Properties

Label 25.4.b
Level $25$
Weight $4$
Character orbit 25.b
Rep. character $\chi_{25}(24,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Decomposition of \(S_{4}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

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 \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-7iq^{3}+7q^{4}+7q^{6}+6iq^{7}+\cdots\)