Properties

Label 24.4.f
Level $24$
Weight $4$
Character orbit 24.f
Rep. character $\chi_{24}(11,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $2$
Sturm bound $16$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 24.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

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

Trace form

\( 10 q - 2 q^{3} + 4 q^{4} - 8 q^{6} - 2 q^{9} + O(q^{10}) \) \( 10 q - 2 q^{3} + 4 q^{4} - 8 q^{6} - 2 q^{9} - 24 q^{10} - 44 q^{12} - 152 q^{16} + 184 q^{18} - 28 q^{19} + 224 q^{22} + 328 q^{24} + 46 q^{25} - 134 q^{27} + 528 q^{28} - 624 q^{30} - 64 q^{33} - 784 q^{34} - 884 q^{36} - 1248 q^{40} + 1320 q^{42} + 428 q^{43} + 1440 q^{46} + 1720 q^{48} - 266 q^{49} + 752 q^{51} + 2112 q^{52} - 2168 q^{54} + 116 q^{57} - 2616 q^{58} - 2640 q^{60} - 2384 q^{64} + 2792 q^{66} - 1636 q^{67} + 3696 q^{70} + 3280 q^{72} + 212 q^{73} - 1958 q^{75} + 3608 q^{76} - 3696 q^{78} + 154 q^{81} - 3136 q^{82} - 4224 q^{84} - 4432 q^{88} + 4104 q^{90} + 3168 q^{91} + 4800 q^{94} + 4240 q^{96} - 52 q^{97} + 4112 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.4.f.a 24.f 24.f $2$ $1.416$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) 24.4.f.a \(0\) \(10\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2\beta q^{2}+(5+\beta )q^{3}-8q^{4}+(-4+10\beta )q^{6}+\cdots\)
24.4.f.b 24.f 24.f $8$ $1.416$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 24.4.f.b \(0\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{4})q^{3}+(3+\beta _{2})q^{4}+\cdots\)