Properties

 Label 3024.2.cx Level 3024 Weight 2 Character orbit cx Rep. character $$\chi_{3024}(559,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 96 Newform subspaces 11 Sturm bound 1152 Trace bound 11

Related objects

Defining parameters

 Level: $$N$$ = $$3024 = 2^{4} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 3024.cx (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$252$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$11$$ Sturm bound: $$1152$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$5$$, $$11$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3024, [\chi])$$.

Total New Old
Modular forms 1224 96 1128
Cusp forms 1080 96 984
Eisenstein series 144 0 144

Trace form

 $$96q + O(q^{10})$$ $$96q + 48q^{25} - 24q^{29} - 24q^{65} + 24q^{77} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(3024, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
3024.2.cx.a $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$-5$$ $$q+(-1-\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+(4+\cdots)q^{11}+\cdots$$
3024.2.cx.b $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$-4$$ $$q+(-1-\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+(2+\cdots)q^{11}+\cdots$$
3024.2.cx.c $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$4$$ $$q+(-1-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+(-2+\cdots)q^{11}+\cdots$$
3024.2.cx.d $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$5$$ $$q+(-1-\zeta_{6})q^{5}+(2+\zeta_{6})q^{7}+(-4+\cdots)q^{11}+\cdots$$
3024.2.cx.e $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$-1$$ $$q+(1+\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+(-2+\zeta_{6})q^{11}+\cdots$$
3024.2.cx.f $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$-1$$ $$q+(1+\zeta_{6})q^{5}+(-2+3\zeta_{6})q^{7}+(4-2\zeta_{6})q^{11}+\cdots$$
3024.2.cx.g $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$1$$ $$q+(1+\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+(-4+2\zeta_{6})q^{11}+\cdots$$
3024.2.cx.h $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$1$$ $$q+(1+\zeta_{6})q^{5}+(-1+3\zeta_{6})q^{7}+(2-\zeta_{6})q^{11}+\cdots$$
3024.2.cx.i $$24$$ $$24.147$$ None $$0$$ $$0$$ $$0$$ $$-6$$
3024.2.cx.j $$24$$ $$24.147$$ None $$0$$ $$0$$ $$0$$ $$6$$
3024.2.cx.k $$32$$ $$24.147$$ None $$0$$ $$0$$ $$0$$ $$0$$

Decomposition of $$S_{2}^{\mathrm{old}}(3024, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3024, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(756, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1008, [\chi])$$$$^{\oplus 2}$$

