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Properties

Label 1870.2.bi
Level $1870$
Weight $2$
Character orbit 1870.bi
Rep. character $\chi_{1870}(951,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $288$
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.bi (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 187 \)
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 288 1040
Cusp forms 1264 288 976
Eisenstein series 64 0 64

Trace form

\( 288 q - 4 q^{2} - 72 q^{4} - 4 q^{8} + 104 q^{9} + O(q^{10}) \) \( 288 q - 4 q^{2} - 72 q^{4} - 4 q^{8} + 104 q^{9} - 16 q^{13} - 24 q^{15} - 72 q^{16} - 24 q^{17} + 40 q^{18} + 36 q^{19} - 48 q^{21} + 72 q^{25} + 24 q^{26} + 8 q^{30} + 16 q^{32} - 4 q^{33} - 12 q^{34} + 8 q^{35} + 44 q^{36} - 8 q^{38} + 40 q^{42} + 88 q^{43} + 32 q^{47} + 96 q^{49} + 4 q^{50} + 22 q^{51} + 24 q^{52} + 16 q^{53} + 48 q^{55} - 4 q^{59} + 16 q^{60} - 72 q^{64} - 40 q^{66} - 72 q^{67} - 24 q^{68} - 32 q^{69} - 20 q^{72} - 24 q^{76} + 72 q^{77} - 60 q^{81} - 4 q^{83} - 48 q^{84} - 24 q^{85} + 52 q^{86} + 16 q^{87} - 80 q^{89} + 88 q^{93} - 128 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1870, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(374, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(935, [\chi])\)\(^{\oplus 2}\)