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Properties

Label 1200.4.cq
Level $1200$
Weight $4$
Character orbit 1200.cq
Rep. character $\chi_{1200}(173,\cdot)$
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.cq (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

\( 5728 q - 10 q^{3} - 20 q^{4} - 6 q^{6} + O(q^{10}) \) \( 5728 q - 10 q^{3} - 20 q^{4} - 6 q^{6} + 16 q^{10} - 62 q^{12} - 20 q^{13} - 16 q^{15} - 372 q^{16} + 214 q^{18} - 20 q^{19} - 276 q^{21} + 232 q^{22} + 108 q^{24} - 10 q^{27} - 192 q^{28} - 642 q^{30} - 24 q^{31} - 16 q^{33} - 20 q^{34} + 250 q^{36} - 20 q^{37} - 216 q^{39} - 1296 q^{40} - 230 q^{42} - 896 q^{43} - 258 q^{45} - 12 q^{46} - 3928 q^{48} - 16 q^{51} + 424 q^{52} + 22 q^{54} - 108 q^{57} - 6528 q^{58} - 4998 q^{60} - 12 q^{61} + 1356 q^{63} - 20 q^{64} - 6 q^{66} - 12 q^{67} + 98 q^{69} - 4944 q^{70} - 2282 q^{72} - 1714 q^{75} - 32 q^{76} - 1948 q^{78} - 40 q^{79} - 12 q^{81} - 9932 q^{82} - 118 q^{84} + 484 q^{85} + 108 q^{87} + 3600 q^{88} + 276 q^{90} - 6872 q^{91} - 20 q^{94} + 264 q^{96} - 32 q^{97} + O(q^{100}) \)

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.