Properties

Label 25.4.b
Level 25
Weight 4
Character orbit b
Rep. character \(\chi_{25}(24,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 2
Sturm bound 10
Trace bound 4

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(25, [\chi])\).

Total New Old
Modular forms 10 6 4
Cusp forms 4 4 0
Eisenstein series 6 2 4

Trace form

\(4q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut -\mathstrut 22q^{11} \) \(\mathstrut +\mathstrut 36q^{14} \) \(\mathstrut -\mathstrut 46q^{16} \) \(\mathstrut -\mathstrut 130q^{19} \) \(\mathstrut +\mathstrut 108q^{21} \) \(\mathstrut +\mathstrut 210q^{24} \) \(\mathstrut +\mathstrut 248q^{26} \) \(\mathstrut -\mathstrut 220q^{29} \) \(\mathstrut -\mathstrut 132q^{31} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 676q^{36} \) \(\mathstrut +\mathstrut 544q^{39} \) \(\mathstrut -\mathstrut 362q^{41} \) \(\mathstrut -\mathstrut 1114q^{44} \) \(\mathstrut +\mathstrut 948q^{46} \) \(\mathstrut +\mathstrut 1228q^{49} \) \(\mathstrut +\mathstrut 1378q^{51} \) \(\mathstrut -\mathstrut 730q^{54} \) \(\mathstrut -\mathstrut 180q^{56} \) \(\mathstrut -\mathstrut 440q^{59} \) \(\mathstrut -\mathstrut 2072q^{61} \) \(\mathstrut +\mathstrut 1358q^{64} \) \(\mathstrut -\mathstrut 1114q^{66} \) \(\mathstrut -\mathstrut 1956q^{69} \) \(\mathstrut +\mathstrut 1648q^{71} \) \(\mathstrut +\mathstrut 2756q^{74} \) \(\mathstrut +\mathstrut 2090q^{76} \) \(\mathstrut -\mathstrut 2220q^{79} \) \(\mathstrut -\mathstrut 836q^{81} \) \(\mathstrut +\mathstrut 396q^{84} \) \(\mathstrut -\mathstrut 3352q^{86} \) \(\mathstrut +\mathstrut 2190q^{89} \) \(\mathstrut -\mathstrut 792q^{91} \) \(\mathstrut -\mathstrut 4504q^{94} \) \(\mathstrut +\mathstrut 3278q^{96} \) \(\mathstrut +\mathstrut 3364q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(25, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
25.4.b.a \(2\) \(1.475\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}+iq^{3}-8q^{4}-8q^{6}-3iq^{7}+\cdots\)
25.4.b.b \(2\) \(1.475\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-7iq^{3}+7q^{4}+7q^{6}+6iq^{7}+\cdots\)