Properties

Label 225.2.m
Level 225
Weight 2
Character orbit m
Rep. character \(\chi_{225}(19,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 48
Newforms 3
Sturm bound 60
Trace bound 1

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Defining parameters

Level: \( N \) = \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 225.m (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 3 \)
Sturm bound: \(60\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 136 56 80
Cusp forms 104 48 56
Eisenstein series 32 8 24

Trace form

\(48q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 20q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(48q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 20q^{8} \) \(\mathstrut -\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut q^{14} \) \(\mathstrut -\mathstrut 31q^{16} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut +\mathstrut 40q^{22} \) \(\mathstrut +\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 20q^{25} \) \(\mathstrut -\mathstrut 18q^{26} \) \(\mathstrut +\mathstrut 45q^{28} \) \(\mathstrut -\mathstrut 11q^{29} \) \(\mathstrut -\mathstrut 21q^{31} \) \(\mathstrut -\mathstrut 13q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 45q^{38} \) \(\mathstrut -\mathstrut 60q^{40} \) \(\mathstrut +\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 24q^{44} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut -\mathstrut 58q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 110q^{52} \) \(\mathstrut -\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 10q^{56} \) \(\mathstrut -\mathstrut 100q^{58} \) \(\mathstrut -\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 40q^{62} \) \(\mathstrut +\mathstrut 14q^{64} \) \(\mathstrut +\mathstrut 65q^{65} \) \(\mathstrut +\mathstrut 60q^{67} \) \(\mathstrut +\mathstrut 90q^{70} \) \(\mathstrut +\mathstrut 2q^{71} \) \(\mathstrut -\mathstrut 25q^{73} \) \(\mathstrut +\mathstrut 64q^{74} \) \(\mathstrut +\mathstrut 36q^{76} \) \(\mathstrut +\mathstrut 30q^{77} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 35q^{83} \) \(\mathstrut +\mathstrut 55q^{85} \) \(\mathstrut +\mathstrut 45q^{86} \) \(\mathstrut +\mathstrut 120q^{88} \) \(\mathstrut +\mathstrut 7q^{89} \) \(\mathstrut +\mathstrut 2q^{91} \) \(\mathstrut -\mathstrut 40q^{92} \) \(\mathstrut -\mathstrut 15q^{94} \) \(\mathstrut +\mathstrut 25q^{95} \) \(\mathstrut +\mathstrut 80q^{97} \) \(\mathstrut -\mathstrut 50q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(225, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
225.2.m.a \(8\) \(1.797\) 8.0.58140625.2 None \(5\) \(0\) \(0\) \(0\) \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
225.2.m.b \(16\) \(1.797\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3}+\beta _{4}-\beta _{10}+\beta _{15})q^{2}+\cdots\)
225.2.m.c \(24\) \(1.797\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(225, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(225, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)