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Properties

Label 1280.4.bf
Level $1280$
Weight $4$
Character orbit 1280.bf
Rep. character $\chi_{1280}(49,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1136$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1280.bf (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 320 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 4672 1168 3504
Cusp forms 4544 1136 3408
Eisenstein series 128 32 96

Trace form

\( 1136 q - 8 q^{5} - 16 q^{9} + O(q^{10}) \) \( 1136 q - 8 q^{5} - 16 q^{9} + 16 q^{11} + 8 q^{15} + 16 q^{19} - 16 q^{21} - 8 q^{25} - 16 q^{29} + 8 q^{35} + 16 q^{39} - 16 q^{41} - 8 q^{45} - 16 q^{49} - 2960 q^{51} + 584 q^{55} - 2736 q^{59} - 16 q^{61} - 16 q^{65} - 16 q^{69} + 464 q^{71} + 4424 q^{75} + 5680 q^{79} - 16 q^{81} - 8 q^{85} - 16 q^{89} + 16 q^{91} + 448 q^{99} + O(q^{100}) \)

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

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