↑

Properties

Label 1870.2.ce
Level $1870$
Weight $2$
Character orbit 1870.ce
Rep. character $\chi_{1870}(9,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $1728$
Sturm bound $648$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1870.ce (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 935 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(648\)

Dimensions

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

Total New Old
Modular forms 5312 1728 3584
Cusp forms 5056 1728 3328
Eisenstein series 256 0 256

Trace form

\( 1728 q + 16 q^{5} + O(q^{10}) \) \( 1728 q + 16 q^{5} + 16 q^{11} + 432 q^{16} - 16 q^{25} - 32 q^{31} - 32 q^{34} + 64 q^{39} + 16 q^{44} - 64 q^{46} - 176 q^{49} + 32 q^{51} + 96 q^{54} + 144 q^{59} + 48 q^{61} + 64 q^{65} - 64 q^{66} + 96 q^{69} - 64 q^{75} - 64 q^{79} + 24 q^{80} - 64 q^{84} + 88 q^{85} - 32 q^{86} + 208 q^{91} - 152 q^{95} + 176 q^{99} + O(q^{100}) \)

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

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