↑

Properties

Label 1400.2.di
Level $1400$
Weight $2$
Character orbit 1400.di
Rep. character $\chi_{1400}(19,\cdot)$
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.di (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

\( 1888 q - 5 q^{2} - 30 q^{3} - 3 q^{4} + 10 q^{8} + 222 q^{9} + O(q^{10}) \) \( 1888 q - 5 q^{2} - 30 q^{3} - 3 q^{4} + 10 q^{8} + 222 q^{9} - 3 q^{10} - 6 q^{11} - 15 q^{12} + 6 q^{14} - 3 q^{16} - 30 q^{17} - 18 q^{19} - 20 q^{22} - 42 q^{24} - 8 q^{25} - 36 q^{26} + 10 q^{28} - 25 q^{30} - 30 q^{33} - 68 q^{35} - 100 q^{36} + 30 q^{38} - 27 q^{40} + 50 q^{42} - 19 q^{44} - 31 q^{46} - 32 q^{49} - 70 q^{50} - 40 q^{51} - 150 q^{52} - 33 q^{54} - 30 q^{56} - 65 q^{58} - 18 q^{59} - 13 q^{60} + 54 q^{64} - 18 q^{65} - 63 q^{66} - 70 q^{67} - 23 q^{70} + 40 q^{72} - 30 q^{73} - 38 q^{74} - 24 q^{75} - 50 q^{78} - 204 q^{80} + 210 q^{81} - 35 q^{84} + 23 q^{86} - 18 q^{89} + 72 q^{91} - 110 q^{92} - 9 q^{94} + 81 q^{96} - 140 q^{98} - 160 q^{99} + O(q^{100}) \)

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.