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Properties

Label 1870.2.cj
Level $1870$
Weight $2$
Character orbit 1870.cj
Rep. character $\chi_{1870}(117,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $1728$
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.cj (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

\( 1728 q - 432 q^{4} + 16 q^{5} + 40 q^{7} + O(q^{10}) \) \( 1728 q - 432 q^{4} + 16 q^{5} + 40 q^{7} - 432 q^{16} + 16 q^{20} - 16 q^{22} - 16 q^{23} - 16 q^{25} + 32 q^{31} + 16 q^{33} + 32 q^{37} + 80 q^{39} + 80 q^{45} - 64 q^{49} + 80 q^{52} + 16 q^{55} - 160 q^{57} - 144 q^{59} + 200 q^{63} - 432 q^{64} - 64 q^{66} - 32 q^{67} + 64 q^{75} - 48 q^{77} + 80 q^{79} - 24 q^{80} + 32 q^{82} + 80 q^{85} + 32 q^{86} - 16 q^{88} - 32 q^{89} - 144 q^{91} - 16 q^{92} + 40 q^{95} + 64 q^{97} + O(q^{100}) \)

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

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