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Properties

Label 1610.2.o
Level $1610$
Weight $2$
Character orbit 1610.o
Rep. character $\chi_{1610}(229,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1610 = 2 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1610.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 805 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1610, [\chi])\).

Total New Old
Modular forms 592 192 400
Cusp forms 560 192 368
Eisenstein series 32 0 32

Trace form

\( 192 q + 96 q^{4} - 100 q^{9} + O(q^{10}) \) \( 192 q + 96 q^{4} - 100 q^{9} - 96 q^{16} - 12 q^{24} + 4 q^{25} + 12 q^{26} - 48 q^{29} - 12 q^{31} - 20 q^{35} - 200 q^{36} + 16 q^{39} + 4 q^{46} - 36 q^{54} + 60 q^{59} - 192 q^{64} - 24 q^{70} - 8 q^{71} - 96 q^{75} - 56 q^{81} + 32 q^{85} + 108 q^{94} - 28 q^{95} - 12 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1610, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1610, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1610, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(805, [\chi])\)\(^{\oplus 2}\)