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Properties

Label 1870.2.bj
Level $1870$
Weight $2$
Character orbit 1870.bj
Rep. character $\chi_{1870}(69,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $384$
Sturm bound $648$

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Defining parameters

Level: \( N \) \(=\) \( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1870.bj (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(648\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1870, [\chi])\).

Total New Old
Modular forms 1328 384 944
Cusp forms 1264 384 880
Eisenstein series 64 0 64

Trace form

\( 384 q + 96 q^{4} - 4 q^{5} - 8 q^{6} + 104 q^{9} + O(q^{10}) \) \( 384 q + 96 q^{4} - 4 q^{5} - 8 q^{6} + 104 q^{9} + 8 q^{10} + 4 q^{11} + 12 q^{14} - 20 q^{15} - 96 q^{16} + 8 q^{19} + 4 q^{20} + 8 q^{24} + 16 q^{25} + 8 q^{26} + 24 q^{29} + 36 q^{30} + 84 q^{35} - 104 q^{36} + 80 q^{39} + 12 q^{40} - 92 q^{41} - 4 q^{44} - 48 q^{45} - 8 q^{46} + 124 q^{49} + 8 q^{50} - 8 q^{51} - 80 q^{54} - 4 q^{55} + 8 q^{56} - 72 q^{59} - 20 q^{60} - 24 q^{61} + 96 q^{64} - 120 q^{65} + 144 q^{66} - 8 q^{69} - 80 q^{70} + 8 q^{71} - 176 q^{75} - 8 q^{76} + 64 q^{79} - 4 q^{80} + 144 q^{81} - 8 q^{85} + 80 q^{86} + 224 q^{89} - 20 q^{90} + 100 q^{91} + 52 q^{94} + 112 q^{95} - 8 q^{96} - 116 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1870, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1870, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1870, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(935, [\chi])\)\(^{\oplus 2}\)