Properties

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

Related objects

Downloads

Learn more

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: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

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 \(-5\) \(-5\) \(0\) \(0\) \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{7})q^{3}+\cdots\)