Properties

Label 24.8.d
Level 24
Weight 8
Character orbit d
Rep. character \(\chi_{24}(13,\cdot)\)
Character field \(\Q\)
Dimension 14
Newforms 1
Sturm bound 32
Trace bound 0

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 24.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(24, [\chi])\).

Total New Old
Modular forms 30 14 16
Cusp forms 26 14 12
Eisenstein series 4 0 4

Trace form

\( 14q - 14q^{2} - 208q^{4} - 54q^{6} + 1372q^{7} - 428q^{8} - 10206q^{9} + O(q^{10}) \) \( 14q - 14q^{2} - 208q^{4} - 54q^{6} + 1372q^{7} - 428q^{8} - 10206q^{9} + 5020q^{10} + 7668q^{12} + 4636q^{14} - 13500q^{15} - 43336q^{16} - 2908q^{17} + 10206q^{18} + 175096q^{20} - 128480q^{22} - 143416q^{23} - 29268q^{24} - 202626q^{25} + 424984q^{26} + 567520q^{28} - 250668q^{30} - 89468q^{31} - 893944q^{32} + 1109820q^{34} + 151632q^{36} - 823816q^{38} + 474552q^{39} - 860888q^{40} - 441284q^{41} + 427788q^{42} + 1275264q^{44} - 2167992q^{46} - 1056408q^{47} - 233280q^{48} + 2158134q^{49} + 324610q^{50} - 2059248q^{52} + 39366q^{54} + 4757504q^{55} + 1643704q^{56} + 1551096q^{57} - 5494676q^{58} - 3203712q^{60} + 5767172q^{62} - 1000188q^{63} + 3852224q^{64} - 2520464q^{65} - 3615840q^{66} - 3735840q^{68} + 12890312q^{70} + 5172696q^{71} + 312012q^{72} - 5446196q^{73} - 6468800q^{74} - 9084624q^{76} + 3542184q^{78} - 14373548q^{79} + 14369088q^{80} + 7440174q^{81} - 7935708q^{82} - 2775816q^{84} + 4738312q^{86} + 7902036q^{87} + 12598720q^{88} - 11952620q^{89} - 3659580q^{90} + 11004480q^{92} - 15440088q^{94} - 69327376q^{95} + 1341576q^{96} + 133732q^{97} + 53030538q^{98} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(24, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.8.d.a \(14\) \(7.497\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-14\) \(0\) \(0\) \(1372\) \(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(-15-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

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