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Properties

Label 1840.2.cw
Level $1840$
Weight $2$
Character orbit 1840.cw
Rep. character $\chi_{1840}(11,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $3840$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.cw (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 368 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1840, [\chi])\).

Total New Old
Modular forms 5840 3840 2000
Cusp forms 5680 3840 1840
Eisenstein series 160 0 160

Trace form

\( 3840 q + 8 q^{4} - 12 q^{6} + O(q^{10}) \) \( 3840 q + 8 q^{4} - 12 q^{6} - 12 q^{12} - 32 q^{16} + 40 q^{18} + 16 q^{23} + 8 q^{24} + 24 q^{27} - 32 q^{29} + 44 q^{34} + 20 q^{36} - 220 q^{38} - 48 q^{39} - 356 q^{46} + 80 q^{48} + 384 q^{49} + 36 q^{50} - 64 q^{52} - 144 q^{54} + 144 q^{58} + 24 q^{59} + 60 q^{62} + 44 q^{64} - 16 q^{69} - 188 q^{72} - 144 q^{77} + 92 q^{78} + 384 q^{81} - 36 q^{82} - 32 q^{85} - 12 q^{92} + 480 q^{93} - 72 q^{94} + 136 q^{96} - 208 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1840, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 2}\)