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Properties

Label 256.6.i
Level $256$
Weight $6$
Character orbit 256.i
Rep. character $\chi_{256}(17,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $312$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 256.i (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(256, [\chi])\).

Total New Old
Modular forms 1312 328 984
Cusp forms 1248 312 936
Eisenstein series 64 16 48

Trace form

\( 312 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + O(q^{10}) \) \( 312 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 41752 q^{51} - 8 q^{53} + 220104 q^{55} - 8 q^{57} - 57912 q^{59} - 8 q^{61} - 317504 q^{63} - 16 q^{65} - 122312 q^{67} - 8 q^{69} + 287688 q^{71} - 8 q^{73} + 386504 q^{75} - 8 q^{77} - 355352 q^{79} - 8 q^{81} + 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} + 1936 q^{93} - 1936 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(256, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(256, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(256, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)