Properties

Label 24.9.e
Level $24$
Weight $9$
Character orbit 24.e
Rep. character $\chi_{24}(17,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 24.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
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 36 8 28
Cusp forms 28 8 20
Eisenstein series 8 0 8

Trace form

\( 8 q + 56 q^{3} + 1584 q^{7} + 328 q^{9} + O(q^{10}) \) \( 8 q + 56 q^{3} + 1584 q^{7} + 328 q^{9} + 25232 q^{13} + 38336 q^{15} + 157936 q^{19} + 30480 q^{21} - 579704 q^{25} - 276040 q^{27} + 805552 q^{31} + 102848 q^{33} - 3985008 q^{37} - 2297104 q^{39} + 6962672 q^{43} + 8670592 q^{45} - 5884520 q^{49} - 15590144 q^{51} + 27101312 q^{55} + 36756688 q^{57} - 51583600 q^{61} - 69759312 q^{63} + 58200688 q^{67} + 94226048 q^{69} - 116854768 q^{73} - 143181896 q^{75} + 172454576 q^{79} + 194700040 q^{81} - 264333824 q^{85} - 242851008 q^{87} + 382128480 q^{91} + 313470352 q^{93} - 337326704 q^{97} - 369701504 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.9.e.a 24.e 3.b $8$ $9.777$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 24.9.e.a \(0\) \(56\) \(0\) \(1584\) $\mathrm{SU}(2)[C_{2}]$ \(q+(7+\beta _{2})q^{3}+(-\beta _{2}+\beta _{4})q^{5}+(198+\cdots)q^{7}+\cdots\)

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

\( S_{9}^{\mathrm{old}}(24, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)