Properties

Label 1856.4.n
Level $1856$
Weight $4$
Character orbit 1856.n
Rep. character $\chi_{1856}(465,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $336$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1856.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
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 336 1120
Cusp forms 1424 336 1088
Eisenstein series 32 0 32

Trace form

\( 336 q + O(q^{10}) \) \( 336 q - 240 q^{15} - 48 q^{19} + 744 q^{31} + 456 q^{35} - 864 q^{43} - 1880 q^{47} - 16464 q^{49} - 2888 q^{51} + 1376 q^{59} - 1824 q^{61} + 1848 q^{67} - 1056 q^{69} - 2208 q^{75} - 8824 q^{79} - 27216 q^{81} - 5120 q^{83} - 480 q^{85} + 3496 q^{91} + 13808 q^{95} + 5312 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1856, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(464, [\chi])\)\(^{\oplus 3}\)