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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

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

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

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