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Properties

Label 1856.4.bp
Level $1856$
Weight $4$
Character orbit 1856.bp
Rep. character $\chi_{1856}(173,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $5744$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1856.bp (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1856 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1856, [\chi])\).

Total New Old
Modular forms 5776 5776 0
Cusp forms 5744 5744 0
Eisenstein series 32 32 0

Trace form

\( 5744 q - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{9} + O(q^{10}) \) \( 5744 q - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{9} - 16 q^{13} - 16 q^{16} - 16 q^{20} - 960 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} + 1504 q^{28} - 8 q^{29} - 16 q^{30} - 16 q^{34} - 16 q^{35} - 16 q^{36} + 864 q^{38} - 16 q^{42} - 16 q^{45} - 16 q^{49} - 16 q^{51} - 3328 q^{52} - 16 q^{53} - 16 q^{54} - 16 q^{57} + 2368 q^{58} - 16 q^{59} - 144 q^{62} - 10112 q^{63} - 12112 q^{64} - 32 q^{65} + 8144 q^{67} - 16 q^{71} + 5248 q^{74} - 17200 q^{78} - 16 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{86} - 8 q^{87} - 6256 q^{88} - 16 q^{91} - 16 q^{92} - 448 q^{93} - 16 q^{94} - 25856 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1856, [\chi])\) into newform subspaces

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