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Properties

Label 1856.4.j
Level $1856$
Weight $4$
Character orbit 1856.j
Rep. character $\chi_{1856}(911,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $356$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1856.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 464 \)
Character field: \(\Q(i)\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1456 364 1092
Cusp forms 1424 356 1068
Eisenstein series 32 8 24

Trace form

\( 356 q + 8 q^{7} - 3132 q^{9} + O(q^{10}) \) \( 356 q + 8 q^{7} - 3132 q^{9} + 44 q^{11} - 108 q^{15} - 4 q^{17} + 8 q^{23} + 198 q^{29} + 12 q^{37} + 604 q^{39} + 812 q^{43} - 504 q^{45} + 16260 q^{49} - 108 q^{51} - 756 q^{53} + 4 q^{55} + 216 q^{57} + 4 q^{59} - 4 q^{61} - 216 q^{63} - 8 q^{65} - 2040 q^{67} - 296 q^{73} + 3700 q^{75} + 528 q^{77} + 600 q^{79} + 26236 q^{81} + 4 q^{83} + 496 q^{85} + 4 q^{87} - 88 q^{89} + 1800 q^{91} + 4380 q^{93} - 500 q^{95} - 4 q^{97} + 1012 q^{99} + O(q^{100}) \)

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

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