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Properties

Label 24.8.d
Level $24$
Weight $8$
Character orbit 24.d
Rep. character $\chi_{24}(13,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.8.d.a 24.d 8.b $14$ $7.497$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-14\) \(0\) \(0\) \(1372\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(-15-\beta _{1}+\cdots)q^{4}+\cdots\)

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

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