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

Related objects

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

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