Properties

Label 1610.2.bt
Level $1610$
Weight $2$
Character orbit 1610.bt
Rep. character $\chi_{1610}(37,\cdot)$
Character field $\Q(\zeta_{132})$
Dimension $3840$
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.bt (of order \(132\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 805 \)
Character field: \(\Q(\zeta_{132})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 11840 3840 8000
Cusp forms 11200 3840 7360
Eisenstein series 640 0 640

Trace form

\( 3840q + 16q^{6} + O(q^{10}) \) \( 3840q + 16q^{6} - 192q^{16} + 72q^{18} + 68q^{23} + 8q^{25} - 8q^{26} - 88q^{28} + 8q^{31} + 8q^{35} - 368q^{36} + 88q^{37} + 32q^{41} - 16q^{46} + 8q^{47} + 44q^{56} - 176q^{57} + 352q^{61} + 48q^{62} - 80q^{70} - 16q^{71} - 16q^{72} - 56q^{73} + 96q^{77} - 64q^{78} - 160q^{81} + 32q^{82} + 136q^{85} - 44q^{86} + 112q^{87} + 40q^{92} - 8q^{93} + 140q^{95} + 8q^{96} - 168q^{98} + O(q^{100}) \)

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

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