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Properties

Label 1870.2.v
Level $1870$
Weight $2$
Character orbit 1870.v
Rep. character $\chi_{1870}(111,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $240$
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.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(648\)

Dimensions

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

Total New Old
Modular forms 1328 240 1088
Cusp forms 1264 240 1024
Eisenstein series 64 0 64

Trace form

\( 240 q + O(q^{10}) \) \( 240 q - 240 q^{16} + 32 q^{17} + 32 q^{19} - 32 q^{29} + 32 q^{33} - 64 q^{39} - 32 q^{41} - 32 q^{42} - 64 q^{43} + 64 q^{45} + 64 q^{46} + 128 q^{51} + 128 q^{53} - 96 q^{54} + 32 q^{58} + 32 q^{59} - 96 q^{62} - 224 q^{63} - 64 q^{71} - 32 q^{76} - 64 q^{78} - 32 q^{79} + 96 q^{87} - 128 q^{91} - 32 q^{92} + 64 q^{93} - 64 q^{94} - 64 q^{95} + 64 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1870, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 2}\)