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Properties

Label 1028.6.k
Level $1028$
Weight $6$
Character orbit 1028.k
Rep. character $\chi_{1028}(17,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $1728$
Sturm bound $774$

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Defining parameters

Level: \( N \) \(=\) \( 1028 = 2^{2} \cdot 257 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1028.k (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 257 \)
Character field: \(\Q(\zeta_{32})\)
Sturm bound: \(774\)

Dimensions

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

Total New Old
Modular forms 10368 1728 8640
Cusp forms 10272 1728 8544
Eisenstein series 96 0 96

Trace form

\( 1728 q + O(q^{10}) \) \( 1728 q - 7648 q^{15} - 12496 q^{17} + 11344 q^{33} - 34512 q^{35} - 80112 q^{37} - 37088 q^{49} - 130384 q^{57} + 270016 q^{59} + 50272 q^{61} - 413312 q^{63} - 55760 q^{65} + 405536 q^{67} + 190048 q^{69} - 54688 q^{71} + 106864 q^{73} + 218352 q^{77} - 60224 q^{79} - 527472 q^{81} + 412752 q^{83} - 276512 q^{89} + 1136192 q^{97} - 919600 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{6}^{\mathrm{old}}(1028, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1028, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(257, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(514, [\chi])\)\(^{\oplus 2}\)