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Properties

Label 1200.2.cp
Level $1200$
Weight $2$
Character orbit 1200.cp
Rep. character $\chi_{1200}(67,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $960$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1200.cp (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1200, [\chi])\).

Total New Old
Modular forms 1952 960 992
Cusp forms 1888 960 928
Eisenstein series 64 0 64

Trace form

\( 960 q - 12 q^{8} + 240 q^{9} + O(q^{10}) \) \( 960 q - 12 q^{8} + 240 q^{9} + 8 q^{12} - 40 q^{16} + 12 q^{20} + 88 q^{22} - 28 q^{28} + 72 q^{30} + 20 q^{32} + 24 q^{35} + 40 q^{38} - 88 q^{40} + 20 q^{42} - 32 q^{43} + 140 q^{44} - 48 q^{47} + 16 q^{48} - 92 q^{50} + 232 q^{52} + 84 q^{58} - 56 q^{62} - 60 q^{64} - 72 q^{67} + 16 q^{68} - 20 q^{70} - 48 q^{72} + 16 q^{73} + 16 q^{75} - 24 q^{78} - 68 q^{80} - 240 q^{81} + 200 q^{86} - 76 q^{88} + 24 q^{92} + 320 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)