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Properties

Label 1840.4.bo
Level $1840$
Weight $4$
Character orbit 1840.bo
Rep. character $\chi_{1840}(81,\cdot)$
Character field $\Q(\zeta_{11})$
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.bo (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
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

\( 1440 q - 28 q^{7} - 1296 q^{9} + O(q^{10}) \) \( 1440 q - 28 q^{7} - 1296 q^{9} + 40 q^{11} - 60 q^{15} - 24 q^{19} - 136 q^{21} + 164 q^{23} - 3600 q^{25} - 132 q^{27} + 456 q^{29} + 264 q^{31} + 16 q^{37} + 300 q^{39} - 296 q^{41} + 1324 q^{43} + 440 q^{45} + 744 q^{47} - 7160 q^{49} + 744 q^{51} - 752 q^{53} + 900 q^{59} + 912 q^{61} - 1260 q^{63} + 280 q^{65} - 1236 q^{67} - 268 q^{69} + 2800 q^{71} + 7256 q^{77} + 7836 q^{79} - 11048 q^{81} + 936 q^{83} - 240 q^{85} - 20976 q^{87} + 7400 q^{89} - 21136 q^{93} + 4392 q^{97} - 9540 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1840, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 2}\)