Properties

Label 24.2
Level 24
Weight 2
Dimension 5
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 64
Trace bound 2

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Defining parameters

Level: \( N \) = \( 24\( 24 = 2^{3} \cdot 3 \) \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(64\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(24))\).

Total New Old
Modular forms 28 9 19
Cusp forms 5 5 0
Eisenstein series 23 4 19

Trace form

\( 5q - 2q^{2} - 3q^{3} - 4q^{4} - 2q^{5} + 2q^{6} - 4q^{7} + 4q^{8} - 3q^{9} + O(q^{10}) \) \( 5q - 2q^{2} - 3q^{3} - 4q^{4} - 2q^{5} + 2q^{6} - 4q^{7} + 4q^{8} - 3q^{9} + 4q^{10} + 4q^{11} + 8q^{12} - 2q^{13} + 4q^{14} + 6q^{15} - 2q^{17} - 6q^{18} - 8q^{20} - 8q^{22} - 12q^{24} - 9q^{25} - 8q^{26} + 9q^{27} + 6q^{29} - 4q^{30} + 12q^{31} + 8q^{32} + 4q^{33} + 20q^{34} + 4q^{36} + 6q^{37} + 8q^{38} - 6q^{39} + 8q^{40} - 2q^{41} + 4q^{42} - 16q^{43} - 2q^{45} - 8q^{46} - 24q^{47} - 8q^{48} + q^{49} - 2q^{50} - 18q^{51} + 16q^{52} - 2q^{53} + 6q^{54} - 8q^{55} - 8q^{56} + 8q^{57} - 12q^{58} + 4q^{59} - 2q^{61} - 4q^{62} + 4q^{63} - 16q^{64} + 20q^{65} + 8q^{66} + 24q^{67} + 8q^{69} - 8q^{70} + 32q^{71} + 12q^{72} + 2q^{73} + 16q^{74} + 11q^{75} - 24q^{76} + 8q^{78} + 12q^{79} - 11q^{81} - 36q^{82} - 4q^{83} - 8q^{84} - 4q^{85} - 8q^{86} - 18q^{87} + 16q^{88} - 26q^{89} - 4q^{90} - 8q^{93} + 24q^{94} - 8q^{95} + 24q^{96} - 22q^{97} + 6q^{98} - 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
24.2.a \(\chi_{24}(1, \cdot)\) 24.2.a.a 1 1
24.2.c \(\chi_{24}(23, \cdot)\) None 0 1
24.2.d \(\chi_{24}(13, \cdot)\) 24.2.d.a 2 1
24.2.f \(\chi_{24}(11, \cdot)\) 24.2.f.a 2 1

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 2 T^{2} \))(\( 1 + 2 T^{2} \))
$3$ (\( 1 + T \))(\( 1 + T^{2} \))(\( 1 + 2 T + 3 T^{2} \))
$5$ (\( 1 + 2 T + 5 T^{2} \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 + 5 T^{2} )^{2} \))
$7$ (\( 1 + 7 T^{2} \))(\( ( 1 + 2 T + 7 T^{2} )^{2} \))(\( ( 1 - 7 T^{2} )^{2} \))
$11$ (\( 1 - 4 T + 11 T^{2} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( ( 1 - 6 T + 11 T^{2} )( 1 + 6 T + 11 T^{2} ) \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( ( 1 - 13 T^{2} )^{2} \))
$17$ (\( 1 - 2 T + 17 T^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )( 1 + 6 T + 17 T^{2} ) \))
$19$ (\( 1 + 4 T + 19 T^{2} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( ( 1 - 2 T + 19 T^{2} )^{2} \))
$23$ (\( 1 + 8 T + 23 T^{2} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))
$29$ (\( 1 - 6 T + 29 T^{2} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( ( 1 + 29 T^{2} )^{2} \))
$31$ (\( 1 - 8 T + 31 T^{2} \))(\( ( 1 - 2 T + 31 T^{2} )^{2} \))(\( ( 1 - 31 T^{2} )^{2} \))
$37$ (\( 1 - 6 T + 37 T^{2} \))(\( 1 - 10 T^{2} + 1369 T^{4} \))(\( ( 1 - 37 T^{2} )^{2} \))
$41$ (\( 1 + 6 T + 41 T^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )( 1 + 6 T + 41 T^{2} ) \))
$43$ (\( 1 - 4 T + 43 T^{2} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( ( 1 + 10 T + 43 T^{2} )^{2} \))
$47$ (\( 1 + 47 T^{2} \))(\( ( 1 + 12 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))
$53$ (\( 1 + 2 T + 53 T^{2} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( ( 1 + 53 T^{2} )^{2} \))
$59$ (\( 1 - 4 T + 59 T^{2} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( ( 1 - 6 T + 59 T^{2} )( 1 + 6 T + 59 T^{2} ) \))
$61$ (\( 1 + 2 T + 61 T^{2} \))(\( ( 1 - 61 T^{2} )^{2} \))(\( ( 1 - 61 T^{2} )^{2} \))
$67$ (\( 1 + 4 T + 67 T^{2} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( ( 1 - 14 T + 67 T^{2} )^{2} \))
$71$ (\( 1 - 8 T + 71 T^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))
$73$ (\( 1 - 10 T + 73 T^{2} \))(\( ( 1 + 6 T + 73 T^{2} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))
$79$ (\( 1 + 8 T + 79 T^{2} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( ( 1 - 79 T^{2} )^{2} \))
$83$ (\( 1 + 4 T + 83 T^{2} \))(\( 1 + 90 T^{2} + 6889 T^{4} \))(\( ( 1 - 18 T + 83 T^{2} )( 1 + 18 T + 83 T^{2} ) \))
$89$ (\( 1 + 6 T + 89 T^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 18 T + 89 T^{2} )( 1 + 18 T + 89 T^{2} ) \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))
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