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Properties

Label 1200.3.co
Level $1200$
Weight $3$
Character orbit 1200.co
Rep. character $\chi_{1200}(203,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $3808$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1200.co (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1200 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1200, [\chi])\).

Total New Old
Modular forms 3872 3872 0
Cusp forms 3808 3808 0
Eisenstein series 64 64 0

Trace form

\( 3808 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 32 q^{7} + O(q^{10}) \) \( 3808 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 32 q^{7} - 32 q^{10} - 26 q^{12} - 12 q^{13} + 36 q^{15} + 188 q^{16} - 30 q^{18} - 20 q^{19} - 96 q^{21} + 56 q^{22} + 36 q^{24} - 10 q^{27} - 96 q^{28} - 46 q^{30} - 16 q^{33} - 20 q^{34} + 58 q^{36} - 12 q^{37} - 20 q^{39} + 104 q^{40} - 66 q^{42} - 160 q^{43} - 58 q^{45} - 12 q^{46} + 232 q^{48} - 16 q^{51} + 712 q^{52} + 6 q^{54} - 32 q^{55} - 36 q^{57} - 80 q^{58} + 1054 q^{60} - 12 q^{61} - 20 q^{64} - 6 q^{66} - 12 q^{67} + 26 q^{69} - 288 q^{70} + 334 q^{72} - 138 q^{75} - 32 q^{76} + 1272 q^{78} - 12 q^{81} - 620 q^{82} - 46 q^{84} - 116 q^{85} + 432 q^{87} - 64 q^{88} - 340 q^{90} + 968 q^{91} - 52 q^{93} - 20 q^{94} + 84 q^{96} - 32 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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