Properties

Label 24.3.h
Level 24
Weight 3
Character orbit h
Rep. character \(\chi_{24}(5,\cdot)\)
Character field \(\Q\)
Dimension 6
Newform subspaces 3
Sturm bound 12
Trace bound 2

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Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 24.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(12\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(24, [\chi])\).

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

Trace form

\( 6q - 4q^{4} - 8q^{6} - 4q^{7} - 2q^{9} + O(q^{10}) \) \( 6q - 4q^{4} - 8q^{6} - 4q^{7} - 2q^{9} - 24q^{10} + 28q^{12} - 20q^{15} + 40q^{16} + 56q^{18} + 64q^{22} - 88q^{24} - 14q^{25} - 128q^{28} - 112q^{30} + 60q^{31} - 12q^{33} - 112q^{34} + 132q^{36} + 112q^{39} + 128q^{40} + 136q^{42} + 224q^{46} - 168q^{48} - 30q^{49} - 112q^{52} - 184q^{54} - 232q^{55} + 56q^{57} - 152q^{58} + 144q^{60} - 260q^{63} + 272q^{64} + 168q^{66} + 16q^{70} - 112q^{72} + 76q^{73} - 56q^{76} - 112q^{78} + 380q^{79} + 38q^{81} - 224q^{82} + 112q^{84} + 396q^{87} - 80q^{88} + 8q^{90} - 16q^{96} + 92q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.3.h.a \(1\) \(0.654\) \(\Q\) \(\Q(\sqrt{-6}) \) \(-2\) \(3\) \(2\) \(-10\) \(q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
24.3.h.b \(1\) \(0.654\) \(\Q\) \(\Q(\sqrt{-6}) \) \(2\) \(-3\) \(-2\) \(-10\) \(q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots\)
24.3.h.c \(4\) \(0.654\) \(\Q(\sqrt{2}, \sqrt{-7})\) None \(0\) \(0\) \(0\) \(16\) \(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T \))(\( 1 - 2 T \))(\( 1 + 6 T^{2} + 16 T^{4} \))
$3$ (\( 1 - 3 T \))(\( 1 + 3 T \))(\( 1 + 10 T^{2} + 81 T^{4} \))
$5$ (\( 1 - 2 T + 25 T^{2} \))(\( 1 + 2 T + 25 T^{2} \))(\( ( 1 + 18 T^{2} + 625 T^{4} )^{2} \))
$7$ (\( 1 + 10 T + 49 T^{2} \))(\( 1 + 10 T + 49 T^{2} \))(\( ( 1 - 4 T + 49 T^{2} )^{4} \))
$11$ (\( 1 + 10 T + 121 T^{2} \))(\( 1 - 10 T + 121 T^{2} \))(\( ( 1 + 170 T^{2} + 14641 T^{4} )^{2} \))
$13$ (\( ( 1 - 13 T )( 1 + 13 T ) \))(\( ( 1 - 13 T )( 1 + 13 T ) \))(\( ( 1 - 226 T^{2} + 28561 T^{4} )^{2} \))
$17$ (\( ( 1 - 17 T )( 1 + 17 T ) \))(\( ( 1 - 17 T )( 1 + 17 T ) \))(\( ( 1 - 354 T^{2} + 83521 T^{4} )^{2} \))
$19$ (\( ( 1 - 19 T )( 1 + 19 T ) \))(\( ( 1 - 19 T )( 1 + 19 T ) \))(\( ( 1 - 694 T^{2} + 130321 T^{4} )^{2} \))
$23$ (\( ( 1 - 23 T )( 1 + 23 T ) \))(\( ( 1 - 23 T )( 1 + 23 T ) \))(\( ( 1 - 162 T^{2} + 279841 T^{4} )^{2} \))
$29$ (\( 1 - 50 T + 841 T^{2} \))(\( 1 + 50 T + 841 T^{2} \))(\( ( 1 + 1394 T^{2} + 707281 T^{4} )^{2} \))
$31$ (\( 1 - 38 T + 961 T^{2} \))(\( 1 - 38 T + 961 T^{2} \))(\( ( 1 + 4 T + 961 T^{2} )^{4} \))
$37$ (\( ( 1 - 37 T )( 1 + 37 T ) \))(\( ( 1 - 37 T )( 1 + 37 T ) \))(\( ( 1 + 62 T^{2} + 1874161 T^{4} )^{2} \))
$41$ (\( ( 1 - 41 T )( 1 + 41 T ) \))(\( ( 1 - 41 T )( 1 + 41 T ) \))(\( ( 1 - 2466 T^{2} + 2825761 T^{4} )^{2} \))
$43$ (\( ( 1 - 43 T )( 1 + 43 T ) \))(\( ( 1 - 43 T )( 1 + 43 T ) \))(\( ( 1 - 3670 T^{2} + 3418801 T^{4} )^{2} \))
$47$ (\( ( 1 - 47 T )( 1 + 47 T ) \))(\( ( 1 - 47 T )( 1 + 47 T ) \))(\( ( 1 - 47 T )^{4}( 1 + 47 T )^{4} \))
$53$ (\( 1 + 94 T + 2809 T^{2} \))(\( 1 - 94 T + 2809 T^{2} \))(\( ( 1 + 3026 T^{2} + 7890481 T^{4} )^{2} \))
$59$ (\( 1 + 10 T + 3481 T^{2} \))(\( 1 - 10 T + 3481 T^{2} \))(\( ( 1 + 4650 T^{2} + 12117361 T^{4} )^{2} \))
$61$ (\( ( 1 - 61 T )( 1 + 61 T ) \))(\( ( 1 - 61 T )( 1 + 61 T ) \))(\( ( 1 + 1630 T^{2} + 13845841 T^{4} )^{2} \))
$67$ (\( ( 1 - 67 T )( 1 + 67 T ) \))(\( ( 1 - 67 T )( 1 + 67 T ) \))(\( ( 1 - 6710 T^{2} + 20151121 T^{4} )^{2} \))
$71$ (\( ( 1 - 71 T )( 1 + 71 T ) \))(\( ( 1 - 71 T )( 1 + 71 T ) \))(\( ( 1 - 110 T + 5041 T^{2} )^{2}( 1 + 110 T + 5041 T^{2} )^{2} \))
$73$ (\( 1 - 50 T + 5329 T^{2} \))(\( 1 - 50 T + 5329 T^{2} \))(\( ( 1 + 6 T + 5329 T^{2} )^{4} \))
$79$ (\( 1 + 58 T + 6241 T^{2} \))(\( 1 + 58 T + 6241 T^{2} \))(\( ( 1 - 124 T + 6241 T^{2} )^{4} \))
$83$ (\( 1 - 134 T + 6889 T^{2} \))(\( 1 + 134 T + 6889 T^{2} \))(\( ( 1 + 13770 T^{2} + 47458321 T^{4} )^{2} \))
$89$ (\( ( 1 - 89 T )( 1 + 89 T ) \))(\( ( 1 - 89 T )( 1 + 89 T ) \))(\( ( 1 - 4866 T^{2} + 62742241 T^{4} )^{2} \))
$97$ (\( 1 + 190 T + 9409 T^{2} \))(\( 1 + 190 T + 9409 T^{2} \))(\( ( 1 - 118 T + 9409 T^{2} )^{4} \))
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