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Properties

Label 1610.2.bo
Level $1610$
Weight $2$
Character orbit 1610.bo
Rep. character $\chi_{1610}(9,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $1920$
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.bo (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 805 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 5920 1920 4000
Cusp forms 5600 1920 3680
Eisenstein series 320 0 320

Trace form

\( 1920 q - 96 q^{4} - 4 q^{5} + 8 q^{6} - 92 q^{9} + O(q^{10}) \) \( 1920 q - 96 q^{4} - 4 q^{5} + 8 q^{6} - 92 q^{9} + 4 q^{11} + 4 q^{14} + 16 q^{15} + 96 q^{16} + 12 q^{19} + 36 q^{20} - 4 q^{21} + 4 q^{24} + 40 q^{25} - 4 q^{26} - 48 q^{29} + 44 q^{30} - 4 q^{31} - 32 q^{34} + 4 q^{35} - 184 q^{36} + 16 q^{39} - 4 q^{44} + 20 q^{45} - 16 q^{46} + 130 q^{49} - 16 q^{51} + 48 q^{54} + 72 q^{55} - 26 q^{56} + 24 q^{59} + 8 q^{60} - 172 q^{61} + 192 q^{64} - 138 q^{65} - 32 q^{66} + 44 q^{69} + 64 q^{70} + 8 q^{71} + 4 q^{74} + 220 q^{75} + 24 q^{76} - 56 q^{79} - 4 q^{80} + 184 q^{81} + 14 q^{84} - 44 q^{85} + 42 q^{86} + 60 q^{89} - 48 q^{90} - 72 q^{91} - 20 q^{94} - 50 q^{95} - 4 q^{96} - 400 q^{99} + O(q^{100}) \)

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

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