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Properties

Label 342.4.n
Level $342$
Weight $4$
Character orbit 342.n
Rep. character $\chi_{342}(293,\cdot)$
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.n (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

\( 120 q + 480 q^{4} + 20 q^{6} + 12 q^{7} + 10 q^{9} + O(q^{10}) \) \( 120 q + 480 q^{4} + 20 q^{6} + 12 q^{7} + 10 q^{9} + 75 q^{11} + 384 q^{15} + 1920 q^{16} + 30 q^{17} - 75 q^{19} + 54 q^{22} + 80 q^{24} + 1500 q^{25} + 396 q^{27} + 48 q^{28} - 360 q^{29} + 292 q^{30} - 90 q^{31} - 162 q^{33} + 40 q^{36} - 318 q^{38} - 1002 q^{39} + 15 q^{41} - 296 q^{42} + 600 q^{43} + 300 q^{44} - 880 q^{45} + 2478 q^{47} - 2700 q^{49} - 1128 q^{50} - 1035 q^{51} + 1056 q^{53} + 548 q^{54} + 1746 q^{57} + 1017 q^{59} + 1536 q^{60} + 840 q^{61} + 468 q^{62} + 2108 q^{63} + 7680 q^{64} + 1770 q^{65} - 632 q^{66} + 120 q^{68} + 1362 q^{69} + 2772 q^{71} - 543 q^{73} - 4209 q^{75} - 300 q^{76} - 4872 q^{77} - 2136 q^{78} - 950 q^{81} + 522 q^{82} - 4332 q^{83} + 2994 q^{87} + 216 q^{88} - 990 q^{89} - 240 q^{90} - 990 q^{91} - 1920 q^{93} + 5772 q^{95} + 320 q^{96} + 2232 q^{98} + 2135 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(342, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)