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Properties

Label 342.5.k
Level $342$
Weight $5$
Character orbit 342.k
Rep. character $\chi_{342}(103,\cdot)$
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.k (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

\( 160 q - 1280 q^{4} + 32 q^{6} - 26 q^{7} - 56 q^{9} + O(q^{10}) \) \( 160 q - 1280 q^{4} + 32 q^{6} - 26 q^{7} - 56 q^{9} - 84 q^{11} - 102 q^{15} + 10240 q^{16} - 474 q^{17} + 512 q^{19} - 1008 q^{22} + 480 q^{23} - 256 q^{24} - 10000 q^{25} - 630 q^{27} + 208 q^{28} - 2646 q^{29} - 800 q^{30} + 1104 q^{31} - 7290 q^{33} + 1188 q^{35} + 448 q^{36} + 2064 q^{38} - 2442 q^{39} + 828 q^{41} + 5824 q^{42} - 976 q^{43} + 672 q^{44} + 1112 q^{45} - 1608 q^{47} - 29286 q^{49} - 6336 q^{50} - 4788 q^{51} - 6984 q^{53} + 14144 q^{54} + 12348 q^{57} - 36126 q^{59} + 816 q^{60} - 1694 q^{61} + 3168 q^{62} - 5116 q^{63} - 81920 q^{64} + 3744 q^{65} + 3520 q^{66} + 3792 q^{68} + 1056 q^{69} - 48762 q^{71} + 8654 q^{73} - 20928 q^{74} - 39606 q^{75} - 4096 q^{76} - 7140 q^{77} - 19200 q^{78} + 25336 q^{81} - 4416 q^{82} - 4146 q^{83} + 55572 q^{87} + 8064 q^{88} - 7344 q^{89} + 19200 q^{90} + 7104 q^{91} - 3840 q^{92} + 240 q^{93} + 23184 q^{95} + 2048 q^{96} - 34560 q^{98} - 15970 q^{99} + O(q^{100}) \)

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

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