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Properties

Label 1400.2.cz
Level $1400$
Weight $2$
Character orbit 1400.cz
Rep. character $\chi_{1400}(131,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1888$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.cz (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

\( 1888 q - 3 q^{2} - 18 q^{3} - 3 q^{4} - 30 q^{8} - 234 q^{9} + O(q^{10}) \) \( 1888 q - 3 q^{2} - 18 q^{3} - 3 q^{4} - 30 q^{8} - 234 q^{9} - 21 q^{10} - 6 q^{11} - 9 q^{12} - 6 q^{14} - 3 q^{16} - 18 q^{17} - 22 q^{18} - 18 q^{19} - 20 q^{22} - 6 q^{24} - 8 q^{25} - 12 q^{26} - 44 q^{28} + 47 q^{30} + 12 q^{32} - 18 q^{33} + 12 q^{35} + 44 q^{36} + 18 q^{38} - 57 q^{40} - 12 q^{42} - 64 q^{43} - 19 q^{44} + 25 q^{46} - 32 q^{49} - 66 q^{50} + 8 q^{51} - 66 q^{52} - 57 q^{54} + 18 q^{56} - 40 q^{57} + 13 q^{58} - 18 q^{59} - 63 q^{60} + 54 q^{64} + 2 q^{65} - 27 q^{66} + 30 q^{67} + 42 q^{68} - 25 q^{70} - 70 q^{72} - 18 q^{73} - 22 q^{74} - 24 q^{75} - 98 q^{78} + 234 q^{80} + 186 q^{81} - 96 q^{82} + 19 q^{84} - 29 q^{86} + 82 q^{88} - 18 q^{89} - 96 q^{91} + 58 q^{92} - 9 q^{94} - 99 q^{96} - 138 q^{98} - 112 q^{99} + O(q^{100}) \)

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.