Properties

Label 24.3.h
Level 24
Weight 3
Character orbit h
Rep. character \(\chi_{24}(5,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 3
Sturm bound 12
Trace bound 2

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 24.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 24 \)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(12\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(24, [\chi])\).

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

Trace form

\(6q \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut -\mathstrut 24q^{10} \) \(\mathstrut +\mathstrut 28q^{12} \) \(\mathstrut -\mathstrut 20q^{15} \) \(\mathstrut +\mathstrut 40q^{16} \) \(\mathstrut +\mathstrut 56q^{18} \) \(\mathstrut +\mathstrut 64q^{22} \) \(\mathstrut -\mathstrut 88q^{24} \) \(\mathstrut -\mathstrut 14q^{25} \) \(\mathstrut -\mathstrut 128q^{28} \) \(\mathstrut -\mathstrut 112q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 112q^{34} \) \(\mathstrut +\mathstrut 132q^{36} \) \(\mathstrut +\mathstrut 112q^{39} \) \(\mathstrut +\mathstrut 128q^{40} \) \(\mathstrut +\mathstrut 136q^{42} \) \(\mathstrut +\mathstrut 224q^{46} \) \(\mathstrut -\mathstrut 168q^{48} \) \(\mathstrut -\mathstrut 30q^{49} \) \(\mathstrut -\mathstrut 112q^{52} \) \(\mathstrut -\mathstrut 184q^{54} \) \(\mathstrut -\mathstrut 232q^{55} \) \(\mathstrut +\mathstrut 56q^{57} \) \(\mathstrut -\mathstrut 152q^{58} \) \(\mathstrut +\mathstrut 144q^{60} \) \(\mathstrut -\mathstrut 260q^{63} \) \(\mathstrut +\mathstrut 272q^{64} \) \(\mathstrut +\mathstrut 168q^{66} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 112q^{72} \) \(\mathstrut +\mathstrut 76q^{73} \) \(\mathstrut -\mathstrut 56q^{76} \) \(\mathstrut -\mathstrut 112q^{78} \) \(\mathstrut +\mathstrut 380q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut -\mathstrut 224q^{82} \) \(\mathstrut +\mathstrut 112q^{84} \) \(\mathstrut +\mathstrut 396q^{87} \) \(\mathstrut -\mathstrut 80q^{88} \) \(\mathstrut +\mathstrut 8q^{90} \) \(\mathstrut -\mathstrut 16q^{96} \) \(\mathstrut +\mathstrut 92q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(24, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.3.h.a \(1\) \(0.654\) \(\Q\) \(\Q(\sqrt{-6}) \) \(-2\) \(3\) \(2\) \(-10\) \(q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
24.3.h.b \(1\) \(0.654\) \(\Q\) \(\Q(\sqrt{-6}) \) \(2\) \(-3\) \(-2\) \(-10\) \(q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots\)
24.3.h.c \(4\) \(0.654\) \(\Q(\sqrt{2}, \sqrt{-7})\) None \(0\) \(0\) \(0\) \(16\) \(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)