Properties

Label 25.3.f
Level 25
Weight 3
Character orbit f
Rep. character \(\chi_{25}(2,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 32
Newform subspaces 1
Sturm bound 7
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 25.f (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(25, [\chi])\).

Total New Old
Modular forms 48 48 0
Cusp forms 32 32 0
Eisenstein series 16 16 0

Trace form

\( 32q - 10q^{2} - 10q^{3} - 10q^{4} - 10q^{5} - 6q^{6} - 10q^{7} - 10q^{8} - 10q^{9} + O(q^{10}) \) \( 32q - 10q^{2} - 10q^{3} - 10q^{4} - 10q^{5} - 6q^{6} - 10q^{7} - 10q^{8} - 10q^{9} - 10q^{10} - 6q^{11} - 10q^{12} - 10q^{13} - 10q^{14} - 10q^{15} + 2q^{16} + 60q^{17} + 140q^{18} + 90q^{19} + 130q^{20} - 6q^{21} + 70q^{22} + 10q^{23} - 40q^{25} + 4q^{26} - 100q^{27} - 250q^{28} - 110q^{29} - 250q^{30} - 6q^{31} - 290q^{32} - 190q^{33} - 260q^{34} - 120q^{35} - 58q^{36} + 50q^{37} + 320q^{38} + 390q^{39} + 440q^{40} - 86q^{41} + 690q^{42} + 230q^{43} + 340q^{44} + 310q^{45} - 6q^{46} + 70q^{47} + 160q^{48} - 100q^{50} - 16q^{51} - 320q^{52} - 190q^{53} - 660q^{54} - 250q^{55} - 70q^{56} - 650q^{57} - 640q^{58} - 260q^{59} - 550q^{60} + 114q^{61} + 60q^{62} - 20q^{63} + 340q^{64} + 360q^{65} + 138q^{66} + 270q^{67} + 710q^{68} + 340q^{69} + 310q^{70} - 66q^{71} + 360q^{72} + 30q^{73} - 90q^{75} - 80q^{76} - 250q^{77} - 500q^{78} - 210q^{79} - 850q^{80} + 62q^{81} + 30q^{82} - 10q^{84} + 600q^{85} - 6q^{86} + 300q^{87} + 190q^{88} - 10q^{89} + 380q^{90} - 6q^{91} - 30q^{92} + 520q^{93} + 790q^{94} + 310q^{95} + 174q^{96} + 270q^{97} + 170q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
25.3.f.a \(32\) \(0.681\) None \(-10\) \(-10\) \(-10\) \(-10\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database