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
Newforms 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: \(\Q(\zeta_{20})\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(25, [\chi])\) into irreducible Hecke orbits

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