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Properties

Label 1024.4.m
Level $1024$
Weight $4$
Character orbit 1024.m
Rep. character $\chi_{1024}(17,\cdot)$
Character field $\Q(\zeta_{64})$
Dimension $3040$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 1024 = 2^{10} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1024.m (of order \(64\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 256 \)
Character field: \(\Q(\zeta_{64})\)
Sturm bound: \(512\)

Dimensions

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

Total New Old
Modular forms 12416 3104 9312
Cusp forms 12160 3040 9120
Eisenstein series 256 64 192

Trace form

\( 3040 q + 32 q^{3} - 32 q^{5} + 32 q^{7} - 32 q^{9} + O(q^{10}) \) \( 3040 q + 32 q^{3} - 32 q^{5} + 32 q^{7} - 32 q^{9} + 32 q^{11} - 32 q^{13} + 32 q^{15} - 32 q^{17} + 32 q^{19} - 32 q^{21} + 32 q^{23} - 32 q^{25} + 32 q^{27} - 32 q^{29} + 32 q^{31} - 32 q^{33} + 32 q^{35} - 32 q^{37} + 32 q^{39} - 32 q^{41} + 32 q^{43} - 32 q^{45} + 32 q^{47} - 32 q^{49} + 32 q^{51} - 32 q^{53} + 32 q^{55} - 32 q^{57} + 32 q^{59} - 32 q^{61} + 32 q^{63} - 32 q^{65} + 32 q^{67} - 32 q^{69} + 32 q^{71} - 32 q^{73} + 32 q^{75} - 32 q^{77} + 32 q^{79} - 32 q^{81} + 32 q^{83} - 32 q^{85} + 32 q^{87} - 32 q^{89} + 32 q^{91} - 32 q^{93} + 32 q^{95} - 32 q^{97} + 32 q^{99} + O(q^{100}) \)

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

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