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Properties

Label 1610.2.k
Level $1610$
Weight $2$
Character orbit 1610.k
Rep. character $\chi_{1610}(183,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 592 144 448
Cusp forms 560 144 416
Eisenstein series 32 0 32

Trace form

\( 144 q - 16 q^{3} + O(q^{10}) \) \( 144 q - 16 q^{3} - 16 q^{12} + 32 q^{13} - 144 q^{16} + 16 q^{18} + 8 q^{23} + 32 q^{25} + 32 q^{27} + 32 q^{31} + 144 q^{36} - 64 q^{41} + 16 q^{46} + 16 q^{48} + 16 q^{50} + 32 q^{52} - 16 q^{62} + 16 q^{70} + 192 q^{71} + 16 q^{72} - 64 q^{73} + 16 q^{75} + 64 q^{78} - 176 q^{81} + 16 q^{82} - 16 q^{85} + 48 q^{87} + 8 q^{92} + 80 q^{93} + 128 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1610, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(805, [\chi])\)\(^{\oplus 2}\)