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Properties

Label 400.4.be
Level $400$
Weight $4$
Character orbit 400.be
Rep. character $\chi_{400}(21,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1424$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 400.be (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(400, [\chi])\).

Total New Old
Modular forms 1456 1456 0
Cusp forms 1424 1424 0
Eisenstein series 32 32 0

Trace form

\( 1424 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} - 132 q^{8} + O(q^{10}) \) \( 1424 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} - 132 q^{8} - 2 q^{10} - 6 q^{11} - 54 q^{12} - 6 q^{13} + 42 q^{14} - 16 q^{15} - 6 q^{16} - 12 q^{17} - 48 q^{18} - 6 q^{19} + 146 q^{20} + 156 q^{21} + 426 q^{22} - 16 q^{24} - 36 q^{26} - 114 q^{27} + 378 q^{28} - 6 q^{29} - 1246 q^{30} - 756 q^{31} - 356 q^{32} - 12 q^{33} + 314 q^{34} + 764 q^{35} + 398 q^{36} - 6 q^{37} - 776 q^{38} - 724 q^{40} + 2610 q^{42} + 848 q^{43} - 804 q^{44} - 204 q^{45} - 38 q^{46} - 12 q^{47} + 2604 q^{48} - 65104 q^{49} - 1086 q^{50} + 92 q^{51} - 4200 q^{52} - 6 q^{53} - 870 q^{54} + 2052 q^{56} + 2010 q^{58} - 6 q^{59} - 2328 q^{60} - 6 q^{61} + 494 q^{62} + 4104 q^{63} - 2904 q^{64} - 1968 q^{65} - 3664 q^{66} + 2766 q^{67} + 1724 q^{68} - 114 q^{69} + 4500 q^{70} - 3434 q^{72} - 2172 q^{74} + 2694 q^{75} + 3044 q^{76} + 2052 q^{77} - 6034 q^{78} + 3148 q^{79} + 318 q^{80} + 26232 q^{81} + 512 q^{82} + 2674 q^{83} - 2432 q^{84} + 242 q^{85} - 5566 q^{86} + 6024 q^{88} + 434 q^{90} + 2052 q^{91} - 10728 q^{92} + 92 q^{93} + 1834 q^{94} - 3880 q^{95} - 7746 q^{96} - 12 q^{97} + 4148 q^{98} - 2824 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(400, [\chi])\) into newform subspaces

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