↑

Properties

Label 24.9.b
Level $24$
Weight $9$
Character orbit 24.b
Rep. character $\chi_{24}(19,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 24.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(24, [\chi])\).

Total New Old
Modular forms 34 16 18
Cusp forms 30 16 14
Eisenstein series 4 0 4

Trace form

\( 16 q - 6 q^{2} + 424 q^{4} - 1134 q^{6} - 4500 q^{8} + 34992 q^{9} + O(q^{10}) \) \( 16 q - 6 q^{2} + 424 q^{4} - 1134 q^{6} - 4500 q^{8} + 34992 q^{9} + 12156 q^{10} - 39552 q^{11} - 11340 q^{12} + 121668 q^{14} - 48968 q^{16} + 77280 q^{17} - 13122 q^{18} + 167552 q^{19} + 354408 q^{20} + 213392 q^{22} - 296460 q^{24} - 1604144 q^{25} - 1703664 q^{26} + 3531312 q^{28} + 2007828 q^{30} - 2645976 q^{32} - 6140452 q^{34} - 2415744 q^{35} + 927288 q^{36} + 10249320 q^{38} - 14903592 q^{40} - 2187360 q^{41} - 4148172 q^{42} + 3525248 q^{43} + 24238272 q^{44} + 14274552 q^{46} - 1448928 q^{48} - 7109552 q^{49} - 26509326 q^{50} + 13862016 q^{51} + 16742928 q^{52} - 2480058 q^{54} - 1672104 q^{56} - 1550016 q^{57} - 28713780 q^{58} + 44938752 q^{59} + 12578976 q^{60} - 19827444 q^{62} + 24152992 q^{64} - 52558464 q^{65} - 5623344 q^{66} + 6892544 q^{67} - 35334576 q^{68} - 73847400 q^{70} - 9841500 q^{72} + 12400160 q^{73} + 135885720 q^{74} + 12918528 q^{75} - 125101072 q^{76} - 57360960 q^{78} + 169182432 q^{80} + 76527504 q^{81} + 90735860 q^{82} - 209328000 q^{83} - 71849592 q^{84} - 135445608 q^{86} + 248505824 q^{88} - 152224800 q^{89} + 26585172 q^{90} + 395802240 q^{91} - 116843616 q^{92} - 213312744 q^{94} + 47701224 q^{96} - 38799136 q^{97} + 230784738 q^{98} - 86500224 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.9.b.a 24.b 8.d $16$ $9.777$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(26-\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(24, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)