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Properties

Label 1710.2.bb
Level $1710$
Weight $2$
Character orbit 1710.bb
Rep. character $\chi_{1710}(221,\cdot)$
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.bb (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

\( 160 q - 6 q^{3} - 80 q^{4} + 2 q^{6} + 4 q^{7} - 2 q^{9} + O(q^{10}) \) \( 160 q - 6 q^{3} - 80 q^{4} + 2 q^{6} + 4 q^{7} - 2 q^{9} - 6 q^{11} - 12 q^{13} - 80 q^{16} - 12 q^{17} + 14 q^{19} + 2 q^{24} - 160 q^{25} + 4 q^{28} - 72 q^{29} + 12 q^{31} - 6 q^{33} - 2 q^{36} + 6 q^{38} - 40 q^{39} + 12 q^{41} - 12 q^{42} + 8 q^{43} + 6 q^{44} - 8 q^{45} + 6 q^{48} - 84 q^{49} - 36 q^{51} + 12 q^{52} - 48 q^{53} + 8 q^{54} + 10 q^{57} + 108 q^{59} - 56 q^{61} - 36 q^{62} - 84 q^{63} + 160 q^{64} + 22 q^{66} + 102 q^{67} + 12 q^{68} - 60 q^{69} + 6 q^{72} - 34 q^{73} + 84 q^{74} + 6 q^{75} - 16 q^{76} + 36 q^{78} - 12 q^{79} + 30 q^{81} - 6 q^{82} - 12 q^{83} - 36 q^{87} - 18 q^{88} - 36 q^{89} + 24 q^{90} + 12 q^{91} + 16 q^{93} - 4 q^{96} + 18 q^{97} + 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)