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Properties

Label 1710.2.ba
Level $1710$
Weight $2$
Character orbit 1710.ba
Rep. character $\chi_{1710}(911,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1710, [\chi])\).

Total New Old
Modular forms 736 160 576
Cusp forms 704 160 544
Eisenstein series 32 0 32

Trace form

\( 160 q - 80 q^{4} - 4 q^{6} - 8 q^{7} + 4 q^{9} + O(q^{10}) \) \( 160 q - 80 q^{4} - 4 q^{6} - 8 q^{7} + 4 q^{9} + 12 q^{11} - 80 q^{16} - 4 q^{19} - 4 q^{24} + 80 q^{25} + 16 q^{28} + 4 q^{36} + 6 q^{38} - 4 q^{39} - 12 q^{42} + 20 q^{43} + 16 q^{45} - 36 q^{47} - 72 q^{49} + 44 q^{54} + 10 q^{57} - 56 q^{61} + 48 q^{63} + 160 q^{64} + 16 q^{66} + 12 q^{68} - 136 q^{73} - 84 q^{74} + 2 q^{76} + 84 q^{81} - 24 q^{82} - 120 q^{83} + 84 q^{87} - 80 q^{93} + 24 q^{95} + 8 q^{96} - 104 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1710, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1710, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \cong \)