# 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

# Related objects

## 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

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