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Properties

Label 342.10.p
Level $342$
Weight $10$
Character orbit 342.p
Rep. character $\chi_{342}(113,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $360$
Sturm bound $600$

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Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 342.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(342, [\chi])\).

Total New Old
Modular forms 1088 360 728
Cusp forms 1072 360 712
Eisenstein series 16 0 16

Trace form

\( 360 q - 46080 q^{4} - 3040 q^{6} - 1368 q^{7} + 13870 q^{9} + O(q^{10}) \) \( 360 q - 46080 q^{4} - 3040 q^{6} - 1368 q^{7} + 13870 q^{9} + 151050 q^{11} - 11796480 q^{16} + 52830 q^{19} - 8435544 q^{23} - 778240 q^{24} + 70312500 q^{25} + 700416 q^{28} - 5230016 q^{30} + 3550720 q^{36} - 17854032 q^{38} - 5299578 q^{39} - 36339104 q^{42} - 17605818 q^{43} + 215180168 q^{45} - 178853286 q^{47} - 1020454740 q^{49} - 437636128 q^{54} + 279069531 q^{57} + 325679760 q^{61} + 335894744 q^{63} + 6039797760 q^{64} - 259787456 q^{66} - 901289472 q^{68} - 1211390676 q^{73} - 939284448 q^{74} - 6762240 q^{76} + 1952310192 q^{77} - 730577186 q^{81} - 1097803584 q^{82} - 2165644632 q^{83} + 2903353854 q^{87} + 2159499264 q^{92} + 4719176388 q^{93} + 192654576 q^{95} + 398458880 q^{96} - 3729764068 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(342, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(342, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)