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Properties

Label 24.4.d
Level $24$
Weight $4$
Character orbit 24.d
Rep. character $\chi_{24}(13,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(16\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 14 6 8
Cusp forms 10 6 4
Eisenstein series 4 0 4

Trace form

\( 6 q + 2 q^{2} + 16 q^{4} - 6 q^{6} + 28 q^{7} - 76 q^{8} - 54 q^{9} + O(q^{10}) \) \( 6 q + 2 q^{2} + 16 q^{4} - 6 q^{6} + 28 q^{7} - 76 q^{8} - 54 q^{9} + 60 q^{10} - 12 q^{12} - 100 q^{14} - 60 q^{15} + 56 q^{16} + 52 q^{17} - 18 q^{18} + 56 q^{20} + 224 q^{22} + 328 q^{23} + 204 q^{24} - 106 q^{25} + 56 q^{26} - 352 q^{28} + 372 q^{30} - 636 q^{31} - 248 q^{32} - 548 q^{34} - 144 q^{36} - 776 q^{38} + 312 q^{39} + 232 q^{40} + 236 q^{41} - 564 q^{42} + 1152 q^{44} + 328 q^{46} - 408 q^{47} + 576 q^{48} + 654 q^{49} + 1970 q^{50} - 368 q^{52} + 54 q^{54} + 1024 q^{55} - 1864 q^{56} - 168 q^{57} + 140 q^{58} - 1152 q^{60} - 2108 q^{62} - 252 q^{63} + 832 q^{64} - 1744 q^{65} - 1440 q^{66} + 2976 q^{68} + 1352 q^{70} - 1704 q^{71} + 684 q^{72} + 956 q^{73} + 1568 q^{74} - 1744 q^{76} + 1608 q^{78} - 44 q^{79} - 2112 q^{80} + 486 q^{81} - 2236 q^{82} - 1992 q^{84} - 760 q^{86} + 1044 q^{87} + 1856 q^{88} - 220 q^{89} - 540 q^{90} + 1728 q^{92} + 2088 q^{94} + 5104 q^{95} + 2184 q^{96} - 2444 q^{97} + 3354 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.4.d.a 24.d 8.b $6$ $1.416$ 6.0.8248384.1 None \(2\) \(0\) \(0\) \(28\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(3-\beta _{5})q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(24, [\chi]) \cong \)