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Properties

Label 392.6.u
Level $392$
Weight $6$
Character orbit 392.u
Rep. character $\chi_{392}(27,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1668$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 392.u (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 392 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(392, [\chi])\).

Total New Old
Modular forms 1692 1692 0
Cusp forms 1668 1668 0
Eisenstein series 24 24 0

Trace form

\( 1668 q - 5 q^{2} - 14 q^{3} - 5 q^{4} - 7 q^{6} - 251 q^{8} + 22184 q^{9} + O(q^{10}) \) \( 1668 q - 5 q^{2} - 14 q^{3} - 5 q^{4} - 7 q^{6} - 251 q^{8} + 22184 q^{9} - 7 q^{10} - 10 q^{11} + 3808 q^{12} + 3059 q^{14} - 765 q^{16} - 14 q^{17} + 3576 q^{18} - 7 q^{20} + 5087 q^{22} - 385 q^{24} - 168760 q^{25} - 7 q^{26} - 14 q^{27} - 32592 q^{28} + 2952 q^{30} + 9415 q^{32} - 14 q^{33} - 27811 q^{34} + 3850 q^{35} + 25337 q^{36} + 217 q^{38} + 105217 q^{40} - 14 q^{41} + 5313 q^{42} - 10 q^{43} - 28295 q^{44} - 39259 q^{46} - 14644 q^{49} + 225944 q^{50} - 17342 q^{51} - 7 q^{52} - 1708 q^{54} + 211274 q^{56} + 28196 q^{57} + 75021 q^{58} - 14 q^{59} - 65419 q^{60} - 231 q^{62} - 27107 q^{64} + 12490 q^{65} - 58667 q^{66} + 89232 q^{67} - 272573 q^{70} - 45188 q^{72} - 14 q^{73} + 154269 q^{74} - 14 q^{75} + 80766 q^{76} + 433677 q^{78} - 1944164 q^{81} + 370258 q^{82} - 14 q^{83} - 233590 q^{84} - 44999 q^{86} - 404413 q^{88} - 14 q^{89} + 383124 q^{90} + 798658 q^{91} - 193666 q^{92} - 185080 q^{94} + 748174 q^{96} - 593873 q^{98} + 235200 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(392, [\chi])\) into newform subspaces

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