Properties

Label 342.5.l
Level $342$
Weight $5$
Character orbit 342.l
Rep. character $\chi_{342}(151,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
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.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(300\)

Dimensions

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

Total New Old
Modular forms 488 160 328
Cusp forms 472 160 312
Eisenstein series 16 0 16

Trace form

\( 160 q + 640 q^{4} + 32 q^{6} + 52 q^{7} - 56 q^{9} + O(q^{10}) \) \( 160 q + 640 q^{4} + 32 q^{6} + 52 q^{7} - 56 q^{9} + 168 q^{11} - 5120 q^{16} - 1752 q^{17} - 100 q^{19} + 480 q^{23} - 256 q^{24} - 10000 q^{25} + 832 q^{28} + 1600 q^{30} + 4752 q^{35} + 448 q^{36} - 2256 q^{38} + 3852 q^{39} - 6752 q^{42} + 1544 q^{43} + 2688 q^{44} - 4924 q^{45} - 5820 q^{47} - 23748 q^{49} - 9952 q^{54} - 21702 q^{57} + 3388 q^{61} + 12672 q^{62} - 17716 q^{63} - 81920 q^{64} - 2624 q^{66} - 7008 q^{68} + 34616 q^{73} + 10464 q^{74} - 400 q^{76} + 14280 q^{77} - 15320 q^{81} - 17664 q^{82} - 3012 q^{83} + 33432 q^{87} - 3840 q^{92} - 66744 q^{93} + 49248 q^{95} - 4096 q^{96} - 7924 q^{99} + O(q^{100}) \)

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

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