↑

Properties

Label 1200.2.db
Level $1200$
Weight $2$
Character orbit 1200.db
Rep. character $\chi_{1200}(11,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1888$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1200.db (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

\( 1888 q - 6 q^{3} - 12 q^{4} - 6 q^{6} - 64 q^{7} + O(q^{10}) \) \( 1888 q - 6 q^{3} - 12 q^{4} - 6 q^{6} - 64 q^{7} - 16 q^{10} - 6 q^{12} - 12 q^{13} - 12 q^{16} - 8 q^{18} - 12 q^{19} - 24 q^{21} - 28 q^{22} - 16 q^{24} - 6 q^{27} - 60 q^{28} - 38 q^{30} - 12 q^{33} + 4 q^{34} + 38 q^{36} - 12 q^{37} - 12 q^{39} + 20 q^{40} - 42 q^{42} - 64 q^{43} + 2 q^{45} - 28 q^{46} - 84 q^{48} + 1632 q^{49} - 28 q^{51} + 4 q^{52} - 6 q^{54} - 64 q^{55} + 20 q^{58} + 8 q^{60} - 12 q^{61} - 12 q^{64} + 76 q^{66} - 12 q^{67} - 18 q^{69} - 200 q^{70} - 34 q^{72} + 14 q^{75} - 128 q^{76} - 90 q^{78} - 12 q^{81} + 24 q^{82} - 124 q^{84} - 36 q^{85} + 100 q^{87} + 100 q^{88} - 30 q^{90} - 96 q^{91} - 28 q^{93} + 24 q^{94} - 6 q^{96} - 24 q^{97} + 20 q^{99} + O(q^{100}) \)

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.