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Properties

Label 1200.4.ct
Level $1200$
Weight $4$
Character orbit 1200.ct
Rep. character $\chi_{1200}(163,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2880$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1200.ct (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1200, [\chi])\).

Total New Old
Modular forms 5792 2880 2912
Cusp forms 5728 2880 2848
Eisenstein series 64 0 64

Trace form

\( 2880 q + 84 q^{8} - 6480 q^{9} + O(q^{10}) \) \( 2880 q + 84 q^{8} - 6480 q^{9} - 24 q^{12} + 360 q^{16} - 348 q^{20} + 1256 q^{22} + 204 q^{28} + 1752 q^{30} + 340 q^{32} - 456 q^{35} - 2032 q^{38} - 4928 q^{40} - 660 q^{42} - 2660 q^{44} + 816 q^{47} + 528 q^{48} + 1308 q^{50} - 5016 q^{52} + 7124 q^{58} + 2608 q^{62} - 9660 q^{64} + 9240 q^{67} + 1464 q^{68} + 4700 q^{70} - 3024 q^{72} + 592 q^{73} - 1104 q^{75} - 72 q^{78} + 5652 q^{80} - 58320 q^{81} - 2360 q^{82} - 5360 q^{83} + 12200 q^{86} + 1796 q^{88} - 4992 q^{92} + 9920 q^{95} + 1264 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)