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Properties

Label 342.4.p
Level $342$
Weight $4$
Character orbit 342.p
Rep. character $\chi_{342}(113,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 342.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(342, [\chi])\).

Total New Old
Modular forms 368 120 248
Cusp forms 352 120 232
Eisenstein series 16 0 16

Trace form

\( 120 q - 240 q^{4} + 20 q^{6} - 24 q^{7} + 10 q^{9} + O(q^{10}) \) \( 120 q - 240 q^{4} + 20 q^{6} - 24 q^{7} + 10 q^{9} - 150 q^{11} - 960 q^{16} - 210 q^{19} - 312 q^{23} + 80 q^{24} + 1500 q^{25} + 192 q^{28} - 584 q^{30} + 40 q^{36} - 282 q^{38} - 450 q^{39} + 1060 q^{42} - 426 q^{43} - 2344 q^{45} - 2478 q^{47} - 3420 q^{49} - 1156 q^{54} + 177 q^{57} - 1680 q^{61} + 1928 q^{63} + 7680 q^{64} + 856 q^{66} - 1608 q^{68} - 2172 q^{73} - 564 q^{74} + 420 q^{76} + 9744 q^{77} + 874 q^{81} + 2088 q^{82} + 3336 q^{83} + 4758 q^{87} + 1248 q^{92} - 6516 q^{93} - 8136 q^{95} - 640 q^{96} - 8548 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(342, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(342, [\chi]) \cong \)