Properties

Label 25.2.e
Level 25
Weight 2
Character orbit e
Rep. character \(\chi_{25}(4,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 8
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 25.e (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(25, [\chi])\).

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

Trace form

\(8q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 10q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 10q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 15q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 13q^{14} \) \(\mathstrut +\mathstrut 15q^{15} \) \(\mathstrut +\mathstrut 3q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 15q^{20} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 5q^{23} \) \(\mathstrut -\mathstrut 20q^{24} \) \(\mathstrut -\mathstrut 10q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 5q^{27} \) \(\mathstrut -\mathstrut 15q^{28} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 9q^{31} \) \(\mathstrut +\mathstrut 10q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 23q^{36} \) \(\mathstrut +\mathstrut 30q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut +\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 15q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut -\mathstrut 30q^{48} \) \(\mathstrut +\mathstrut 14q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 10q^{52} \) \(\mathstrut -\mathstrut 10q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut -\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 10q^{56} \) \(\mathstrut +\mathstrut 20q^{58} \) \(\mathstrut -\mathstrut 10q^{60} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut +\mathstrut 10q^{63} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 12q^{66} \) \(\mathstrut +\mathstrut 20q^{67} \) \(\mathstrut +\mathstrut 17q^{69} \) \(\mathstrut +\mathstrut 30q^{70} \) \(\mathstrut +\mathstrut 6q^{71} \) \(\mathstrut +\mathstrut 5q^{72} \) \(\mathstrut +\mathstrut 15q^{73} \) \(\mathstrut -\mathstrut 12q^{74} \) \(\mathstrut -\mathstrut 10q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 10q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut +\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 28q^{81} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut +\mathstrut 18q^{84} \) \(\mathstrut -\mathstrut 15q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 25q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut +\mathstrut 30q^{92} \) \(\mathstrut -\mathstrut 27q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 16q^{96} \) \(\mathstrut -\mathstrut 60q^{97} \) \(\mathstrut -\mathstrut 10q^{98} \) \(\mathstrut -\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(25, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
25.2.e.a \(8\) \(0.200\) 8.0.58140625.2 None \(-5\) \(-5\) \(0\) \(0\) \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{7})q^{3}+\cdots\)