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Properties

Label 800.2.ca
Level $800$
Weight $2$
Character orbit 800.ca
Rep. character $\chi_{800}(21,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $1888$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 800.ca (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 800 \)
Character field: \(\Q(\zeta_{40})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(800, [\chi])\).

Total New Old
Modular forms 1952 1952 0
Cusp forms 1888 1888 0
Eisenstein series 64 64 0

Trace form

\( 1888 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 16 q^{5} - 12 q^{6} - 32 q^{7} - 12 q^{8} - 12 q^{9} + O(q^{10}) \) \( 1888 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 16 q^{5} - 12 q^{6} - 32 q^{7} - 12 q^{8} - 12 q^{9} - 16 q^{10} - 12 q^{11} - 44 q^{12} - 12 q^{13} - 12 q^{14} - 12 q^{16} - 32 q^{18} - 12 q^{19} - 16 q^{20} - 12 q^{21} - 44 q^{22} - 12 q^{23} - 32 q^{24} - 16 q^{25} + 8 q^{26} - 12 q^{27} - 12 q^{28} - 12 q^{29} + 16 q^{30} - 72 q^{31} - 32 q^{32} - 24 q^{33} - 28 q^{34} - 40 q^{35} - 132 q^{36} - 12 q^{37} + 72 q^{38} - 12 q^{39} - 128 q^{40} - 12 q^{41} - 12 q^{42} - 32 q^{43} - 12 q^{44} - 28 q^{45} - 12 q^{46} + 144 q^{48} - 56 q^{50} - 56 q^{51} - 12 q^{52} - 12 q^{53} - 12 q^{54} + 16 q^{55} - 12 q^{56} - 32 q^{57} - 76 q^{58} - 12 q^{59} + 128 q^{60} - 12 q^{61} + 4 q^{62} - 24 q^{63} + 24 q^{64} - 32 q^{65} + 4 q^{66} - 12 q^{67} - 120 q^{68} - 12 q^{69} - 4 q^{70} - 12 q^{71} - 132 q^{72} - 12 q^{73} - 120 q^{74} + 16 q^{75} - 32 q^{76} - 12 q^{77} - 164 q^{78} - 44 q^{80} - 32 q^{82} - 12 q^{83} - 164 q^{84} - 36 q^{85} - 12 q^{86} - 124 q^{87} + 120 q^{88} - 12 q^{89} - 100 q^{90} - 12 q^{91} + 248 q^{92} - 8 q^{93} - 44 q^{94} - 32 q^{95} + 108 q^{96} - 24 q^{97} - 12 q^{98} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
800.2.ca.a 800.ca 800.ba $1888$ $6.388$ None \(-12\) \(-12\) \(-16\) \(-32\) $\mathrm{SU}(2)[C_{40}]$