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Properties

Label 392.4.z
Level $392$
Weight $4$
Character orbit 392.z
Rep. character $\chi_{392}(37,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1992$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 392.z (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 392 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(392, [\chi])\).

Total New Old
Modular forms 2040 2040 0
Cusp forms 1992 1992 0
Eisenstein series 48 48 0

Trace form

\( 1992 q - 13 q^{2} - 13 q^{4} + 6 q^{6} - 24 q^{7} + 32 q^{8} - 1484 q^{9} + O(q^{10}) \) \( 1992 q - 13 q^{2} - 13 q^{4} + 6 q^{6} - 24 q^{7} + 32 q^{8} - 1484 q^{9} + 481 q^{12} + 59 q^{14} + 88 q^{15} + 15 q^{16} - 26 q^{17} - 14 q^{18} - 270 q^{20} + 258 q^{22} - 26 q^{23} + 430 q^{24} - 3976 q^{25} + 288 q^{26} + 502 q^{28} + 99 q^{30} - 2244 q^{31} + 267 q^{32} + 82 q^{33} - 1686 q^{34} - 784 q^{36} - 122 q^{38} - 80 q^{39} - 168 q^{40} - 20 q^{41} + 1696 q^{42} + 2194 q^{44} + 356 q^{46} + 710 q^{47} - 964 q^{48} - 384 q^{49} + 4788 q^{50} - 110 q^{52} - 1147 q^{54} + 2240 q^{55} - 112 q^{56} + 46 q^{57} + 140 q^{58} - 3856 q^{60} - 1374 q^{62} - 696 q^{63} + 1796 q^{64} - 276 q^{65} + 4634 q^{66} + 57 q^{68} - 7006 q^{70} - 580 q^{71} + 7574 q^{72} + 190 q^{73} - 634 q^{74} - 2789 q^{76} - 4224 q^{78} - 12 q^{79} - 1856 q^{80} + 16998 q^{81} + 16232 q^{82} - 8260 q^{84} + 5957 q^{86} - 2168 q^{87} + 679 q^{88} - 450 q^{89} - 7068 q^{90} - 10750 q^{92} - 11828 q^{94} + 656 q^{95} + 17074 q^{96} - 1728 q^{97} - 10833 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(392, [\chi])\) into newform subspaces

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