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Properties

Label 1856.2.bn
Level $1856$
Weight $2$
Character orbit 1856.bn
Rep. character $\chi_{1856}(117,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1792$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1856.bn (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1856, [\chi])\).

Total New Old
Modular forms 1936 1792 144
Cusp forms 1904 1792 112
Eisenstein series 32 0 32

Trace form

\( 1792 q + O(q^{10}) \) \( 1792 q - 80 q^{24} - 80 q^{26} - 160 q^{30} - 80 q^{32} - 80 q^{34} - 160 q^{36} - 80 q^{40} - 80 q^{42} + 48 q^{50} - 64 q^{51} + 48 q^{52} + 128 q^{54} - 128 q^{55} - 128 q^{59} + 96 q^{62} + 96 q^{68} - 128 q^{71} - 128 q^{75} + 128 q^{76} + 48 q^{78} - 64 q^{79} - 80 q^{80} - 160 q^{82} - 224 q^{84} - 208 q^{86} - 304 q^{92} - 192 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1856, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1856, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1856, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)