Properties

Label 24.4.f
Level 24
Weight 4
Character orbit 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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.4.f.a \(2\) \(1.416\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(10\) \(0\) \(0\) \(q+2\beta q^{2}+(5+\beta )q^{3}-8q^{4}+(-4+10\beta )q^{6}+\cdots\)
24.4.f.b \(8\) \(1.416\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-12\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2+\beta _{4})q^{3}+(3+\beta _{2})q^{4}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 8 T^{2} \))(\( 1 - 10 T^{2} + 120 T^{4} - 640 T^{6} + 4096 T^{8} \))
$3$ (\( 1 - 10 T + 27 T^{2} \))(\( ( 1 + 6 T + 30 T^{2} + 162 T^{3} + 729 T^{4} )^{2} \))
$5$ (\( ( 1 + 125 T^{2} )^{2} \))(\( ( 1 + 176 T^{2} + 38862 T^{4} + 2750000 T^{6} + 244140625 T^{8} )^{2} \))
$7$ (\( ( 1 - 343 T^{2} )^{2} \))(\( ( 1 - 448 T^{2} + 215646 T^{4} - 52706752 T^{6} + 13841287201 T^{8} )^{2} \))
$11$ (\( ( 1 - 18 T + 1331 T^{2} )( 1 + 18 T + 1331 T^{2} ) \))(\( ( 1 - 4840 T^{2} + 9341310 T^{4} - 8574355240 T^{6} + 3138428376721 T^{8} )^{2} \))
$13$ (\( ( 1 - 2197 T^{2} )^{2} \))(\( ( 1 - 2980 T^{2} + 4014966 T^{4} - 14383890820 T^{6} + 23298085122481 T^{8} )^{2} \))
$17$ (\( ( 1 - 90 T + 4913 T^{2} )( 1 + 90 T + 4913 T^{2} ) \))(\( ( 1 - 17188 T^{2} + 120704262 T^{4} - 414876535972 T^{6} + 582622237229761 T^{8} )^{2} \))
$19$ (\( ( 1 + 106 T + 6859 T^{2} )^{2} \))(\( ( 1 - 46 T + 10254 T^{2} - 315514 T^{3} + 47045881 T^{4} )^{4} \))
$23$ (\( ( 1 + 12167 T^{2} )^{2} \))(\( ( 1 + 31196 T^{2} + 464722854 T^{4} + 4618127593244 T^{6} + 21914624432020321 T^{8} )^{2} \))
$29$ (\( ( 1 + 24389 T^{2} )^{2} \))(\( ( 1 + 53936 T^{2} + 1889351598 T^{4} + 32082390641456 T^{6} + 353814783205469041 T^{8} )^{2} \))
$31$ (\( ( 1 - 29791 T^{2} )^{2} \))(\( ( 1 - 98176 T^{2} + 4116020094 T^{4} - 87131561385856 T^{6} + 787662783788549761 T^{8} )^{2} \))
$37$ (\( ( 1 - 50653 T^{2} )^{2} \))(\( ( 1 - 124996 T^{2} + 9025572822 T^{4} - 320705538219364 T^{6} + 6582952005840035281 T^{8} )^{2} \))
$41$ (\( ( 1 - 522 T + 68921 T^{2} )( 1 + 522 T + 68921 T^{2} ) \))(\( ( 1 - 82084 T^{2} + 4965540774 T^{4} - 389907556518244 T^{6} + 22563490300366186081 T^{8} )^{2} \))
$43$ (\( ( 1 - 290 T + 79507 T^{2} )^{2} \))(\( ( 1 + 38 T + 109182 T^{2} + 3021266 T^{3} + 6321363049 T^{4} )^{4} \))
$47$ (\( ( 1 + 103823 T^{2} )^{2} \))(\( ( 1 + 93500 T^{2} - 1715710650 T^{4} + 1007856633261500 T^{6} + \)\(11\!\cdots\!41\)\( T^{8} )^{2} \))
$53$ (\( ( 1 + 148877 T^{2} )^{2} \))(\( ( 1 + 418352 T^{2} + 87270813582 T^{4} + 9272504807039408 T^{6} + \)\(49\!\cdots\!41\)\( T^{8} )^{2} \))
$59$ (\( ( 1 - 846 T + 205379 T^{2} )( 1 + 846 T + 205379 T^{2} ) \))(\( ( 1 - 799912 T^{2} + 244209482046 T^{4} - 33740715025839592 T^{6} + \)\(17\!\cdots\!81\)\( T^{8} )^{2} \))
$61$ (\( ( 1 - 226981 T^{2} )^{2} \))(\( ( 1 - 357220 T^{2} + 77943572022 T^{4} - 18404108129236420 T^{6} + \)\(26\!\cdots\!21\)\( T^{8} )^{2} \))
$67$ (\( ( 1 + 70 T + 300763 T^{2} )^{2} \))(\( ( 1 + 374 T + 633822 T^{2} + 112485362 T^{3} + 90458382169 T^{4} )^{4} \))
$71$ (\( ( 1 + 357911 T^{2} )^{2} \))(\( ( 1 + 776732 T^{2} + 403415373030 T^{4} + 99499589730526172 T^{6} + \)\(16\!\cdots\!41\)\( T^{8} )^{2} \))
$73$ (\( ( 1 + 430 T + 389017 T^{2} )^{2} \))(\( ( 1 - 268 T + 73158 T^{2} - 104256556 T^{3} + 151334226289 T^{4} )^{4} \))
$79$ (\( ( 1 - 493039 T^{2} )^{2} \))(\( ( 1 - 943744 T^{2} + 544083847614 T^{4} - 229412327623210624 T^{6} + \)\(59\!\cdots\!41\)\( T^{8} )^{2} \))
$83$ (\( ( 1 - 1350 T + 571787 T^{2} )( 1 + 1350 T + 571787 T^{2} ) \))(\( ( 1 - 1890664 T^{2} + 1510361878110 T^{4} - 618134394075327016 T^{6} + \)\(10\!\cdots\!61\)\( T^{8} )^{2} \))
$89$ (\( ( 1 - 1026 T + 704969 T^{2} )( 1 + 1026 T + 704969 T^{2} ) \))(\( ( 1 - 175300 T^{2} - 599506777050 T^{4} - 87120820305463300 T^{6} + \)\(24\!\cdots\!21\)\( T^{8} )^{2} \))
$97$ (\( ( 1 - 1910 T + 912673 T^{2} )^{2} \))(\( ( 1 + 968 T + 1792302 T^{2} + 883467464 T^{3} + 832972004929 T^{4} )^{4} \))
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