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Properties

Label 1200.2.cm
Level $1200$
Weight $2$
Character orbit 1200.cm
Rep. character $\chi_{1200}(53,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1888$
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.cm (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1200 \)
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 1952 0
Cusp forms 1888 1888 0
Eisenstein series 64 64 0

Trace form

\( 1888 q - 6 q^{3} - 20 q^{4} - 6 q^{6} + O(q^{10}) \) \( 1888 q - 6 q^{3} - 20 q^{4} - 6 q^{6} - 24 q^{10} - 2 q^{12} - 12 q^{13} - 16 q^{15} + 28 q^{16} + 2 q^{18} - 20 q^{19} + 24 q^{21} - 16 q^{22} - 12 q^{24} - 6 q^{27} - 16 q^{28} + 18 q^{30} - 24 q^{31} - 16 q^{33} - 20 q^{34} + 10 q^{36} - 12 q^{37} + 24 q^{39} + 24 q^{40} - 50 q^{42} - 18 q^{45} - 12 q^{46} + 88 q^{48} - 16 q^{51} - 72 q^{52} - 18 q^{54} + 12 q^{57} - 120 q^{58} - 138 q^{60} - 12 q^{61} + 12 q^{63} - 20 q^{64} - 6 q^{66} - 20 q^{67} - 22 q^{69} + 56 q^{70} - 34 q^{72} + 26 q^{75} - 32 q^{76} + 60 q^{78} - 40 q^{79} - 12 q^{81} - 44 q^{82} + 2 q^{84} - 36 q^{85} - 12 q^{87} - 64 q^{88} - 4 q^{90} + 128 q^{91} - 4 q^{93} - 20 q^{94} - 36 q^{96} - 32 q^{97} + O(q^{100}) \)

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.