Properties

Label 1856.2.n
Level $1856$
Weight $2$
Character orbit 1856.n
Rep. character $\chi_{1856}(465,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $112$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1856.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 496 112 384
Cusp forms 464 112 352
Eisenstein series 32 0 32

Trace form

\( 112 q + O(q^{10}) \) \( 112 q + 16 q^{15} + 16 q^{19} - 24 q^{31} - 24 q^{35} + 32 q^{43} + 40 q^{47} - 112 q^{49} + 24 q^{51} - 32 q^{59} + 32 q^{61} + 24 q^{67} + 32 q^{69} - 32 q^{75} + 8 q^{79} - 112 q^{81} - 32 q^{85} + 8 q^{91} - 16 q^{95} - 64 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1856, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(464, [\chi])\)\(^{\oplus 3}\)