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Properties

Label 1716.2.bg
Level $1716$
Weight $2$
Character orbit 1716.bg
Rep. character $\chi_{1716}(419,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $560$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1716.bg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 156 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1716, [\chi])\).

Total New Old
Modular forms 688 560 128
Cusp forms 656 560 96
Eisenstein series 32 0 32

Trace form

\( 560 q - 6 q^{6} + O(q^{10}) \) \( 560 q - 6 q^{6} + 12 q^{12} + 8 q^{13} + 24 q^{18} - 560 q^{25} - 4 q^{36} - 32 q^{37} + 40 q^{40} - 10 q^{42} - 20 q^{46} + 24 q^{48} + 304 q^{49} - 92 q^{52} + 26 q^{54} + 32 q^{57} + 84 q^{58} + 52 q^{60} + 24 q^{61} - 96 q^{64} - 20 q^{66} - 88 q^{70} - 56 q^{72} + 48 q^{73} + 16 q^{81} - 4 q^{82} + 84 q^{84} - 32 q^{85} - 12 q^{88} - 252 q^{90} - 96 q^{93} - 72 q^{94} - 168 q^{96} - 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1716, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1716, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1716, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)