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Properties

Label 1856.2.k
Level $1856$
Weight $2$
Character orbit 1856.k
Rep. character $\chi_{1856}(191,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $116$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1856.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 116 \)
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 504 124 380
Cusp forms 456 116 340
Eisenstein series 48 8 40

Trace form

\( 116 q + O(q^{10}) \) \( 116 q + 4 q^{17} - 8 q^{21} - 92 q^{25} + 4 q^{29} - 12 q^{37} + 4 q^{41} - 32 q^{45} - 100 q^{49} + 40 q^{53} + 4 q^{61} + 32 q^{65} - 8 q^{69} + 4 q^{73} - 40 q^{77} - 28 q^{81} - 16 q^{85} + 20 q^{89} + 20 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1856, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(232, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(464, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(928, [\chi])\)\(^{\oplus 2}\)