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Properties

Label 1870.2.ck
Level $1870$
Weight $2$
Character orbit 1870.ck
Rep. character $\chi_{1870}(291,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $1152$
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.ck (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 187 \)
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 1152 4160
Cusp forms 5056 1152 3904
Eisenstein series 256 0 256

Trace form

\( 1152 q - 16 q^{9} + O(q^{10}) \) \( 1152 q - 16 q^{9} - 8 q^{11} + 16 q^{12} + 32 q^{14} + 48 q^{15} + 288 q^{16} + 48 q^{17} + 16 q^{18} + 16 q^{22} - 64 q^{23} - 24 q^{24} - 72 q^{27} + 128 q^{31} - 32 q^{33} - 32 q^{34} - 32 q^{35} + 24 q^{36} + 32 q^{37} + 64 q^{39} - 144 q^{41} - 32 q^{42} + 112 q^{43} + 32 q^{49} + 16 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} + 16 q^{54} + 40 q^{57} - 32 q^{58} + 56 q^{59} + 32 q^{60} + 96 q^{61} - 144 q^{63} + 32 q^{65} + 72 q^{66} + 128 q^{67} + 64 q^{69} + 24 q^{75} - 112 q^{77} + 256 q^{78} - 32 q^{79} + 72 q^{82} - 120 q^{83} + 96 q^{84} + 32 q^{86} - 96 q^{87} - 24 q^{88} - 144 q^{91} + 64 q^{93} + 72 q^{97} + 304 q^{99} + O(q^{100}) \)

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

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