Properties

Label 400.2.bm
Level $400$
Weight $2$
Character orbit 400.bm
Rep. character $\chi_{400}(67,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $464$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.bm (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(400, [\chi])\).

Total New Old
Modular forms 496 496 0
Cusp forms 464 464 0
Eisenstein series 32 32 0

Trace form

\( 464 q - 8 q^{2} - 10 q^{3} - 10 q^{4} - 8 q^{5} - 6 q^{6} - 16 q^{7} - 2 q^{8} + 108 q^{9} + O(q^{10}) \) \( 464 q - 8 q^{2} - 10 q^{3} - 10 q^{4} - 8 q^{5} - 6 q^{6} - 16 q^{7} - 2 q^{8} + 108 q^{9} - 4 q^{10} - 6 q^{11} - 22 q^{12} - 6 q^{13} - 10 q^{14} - 12 q^{15} + 34 q^{16} - 16 q^{17} - 24 q^{18} - 10 q^{19} - 14 q^{20} - 36 q^{21} - 60 q^{22} - 16 q^{23} - 12 q^{24} - 16 q^{26} - 10 q^{27} + 6 q^{28} - 10 q^{29} - 106 q^{30} + 2 q^{32} - 16 q^{33} - 10 q^{34} - 60 q^{35} + 10 q^{36} - 6 q^{37} - 38 q^{38} - 20 q^{39} + 16 q^{40} - 38 q^{42} + 16 q^{43} - 80 q^{44} - 4 q^{45} - 6 q^{46} + 24 q^{47} + 60 q^{48} + 38 q^{50} - 16 q^{51} - 160 q^{52} - 10 q^{53} - 16 q^{55} - 6 q^{56} - 12 q^{57} - 110 q^{58} - 10 q^{59} - 50 q^{60} - 6 q^{61} - 14 q^{62} - 12 q^{63} + 20 q^{64} - 16 q^{65} - 6 q^{66} + 30 q^{67} - 50 q^{68} - 22 q^{69} + 38 q^{70} - 12 q^{71} + 172 q^{72} - 8 q^{73} + 8 q^{74} - 58 q^{75} - 16 q^{76} + 60 q^{77} - 48 q^{78} + 208 q^{80} - 96 q^{81} - 14 q^{82} - 10 q^{83} - 22 q^{84} + 2 q^{85} - 126 q^{86} - 72 q^{87} + 86 q^{88} + 110 q^{90} + 64 q^{91} - 66 q^{92} - 28 q^{93} - 10 q^{94} - 160 q^{95} - 36 q^{96} - 16 q^{97} - 44 q^{98} - 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(400, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
400.2.bm.a 400.bm 400.am $464$ $3.194$ None \(-8\) \(-10\) \(-8\) \(-16\) $\mathrm{SU}(2)[C_{20}]$