Properties

Label 24.4.f
Level 24
Weight 4
Character orbit f
Rep. character \(\chi_{24}(11,\cdot)\)
Character field \(\Q\)
Dimension 10
Newforms 2
Sturm bound 16
Trace bound 1

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 24.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 24 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(24, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

Trace form

\(10q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut -\mathstrut 24q^{10} \) \(\mathstrut -\mathstrut 44q^{12} \) \(\mathstrut -\mathstrut 152q^{16} \) \(\mathstrut +\mathstrut 184q^{18} \) \(\mathstrut -\mathstrut 28q^{19} \) \(\mathstrut +\mathstrut 224q^{22} \) \(\mathstrut +\mathstrut 328q^{24} \) \(\mathstrut +\mathstrut 46q^{25} \) \(\mathstrut -\mathstrut 134q^{27} \) \(\mathstrut +\mathstrut 528q^{28} \) \(\mathstrut -\mathstrut 624q^{30} \) \(\mathstrut -\mathstrut 64q^{33} \) \(\mathstrut -\mathstrut 784q^{34} \) \(\mathstrut -\mathstrut 884q^{36} \) \(\mathstrut -\mathstrut 1248q^{40} \) \(\mathstrut +\mathstrut 1320q^{42} \) \(\mathstrut +\mathstrut 428q^{43} \) \(\mathstrut +\mathstrut 1440q^{46} \) \(\mathstrut +\mathstrut 1720q^{48} \) \(\mathstrut -\mathstrut 266q^{49} \) \(\mathstrut +\mathstrut 752q^{51} \) \(\mathstrut +\mathstrut 2112q^{52} \) \(\mathstrut -\mathstrut 2168q^{54} \) \(\mathstrut +\mathstrut 116q^{57} \) \(\mathstrut -\mathstrut 2616q^{58} \) \(\mathstrut -\mathstrut 2640q^{60} \) \(\mathstrut -\mathstrut 2384q^{64} \) \(\mathstrut +\mathstrut 2792q^{66} \) \(\mathstrut -\mathstrut 1636q^{67} \) \(\mathstrut +\mathstrut 3696q^{70} \) \(\mathstrut +\mathstrut 3280q^{72} \) \(\mathstrut +\mathstrut 212q^{73} \) \(\mathstrut -\mathstrut 1958q^{75} \) \(\mathstrut +\mathstrut 3608q^{76} \) \(\mathstrut -\mathstrut 3696q^{78} \) \(\mathstrut +\mathstrut 154q^{81} \) \(\mathstrut -\mathstrut 3136q^{82} \) \(\mathstrut -\mathstrut 4224q^{84} \) \(\mathstrut -\mathstrut 4432q^{88} \) \(\mathstrut +\mathstrut 4104q^{90} \) \(\mathstrut +\mathstrut 3168q^{91} \) \(\mathstrut +\mathstrut 4800q^{94} \) \(\mathstrut +\mathstrut 4240q^{96} \) \(\mathstrut -\mathstrut 52q^{97} \) \(\mathstrut +\mathstrut 4112q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(24, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.4.f.a \(2\) \(1.416\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(10\) \(0\) \(0\) \(q+2\beta q^{2}+(5+\beta )q^{3}-8q^{4}+(-4+10\beta )q^{6}+\cdots\)
24.4.f.b \(8\) \(1.416\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-12\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2+\beta _{4})q^{3}+(3+\beta _{2})q^{4}+\cdots\)