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Properties

Label 1856.2.q
Level $1856$
Weight $2$
Character orbit 1856.q
Rep. character $\chi_{1856}(1119,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $120$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1856.q (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 232 \)
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 504 120 384
Cusp forms 456 120 336
Eisenstein series 48 0 48

Trace form

\( 120 q + O(q^{10}) \) \( 120 q - 24 q^{17} + 168 q^{25} + 24 q^{41} - 120 q^{49} + 24 q^{73} - 312 q^{81} + 72 q^{89} + 120 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1856, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(232, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(464, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(928, [\chi])\)\(^{\oplus 2}\)