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Properties

Label 1840.4.bw
Level $1840$
Weight $4$
Character orbit 1840.bw
Rep. character $\chi_{1840}(111,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1440$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1840.bw (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 92 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1840, [\chi])\).

Total New Old
Modular forms 8760 1440 7320
Cusp forms 8520 1440 7080
Eisenstein series 240 0 240

Trace form

\( 1440 q + 1296 q^{9} + O(q^{10}) \) \( 1440 q + 1296 q^{9} + 3600 q^{25} - 168 q^{29} - 888 q^{41} - 7368 q^{49} + 1596 q^{69} - 3936 q^{77} - 9816 q^{81} - 22440 q^{89} - 672 q^{93} - 16104 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1840, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1840, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1840, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 2}\)