↑

Properties

Label 1400.2.cx
Level $1400$
Weight $2$
Character orbit 1400.cx
Rep. character $\chi_{1400}(221,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1888$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.cx (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1400 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1400, [\chi])\).

Total New Old
Modular forms 1952 1952 0
Cusp forms 1888 1888 0
Eisenstein series 64 64 0

Trace form

\( 1888 q - 3 q^{2} - 3 q^{4} - 4 q^{6} - 32 q^{7} + 6 q^{8} - 234 q^{9} + O(q^{10}) \) \( 1888 q - 3 q^{2} - 3 q^{4} - 4 q^{6} - 32 q^{7} + 6 q^{8} - 234 q^{9} + 3 q^{10} + 9 q^{12} + 6 q^{14} - 20 q^{15} - 3 q^{16} - 6 q^{17} - 22 q^{18} - 20 q^{20} - 4 q^{22} - 6 q^{23} - 14 q^{24} - 8 q^{25} - 12 q^{26} - 20 q^{28} + 21 q^{30} - 30 q^{31} + 12 q^{32} + 18 q^{33} - 52 q^{34} - 76 q^{36} + 14 q^{38} - 18 q^{39} - 15 q^{40} - 24 q^{41} - 52 q^{42} + 13 q^{44} - 31 q^{46} - 30 q^{47} - 32 q^{48} - 32 q^{49} - 118 q^{50} - 98 q^{52} - 13 q^{54} - 12 q^{55} - 30 q^{56} - 40 q^{57} - 27 q^{58} + 25 q^{60} + 52 q^{62} + 42 q^{63} - 42 q^{64} - 18 q^{65} - 29 q^{66} - 46 q^{68} + 53 q^{70} - 24 q^{71} + 60 q^{72} - 6 q^{73} + 22 q^{74} - 76 q^{76} - 114 q^{78} - 6 q^{79} + 54 q^{80} + 186 q^{81} + 76 q^{82} + 39 q^{84} - 17 q^{86} - 18 q^{87} - 88 q^{88} - 6 q^{89} - 236 q^{90} + 26 q^{92} - 11 q^{94} + 24 q^{95} - 51 q^{96} + 24 q^{97} + 94 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1400, [\chi])\) into newform subspaces

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