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Properties

Label 1610.2.bm
Level $1610$
Weight $2$
Character orbit 1610.bm
Rep. character $\chi_{1610}(61,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $1280$
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.bm (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
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 1280 4640
Cusp forms 5600 1280 4320
Eisenstein series 320 0 320

Trace form

\( 1280 q + 64 q^{4} - 60 q^{9} + O(q^{10}) \) \( 1280 q + 64 q^{4} - 60 q^{9} + 64 q^{16} - 16 q^{18} + 264 q^{21} + 12 q^{23} + 12 q^{24} + 64 q^{25} - 36 q^{26} + 16 q^{29} - 12 q^{31} + 14 q^{35} + 120 q^{36} + 24 q^{39} + 176 q^{43} - 12 q^{46} + 72 q^{47} - 6 q^{49} - 88 q^{51} + 108 q^{54} + 22 q^{56} + 56 q^{58} + 108 q^{59} + 220 q^{63} - 128 q^{64} + 12 q^{70} - 120 q^{71} + 72 q^{72} + 72 q^{73} + 220 q^{77} - 32 q^{78} + 88 q^{79} + 40 q^{81} + 22 q^{84} - 8 q^{85} + 22 q^{86} + 444 q^{87} - 24 q^{92} - 40 q^{93} - 60 q^{94} - 16 q^{95} - 12 q^{96} - 264 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1610, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(805, [\chi])\)\(^{\oplus 2}\)