Properties

Label 24.4.d
Level 24
Weight 4
Character orbit d
Rep. character \(\chi_{24}(13,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 1
Sturm bound 16
Trace bound 0

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 24.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 14 6 8
Cusp forms 10 6 4
Eisenstein series 4 0 4

Trace form

\(6q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 28q^{7} \) \(\mathstrut -\mathstrut 76q^{8} \) \(\mathstrut -\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 28q^{7} \) \(\mathstrut -\mathstrut 76q^{8} \) \(\mathstrut -\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut 60q^{10} \) \(\mathstrut -\mathstrut 12q^{12} \) \(\mathstrut -\mathstrut 100q^{14} \) \(\mathstrut -\mathstrut 60q^{15} \) \(\mathstrut +\mathstrut 56q^{16} \) \(\mathstrut +\mathstrut 52q^{17} \) \(\mathstrut -\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut 224q^{22} \) \(\mathstrut +\mathstrut 328q^{23} \) \(\mathstrut +\mathstrut 204q^{24} \) \(\mathstrut -\mathstrut 106q^{25} \) \(\mathstrut +\mathstrut 56q^{26} \) \(\mathstrut -\mathstrut 352q^{28} \) \(\mathstrut +\mathstrut 372q^{30} \) \(\mathstrut -\mathstrut 636q^{31} \) \(\mathstrut -\mathstrut 248q^{32} \) \(\mathstrut -\mathstrut 548q^{34} \) \(\mathstrut -\mathstrut 144q^{36} \) \(\mathstrut -\mathstrut 776q^{38} \) \(\mathstrut +\mathstrut 312q^{39} \) \(\mathstrut +\mathstrut 232q^{40} \) \(\mathstrut +\mathstrut 236q^{41} \) \(\mathstrut -\mathstrut 564q^{42} \) \(\mathstrut +\mathstrut 1152q^{44} \) \(\mathstrut +\mathstrut 328q^{46} \) \(\mathstrut -\mathstrut 408q^{47} \) \(\mathstrut +\mathstrut 576q^{48} \) \(\mathstrut +\mathstrut 654q^{49} \) \(\mathstrut +\mathstrut 1970q^{50} \) \(\mathstrut -\mathstrut 368q^{52} \) \(\mathstrut +\mathstrut 54q^{54} \) \(\mathstrut +\mathstrut 1024q^{55} \) \(\mathstrut -\mathstrut 1864q^{56} \) \(\mathstrut -\mathstrut 168q^{57} \) \(\mathstrut +\mathstrut 140q^{58} \) \(\mathstrut -\mathstrut 1152q^{60} \) \(\mathstrut -\mathstrut 2108q^{62} \) \(\mathstrut -\mathstrut 252q^{63} \) \(\mathstrut +\mathstrut 832q^{64} \) \(\mathstrut -\mathstrut 1744q^{65} \) \(\mathstrut -\mathstrut 1440q^{66} \) \(\mathstrut +\mathstrut 2976q^{68} \) \(\mathstrut +\mathstrut 1352q^{70} \) \(\mathstrut -\mathstrut 1704q^{71} \) \(\mathstrut +\mathstrut 684q^{72} \) \(\mathstrut +\mathstrut 956q^{73} \) \(\mathstrut +\mathstrut 1568q^{74} \) \(\mathstrut -\mathstrut 1744q^{76} \) \(\mathstrut +\mathstrut 1608q^{78} \) \(\mathstrut -\mathstrut 44q^{79} \) \(\mathstrut -\mathstrut 2112q^{80} \) \(\mathstrut +\mathstrut 486q^{81} \) \(\mathstrut -\mathstrut 2236q^{82} \) \(\mathstrut -\mathstrut 1992q^{84} \) \(\mathstrut -\mathstrut 760q^{86} \) \(\mathstrut +\mathstrut 1044q^{87} \) \(\mathstrut +\mathstrut 1856q^{88} \) \(\mathstrut -\mathstrut 220q^{89} \) \(\mathstrut -\mathstrut 540q^{90} \) \(\mathstrut +\mathstrut 1728q^{92} \) \(\mathstrut +\mathstrut 2088q^{94} \) \(\mathstrut +\mathstrut 5104q^{95} \) \(\mathstrut +\mathstrut 2184q^{96} \) \(\mathstrut -\mathstrut 2444q^{97} \) \(\mathstrut +\mathstrut 3354q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.d.a \(6\) \(1.416\) 6.0.8248384.1 None \(2\) \(0\) \(0\) \(28\) \(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(3-\beta _{5})q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(24, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)