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Properties

Label 1610.2.q
Level $1610$
Weight $2$
Character orbit 1610.q
Rep. character $\chi_{1610}(599,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $176$
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.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 592 176 416
Cusp forms 560 176 384
Eisenstein series 32 0 32

Trace form

\( 176 q + 88 q^{4} + 16 q^{6} + 80 q^{9} + O(q^{10}) \) \( 176 q + 88 q^{4} + 16 q^{6} + 80 q^{9} - 4 q^{10} + 8 q^{11} + 32 q^{15} - 88 q^{16} + 16 q^{19} - 8 q^{21} + 8 q^{24} + 4 q^{25} - 24 q^{26} + 8 q^{29} - 12 q^{30} + 36 q^{31} - 56 q^{35} + 160 q^{36} - 40 q^{39} + 4 q^{40} - 8 q^{44} - 68 q^{45} - 12 q^{49} + 64 q^{50} + 40 q^{51} + 32 q^{54} - 24 q^{55} + 28 q^{59} + 16 q^{60} - 16 q^{61} - 176 q^{64} - 12 q^{65} + 32 q^{66} - 32 q^{69} + 28 q^{70} - 8 q^{71} + 24 q^{74} + 40 q^{75} + 32 q^{76} - 48 q^{79} - 24 q^{81} + 56 q^{84} - 16 q^{85} + 8 q^{86} - 40 q^{89} - 72 q^{90} + 32 q^{91} + 16 q^{94} - 4 q^{95} - 8 q^{96} - 112 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1610, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(805, [\chi])\)\(^{\oplus 2}\)