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Properties

Label 1200.4.cm
Level $1200$
Weight $4$
Character orbit 1200.cm
Rep. character $\chi_{1200}(53,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $5728$
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.cm (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1200 \)
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 5792 0
Cusp forms 5728 5728 0
Eisenstein series 64 64 0

Trace form

\( 5728 q - 6 q^{3} - 20 q^{4} - 6 q^{6} + O(q^{10}) \) \( 5728 q - 6 q^{3} - 20 q^{4} - 6 q^{6} - 48 q^{10} + 46 q^{12} - 12 q^{13} - 16 q^{15} + 348 q^{16} - 262 q^{18} - 20 q^{19} + 264 q^{21} + 168 q^{22} - 108 q^{24} - 6 q^{27} + 672 q^{28} - 534 q^{30} - 24 q^{31} - 16 q^{33} - 20 q^{34} + 250 q^{36} - 12 q^{37} + 216 q^{39} - 296 q^{40} - 650 q^{42} - 258 q^{45} - 12 q^{46} - 5864 q^{48} - 16 q^{51} + 1416 q^{52} - 42 q^{54} + 108 q^{57} + 4480 q^{58} - 5034 q^{60} - 12 q^{61} + 1356 q^{63} - 20 q^{64} - 6 q^{66} - 20 q^{67} - 118 q^{69} - 1712 q^{70} + 1598 q^{72} - 1606 q^{75} - 32 q^{76} + 7752 q^{78} - 40 q^{79} - 12 q^{81} + 6484 q^{82} + 98 q^{84} - 516 q^{85} - 108 q^{87} + 6112 q^{88} + 764 q^{90} + 6848 q^{91} + 92 q^{93} - 20 q^{94} - 276 q^{96} - 32 q^{97} + O(q^{100}) \)

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.