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Properties

Label 1280.3.bi
Level $1280$
Weight $3$
Character orbit 1280.bi
Rep. character $\chi_{1280}(177,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $752$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1280.bi (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 320 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1280, [\chi])\).

Total New Old
Modular forms 3136 784 2352
Cusp forms 3008 752 2256
Eisenstein series 128 32 96

Trace form

\( 752 q + 8 q^{3} - 8 q^{5} + 8 q^{7} + O(q^{10}) \) \( 752 q + 8 q^{3} - 8 q^{5} + 8 q^{7} + 16 q^{11} - 8 q^{13} + 8 q^{15} - 16 q^{17} - 16 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{35} - 8 q^{37} - 16 q^{41} + 8 q^{43} - 80 q^{45} + 16 q^{47} - 368 q^{51} - 8 q^{53} + 8 q^{55} - 8 q^{57} - 16 q^{61} + 16 q^{63} - 16 q^{65} + 8 q^{67} + 384 q^{69} + 528 q^{71} - 8 q^{73} + 8 q^{75} - 8 q^{77} - 512 q^{79} - 16 q^{81} + 8 q^{83} - 208 q^{85} + 904 q^{87} + 16 q^{91} + 64 q^{93} - 512 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1280, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1280, [\chi])\) into lower level spaces

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