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Properties

Label 400.6.bl
Level $400$
Weight $6$
Character orbit 400.bl
Rep. character $\chi_{400}(29,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2384$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 400.bl (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(400, [\chi])\).

Total New Old
Modular forms 2416 2416 0
Cusp forms 2384 2384 0
Eisenstein series 32 32 0

Trace form

\( 2384 q - 10 q^{2} - 10 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} - 1240 q^{8} + O(q^{10}) \) \( 2384 q - 10 q^{2} - 10 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} - 1240 q^{8} - 542 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 198 q^{14} - 16 q^{15} - 6 q^{16} - 20 q^{17} - 6 q^{19} - 834 q^{20} - 1464 q^{21} - 10 q^{22} - 16 q^{24} + 12964 q^{26} - 10 q^{27} - 10250 q^{28} - 6 q^{29} - 746 q^{30} - 23076 q^{31} - 20 q^{33} + 24474 q^{34} - 27396 q^{35} - 50842 q^{36} - 10 q^{37} - 86040 q^{38} + 62796 q^{40} - 77770 q^{42} - 31044 q^{44} - 6744 q^{45} + 122 q^{46} - 20 q^{47} - 280940 q^{48} + 5493456 q^{49} - 56126 q^{50} - 988 q^{51} + 124280 q^{52} - 10 q^{53} - 31110 q^{54} - 100848 q^{56} - 10 q^{58} - 6 q^{59} - 233048 q^{60} - 6 q^{61} - 10 q^{62} - 336160 q^{63} - 207384 q^{64} - 110768 q^{65} - 2924 q^{66} + 223130 q^{67} + 966 q^{69} - 303340 q^{70} - 10 q^{72} + 24228 q^{74} + 33234 q^{75} + 42044 q^{76} - 168080 q^{77} - 10 q^{78} - 249652 q^{79} + 129118 q^{80} + 3700392 q^{81} - 10 q^{83} + 4108 q^{84} - 6258 q^{85} - 1166 q^{86} - 778700 q^{88} - 449586 q^{90} - 100848 q^{91} - 865720 q^{92} - 282926 q^{94} - 38440 q^{95} - 297546 q^{96} - 20 q^{97} - 168400 q^{98} - 237184 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(400, [\chi])\) into newform subspaces

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