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Properties

Label 1670.2.j
Level $1670$
Weight $2$
Character orbit 1670.j
Rep. character $\chi_{1670}(9,\cdot)$
Character field $\Q(\zeta_{166})$
Dimension $6888$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 1670 = 2 \cdot 5 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1670.j (of order \(166\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 835 \)
Character field: \(\Q(\zeta_{166})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1670, [\chi])\).

Total New Old
Modular forms 20992 6888 14104
Cusp forms 20336 6888 13448
Eisenstein series 656 0 656

Trace form

\( 6888 q + 84 q^{4} - 4 q^{6} + 96 q^{9} + O(q^{10}) \) \( 6888 q + 84 q^{4} - 4 q^{6} + 96 q^{9} - 12 q^{11} + 8 q^{14} - 4 q^{15} - 84 q^{16} - 12 q^{19} + 8 q^{21} + 4 q^{24} + 16 q^{25} + 8 q^{26} - 4 q^{29} - 12 q^{30} - 8 q^{31} - 96 q^{36} + 16 q^{41} + 12 q^{44} - 8 q^{45} - 16 q^{46} + 100 q^{49} - 16 q^{50} + 16 q^{54} - 36 q^{55} - 8 q^{56} + 4 q^{60} + 12 q^{61} + 84 q^{64} - 20 q^{65} + 24 q^{66} - 8 q^{69} + 24 q^{70} + 48 q^{71} - 8 q^{74} + 24 q^{75} + 12 q^{76} + 32 q^{79} - 148 q^{81} - 8 q^{84} - 20 q^{85} + 8 q^{86} - 48 q^{89} - 28 q^{90} + 32 q^{91} + 8 q^{94} - 4 q^{96} - 44 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1670, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1670, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1670, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(835, [\chi])\)\(^{\oplus 2}\)