Properties

Label 25.2.d
Level 25
Weight 2
Character orbit d
Rep. character \(\chi_{25}(6,\cdot)\)
Character field \(\Q(\zeta_{5})\)
Dimension 4
Newforms 1
Sturm bound 5
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 25.d (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{5})\)
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 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

Trace form

\(4q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut +\mathstrut q^{14} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 6q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 4q^{18} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 2q^{21} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 11q^{23} \) \(\mathstrut -\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 12q^{26} \) \(\mathstrut +\mathstrut 5q^{27} \) \(\mathstrut +\mathstrut q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 5q^{30} \) \(\mathstrut +\mathstrut 3q^{31} \) \(\mathstrut +\mathstrut 18q^{32} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut 6q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 5q^{38} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut +\mathstrut 5q^{40} \) \(\mathstrut +\mathstrut 8q^{41} \) \(\mathstrut +\mathstrut q^{42} \) \(\mathstrut -\mathstrut 6q^{43} \) \(\mathstrut +\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 10q^{45} \) \(\mathstrut +\mathstrut 13q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 6q^{48} \) \(\mathstrut -\mathstrut 22q^{49} \) \(\mathstrut -\mathstrut 10q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 12q^{52} \) \(\mathstrut +\mathstrut 9q^{53} \) \(\mathstrut -\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 10q^{58} \) \(\mathstrut +\mathstrut 13q^{61} \) \(\mathstrut +\mathstrut 6q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut +\mathstrut 3q^{64} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 2q^{67} \) \(\mathstrut -\mathstrut 4q^{68} \) \(\mathstrut -\mathstrut q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 10q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut +\mathstrut 20q^{75} \) \(\mathstrut +\mathstrut 20q^{76} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut +\mathstrut 3q^{78} \) \(\mathstrut +\mathstrut 15q^{79} \) \(\mathstrut -\mathstrut 15q^{80} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 4q^{82} \) \(\mathstrut +\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 4q^{84} \) \(\mathstrut -\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 3q^{86} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut -\mathstrut 12q^{91} \) \(\mathstrut -\mathstrut 12q^{92} \) \(\mathstrut -\mathstrut 12q^{93} \) \(\mathstrut +\mathstrut q^{94} \) \(\mathstrut -\mathstrut 5q^{95} \) \(\mathstrut -\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 11q^{98} \) \(\mathstrut +\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.d.a \(4\) \(0.200\) \(\Q(\zeta_{10})\) None \(-2\) \(-1\) \(-5\) \(-2\) \(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)