Properties

Label 1870.2.s
Level $1870$
Weight $2$
Character orbit 1870.s
Rep. character $\chi_{1870}(1143,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $216$
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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 935 \)
Character field: \(\Q(i)\)
Sturm bound: \(648\)

Dimensions

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

Total New Old
Modular forms 664 216 448
Cusp forms 632 216 416
Eisenstein series 32 0 32

Trace form

\( 216 q + 8 q^{5} + 248 q^{9} + O(q^{10}) \) \( 216 q + 8 q^{5} + 248 q^{9} + 8 q^{11} + 16 q^{15} - 216 q^{16} - 8 q^{20} + 16 q^{25} - 16 q^{31} + 8 q^{33} + 8 q^{44} + 40 q^{45} - 216 q^{49} + 8 q^{55} + 48 q^{67} - 16 q^{71} - 48 q^{75} - 8 q^{77} - 8 q^{80} + 344 q^{81} - 16 q^{86} + 16 q^{88} - 16 q^{91} + 16 q^{92} + 96 q^{99} + O(q^{100}) \)

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

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