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Properties

Label 1024.4.k
Level $1024$
Weight $4$
Character orbit 1024.k
Rep. character $\chi_{1024}(33,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $1504$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 1024 = 2^{10} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1024.k (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 128 \)
Character field: \(\Q(\zeta_{32})\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1024, [\chi])\).

Total New Old
Modular forms 6272 1568 4704
Cusp forms 6016 1504 4512
Eisenstein series 256 64 192

Trace form

\( 1504 q + 32 q^{5} - 32 q^{9} + O(q^{10}) \) \( 1504 q + 32 q^{5} - 32 q^{9} + 32 q^{13} - 32 q^{17} + 32 q^{21} - 32 q^{25} + 32 q^{29} - 32 q^{33} + 32 q^{37} - 32 q^{41} + 32 q^{45} - 32 q^{49} + 32 q^{53} - 32 q^{57} + 32 q^{61} + 32 q^{69} - 32 q^{73} + 32 q^{77} - 32 q^{81} + 32 q^{85} - 32 q^{89} + 32 q^{93} - 32 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1024, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1024, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1024, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 2}\)