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Properties

Label 1028.6.q
Level $1028$
Weight $6$
Character orbit 1028.q
Rep. character $\chi_{1028}(3,\cdot)$
Character field $\Q(\zeta_{256})$
Dimension $82304$
Sturm bound $774$

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Defining parameters

Level: \( N \) \(=\) \( 1028 = 2^{2} \cdot 257 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1028.q (of order \(256\) and degree \(128\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1028 \)
Character field: \(\Q(\zeta_{256})\)
Sturm bound: \(774\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1028, [\chi])\).

Total New Old
Modular forms 82816 82816 0
Cusp forms 82304 82304 0
Eisenstein series 512 512 0

Trace form

\( 82304 q - 128 q^{2} - 128 q^{4} - 256 q^{5} - 128 q^{6} - 128 q^{8} - 256 q^{9} + O(q^{10}) \) \( 82304 q - 128 q^{2} - 128 q^{4} - 256 q^{5} - 128 q^{6} - 128 q^{8} - 256 q^{9} - 128 q^{10} - 128 q^{12} - 256 q^{13} - 128 q^{14} - 128 q^{16} - 256 q^{17} - 128 q^{18} - 128 q^{20} - 256 q^{21} - 128 q^{22} - 128 q^{24} - 256 q^{25} - 128 q^{26} - 128 q^{28} - 256 q^{29} - 128 q^{30} - 128 q^{32} - 256 q^{33} - 128 q^{34} - 128 q^{36} - 256 q^{37} - 128 q^{38} - 128 q^{40} - 256 q^{41} - 128 q^{42} - 128 q^{44} - 256 q^{45} - 128 q^{46} - 128 q^{48} - 256 q^{49} - 128 q^{50} - 128 q^{52} - 256 q^{53} - 128 q^{54} - 128 q^{56} - 256 q^{57} - 128 q^{58} - 128 q^{60} - 256 q^{61} - 128 q^{62} - 128 q^{64} - 256 q^{65} - 128 q^{66} - 128 q^{68} - 256 q^{69} - 128 q^{70} - 128 q^{72} - 256 q^{73} - 128 q^{74} - 128 q^{76} - 256 q^{77} - 128 q^{78} - 128 q^{80} - 256 q^{81} - 128 q^{82} - 128 q^{84} - 256 q^{85} - 128 q^{86} - 128 q^{88} - 256 q^{89} - 128 q^{90} - 128 q^{92} - 256 q^{93} - 128 q^{94} - 128 q^{96} - 256 q^{97} - 128 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(1028, [\chi])\) into newform subspaces

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