Properties

Label 225.2.u
Level 225
Weight 2
Character orbit u
Rep. character \(\chi_{225}(4,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 224
Newform subspaces 1
Sturm bound 60
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 225.u (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(225, [\chi])\).

Total New Old
Modular forms 256 256 0
Cusp forms 224 224 0
Eisenstein series 32 32 0

Trace form

\( 224q - 5q^{2} - 10q^{3} - 29q^{4} - 2q^{6} - 20q^{8} - 8q^{9} + O(q^{10}) \) \( 224q - 5q^{2} - 10q^{3} - 29q^{4} - 2q^{6} - 20q^{8} - 8q^{9} - 12q^{10} + 5q^{11} - 30q^{12} - 5q^{13} - 23q^{14} + 18q^{15} + 15q^{16} - 20q^{17} - 12q^{19} - 17q^{20} - 27q^{21} - 5q^{22} - 5q^{23} - 46q^{24} - 16q^{25} + 72q^{26} - 25q^{27} - 60q^{28} - 15q^{29} + 2q^{30} - 9q^{31} - 35q^{33} - 7q^{34} - 46q^{35} - 66q^{36} - 20q^{37} - 75q^{38} + 32q^{39} - q^{40} + 13q^{41} - 140q^{42} + 20q^{44} + 90q^{45} - 4q^{46} + 20q^{47} + 165q^{48} + 56q^{49} - 29q^{50} - 6q^{51} - 15q^{52} - 20q^{53} + 61q^{54} - 44q^{55} + 22q^{56} - 5q^{58} - 30q^{59} - 149q^{60} - 3q^{61} + 40q^{62} - 12q^{64} + 45q^{65} + 98q^{66} + 10q^{67} - 14q^{69} - 12q^{70} - 106q^{71} + 40q^{72} - 20q^{73} + 82q^{74} + 43q^{75} + 8q^{76} - 115q^{77} + 110q^{78} - 15q^{79} - 22q^{80} + 72q^{81} + 65q^{83} + 57q^{84} - 21q^{85} - 15q^{86} + 115q^{87} - 5q^{88} + 26q^{89} - 29q^{90} - 54q^{91} + 95q^{92} + 41q^{94} - 17q^{95} - 47q^{96} - 5q^{97} - 70q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(225, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
225.2.u.a \(224\) \(1.797\) None \(-5\) \(-10\) \(0\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database