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Properties

Label 1280.4.ba
Level $1280$
Weight $4$
Character orbit 1280.ba
Rep. character $\chi_{1280}(223,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $560$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1280.ba (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1280, [\chi])\).

Total New Old
Modular forms 2368 592 1776
Cusp forms 2240 560 1680
Eisenstein series 128 32 96

Trace form

\( 560 q + 8 q^{5} + O(q^{10}) \) \( 560 q + 8 q^{5} + 8 q^{13} + 16 q^{21} - 8 q^{25} - 16 q^{33} + 8 q^{37} - 16 q^{41} + 8 q^{45} + 22736 q^{49} + 8 q^{53} - 3632 q^{61} - 16 q^{65} + 432 q^{69} + 2752 q^{77} + 8 q^{85} - 208 q^{93} - 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1280, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1280, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1280, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)