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Properties

Label 1856.4.cb
Level $1856$
Weight $4$
Character orbit 1856.cb
Rep. character $\chi_{1856}(127,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $2136$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1856.cb (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 116 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 8784 2184 6600
Cusp forms 8496 2136 6360
Eisenstein series 288 48 240

Trace form

\( 2136 q + 28 q^{5} - 28 q^{9} + O(q^{10}) \) \( 2136 q + 28 q^{5} - 28 q^{9} + 28 q^{13} + 80 q^{17} + 132 q^{21} + 8304 q^{25} + 24 q^{29} - 28 q^{33} + 8 q^{37} - 496 q^{41} + 1020 q^{45} + 16248 q^{49} - 1484 q^{53} + 24 q^{61} - 1020 q^{65} + 132 q^{69} + 272 q^{73} + 3300 q^{77} + 31152 q^{81} + 524 q^{85} + 1760 q^{89} + 28 q^{93} - 7944 q^{97} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(1856, [\chi])\) into lower level spaces

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