Properties

Label 1856.4.cc
Level $1856$
Weight $4$
Character orbit 1856.cc
Rep. character $\chi_{1856}(15,\cdot)$
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.cc (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 464 \)
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 8736 2184 6552
Cusp forms 8544 2136 6408
Eisenstein series 192 48 144

Trace form

\( 2136 q + 14 q^{3} - 14 q^{5} + 20 q^{7} + 3132 q^{9} + O(q^{10}) \) \( 2136 q + 14 q^{3} - 14 q^{5} + 20 q^{7} + 3132 q^{9} + 110 q^{11} - 14 q^{13} + 108 q^{15} - 24 q^{17} + 14 q^{19} - 14 q^{21} + 20 q^{23} + 14 q^{27} - 212 q^{29} - 28 q^{33} + 14 q^{35} - 26 q^{37} - 576 q^{39} - 798 q^{43} + 490 q^{45} - 16288 q^{49} - 256 q^{51} + 742 q^{53} + 24 q^{55} - 216 q^{57} + 24 q^{59} - 10 q^{61} + 216 q^{63} - 20 q^{65} + 2054 q^{67} - 14 q^{69} + 28 q^{71} - 1776 q^{73} - 3672 q^{75} - 542 q^{77} + 3600 q^{79} - 26264 q^{81} + 10 q^{83} + 1240 q^{85} + 24 q^{87} + 88 q^{89} - 1786 q^{91} + 10558 q^{93} + 500 q^{95} - 24 q^{97} - 984 q^{99} + O(q^{100}) \)

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

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