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Properties

Label 625.2.j
Level $625$
Weight $2$
Character orbit 625.j
Rep. character $\chi_{625}(6,\cdot)$
Character field $\Q(\zeta_{125})$
Dimension $6100$
Newform subspaces $1$
Sturm bound $125$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 625 = 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 625.j (of order \(125\) and degree \(100\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 625 \)
Character field: \(\Q(\zeta_{125})\)
Newform subspaces: \( 1 \)
Sturm bound: \(125\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(625, [\chi])\).

Total New Old
Modular forms 6300 6300 0
Cusp forms 6100 6100 0
Eisenstein series 200 200 0

Trace form

\( 6100 q - 100 q^{2} - 100 q^{3} - 100 q^{4} - 100 q^{5} - 100 q^{6} - 100 q^{7} - 100 q^{8} - 100 q^{9} + O(q^{10}) \) \( 6100 q - 100 q^{2} - 100 q^{3} - 100 q^{4} - 100 q^{5} - 100 q^{6} - 100 q^{7} - 100 q^{8} - 100 q^{9} - 100 q^{10} - 100 q^{11} - 100 q^{13} - 100 q^{14} - 100 q^{15} - 100 q^{16} - 100 q^{17} - 100 q^{18} - 100 q^{19} - 100 q^{20} - 100 q^{21} - 100 q^{22} - 100 q^{24} - 300 q^{25} - 100 q^{26} - 100 q^{27} - 100 q^{28} - 100 q^{29} - 100 q^{30} - 100 q^{31} - 100 q^{32} - 100 q^{33} - 100 q^{34} - 100 q^{35} + 150 q^{36} - 100 q^{37} - 100 q^{38} - 100 q^{39} - 100 q^{40} - 100 q^{41} - 100 q^{42} - 100 q^{43} - 100 q^{44} + 50 q^{45} - 100 q^{46} + 25 q^{47} - 100 q^{48} - 100 q^{49} - 100 q^{50} - 100 q^{51} - 100 q^{52} - 100 q^{53} - 100 q^{54} - 100 q^{55} - 700 q^{56} - 75 q^{57} + 200 q^{58} - 100 q^{59} + 50 q^{60} - 100 q^{61} - 100 q^{62} - 100 q^{63} - 100 q^{64} - 100 q^{65} - 100 q^{66} + 50 q^{67} - 75 q^{68} - 100 q^{69} - 100 q^{70} - 100 q^{72} - 100 q^{73} - 100 q^{74} - 100 q^{75} - 100 q^{76} - 100 q^{77} + 50 q^{78} - 100 q^{79} - 2000 q^{80} - 100 q^{81} + 100 q^{82} - 100 q^{83} - 100 q^{84} - 100 q^{85} - 100 q^{86} - 100 q^{87} - 100 q^{88} - 100 q^{89} - 100 q^{90} + 50 q^{91} - 100 q^{92} + 200 q^{93} - 100 q^{94} - 50 q^{95} - 100 q^{96} - 100 q^{97} - 100 q^{98} - 100 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(625, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
625.2.j.a 625.j 625.j $6100$ $4.991$ None \(-100\) \(-100\) \(-100\) \(-100\) $\mathrm{SU}(2)[C_{125}]$