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Properties

Label 1610.2.be
Level $1610$
Weight $2$
Character orbit 1610.be
Rep. character $\chi_{1610}(111,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $640$
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.be (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 2960 640 2320
Cusp forms 2800 640 2160
Eisenstein series 160 0 160

Trace form

\( 640 q - 64 q^{4} + 72 q^{9} + O(q^{10}) \) \( 640 q - 64 q^{4} + 72 q^{9} - 64 q^{16} - 32 q^{18} + 132 q^{21} + 24 q^{23} - 64 q^{25} - 16 q^{29} - 14 q^{35} + 72 q^{36} + 48 q^{39} + 88 q^{43} - 78 q^{49} + 88 q^{51} - 22 q^{56} + 160 q^{58} - 220 q^{63} - 64 q^{64} - 12 q^{70} + 24 q^{71} + 144 q^{72} - 196 q^{77} - 16 q^{78} + 176 q^{79} - 16 q^{81} - 22 q^{84} + 8 q^{85} + 44 q^{86} + 24 q^{92} + 16 q^{93} - 32 q^{95} + 264 q^{99} + O(q^{100}) \)

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

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