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ ($$1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4}$$)($$1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4}$$)($$1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4}$$)($$1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4}$$)($$1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4}$$)($$1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4}$$)($$1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4}$$)($$1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4}$$)
$7$ ($$1 + 5 T + 7 T^{2}$$)($$1 + 4 T + 7 T^{2}$$)($$1 - 4 T + 7 T^{2}$$)($$1 - 5 T + 7 T^{2}$$)($$1 + T + 7 T^{2}$$)($$1 + T + 7 T^{2}$$)($$1 - T + 7 T^{2}$$)($$1 - T + 7 T^{2}$$)
$11$ ($$1 - 6 T + 23 T^{2} - 66 T^{3} + 121 T^{4}$$)($$1 - 3 T + 14 T^{2} - 33 T^{3} + 121 T^{4}$$)($$1 + 3 T + 14 T^{2} + 33 T^{3} + 121 T^{4}$$)($$1 + 6 T + 23 T^{2} + 66 T^{3} + 121 T^{4}$$)($$1 + 3 T + 14 T^{2} + 33 T^{3} + 121 T^{4}$$)($$1 - 6 T + 23 T^{2} - 66 T^{3} + 121 T^{4}$$)($$1 + 6 T + 23 T^{2} + 66 T^{3} + 121 T^{4}$$)($$1 - 3 T + 14 T^{2} - 33 T^{3} + 121 T^{4}$$)
$13$ ($$1 + 13 T^{2} + 169 T^{4}$$)($$( 1 + 2 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} )$$)($$( 1 + 2 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} )$$)($$1 + 13 T^{2} + 169 T^{4}$$)($$( 1 - 7 T + 13 T^{2} )( 1 - 2 T + 13 T^{2} )$$)($$1 + 13 T^{2} + 169 T^{4}$$)($$1 + 13 T^{2} + 169 T^{4}$$)($$( 1 - 7 T + 13 T^{2} )( 1 - 2 T + 13 T^{2} )$$)
$17$ ($$1 - 22 T^{2} + 289 T^{4}$$)($$1 + 14 T^{2} + 289 T^{4}$$)($$1 + 14 T^{2} + 289 T^{4}$$)($$1 - 22 T^{2} + 289 T^{4}$$)($$1 + 14 T^{2} + 289 T^{4}$$)($$1 - 22 T^{2} + 289 T^{4}$$)($$1 - 22 T^{2} + 289 T^{4}$$)($$1 + 14 T^{2} + 289 T^{4}$$)
$19$ ($$( 1 + 5 T + 19 T^{2} )^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 - 4 T + 19 T^{2} )^{2}$$)($$( 1 - 5 T + 19 T^{2} )^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 - 5 T + 19 T^{2} )^{2}$$)($$( 1 + 5 T + 19 T^{2} )^{2}$$)($$( 1 - 4 T + 19 T^{2} )^{2}$$)
$23$ ($$1 - 9 T + 50 T^{2} - 207 T^{3} + 529 T^{4}$$)($$1 - 9 T + 50 T^{2} - 207 T^{3} + 529 T^{4}$$)($$1 + 9 T + 50 T^{2} + 207 T^{3} + 529 T^{4}$$)($$1 + 9 T + 50 T^{2} + 207 T^{3} + 529 T^{4}$$)($$1 + 9 T + 50 T^{2} + 207 T^{3} + 529 T^{4}$$)($$1 - 9 T + 50 T^{2} - 207 T^{3} + 529 T^{4}$$)($$1 + 9 T + 50 T^{2} + 207 T^{3} + 529 T^{4}$$)($$1 - 9 T + 50 T^{2} - 207 T^{3} + 529 T^{4}$$)
$29$ ($$1 - 29 T^{2} + 841 T^{4}$$)($$1 + 9 T + 52 T^{2} + 261 T^{3} + 841 T^{4}$$)($$1 + 9 T + 52 T^{2} + 261 T^{3} + 841 T^{4}$$)($$1 - 29 T^{2} + 841 T^{4}$$)($$1 + 9 T + 52 T^{2} + 261 T^{3} + 841 T^{4}$$)($$1 - 29 T^{2} + 841 T^{4}$$)($$1 - 29 T^{2} + 841 T^{4}$$)($$1 + 9 T + 52 T^{2} + 261 T^{3} + 841 T^{4}$$)
$31$ ($$1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4}$$)($$( 1 - 4 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} )$$)($$( 1 - 11 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} )$$)($$1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4}$$)($$( 1 - 4 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} )$$)($$1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4}$$)($$1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4}$$)($$( 1 - 11 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} )$$)
$37$ ($$( 1 + 8 T + 37 T^{2} )^{2}$$)($$( 1 - 10 T + 37 T^{2} )^{2}$$)($$( 1 - 10 T + 37 T^{2} )^{2}$$)($$( 1 + 8 T + 37 T^{2} )^{2}$$)($$( 1 - 10 T + 37 T^{2} )^{2}$$)($$( 1 + 8 T + 37 T^{2} )^{2}$$)($$( 1 + 8 T + 37 T^{2} )^{2}$$)($$( 1 - 10 T + 37 T^{2} )^{2}$$)
$41$ ($$1 + 41 T^{2} + 1681 T^{4}$$)($$1 - 9 T + 68 T^{2} - 369 T^{3} + 1681 T^{4}$$)($$1 - 9 T + 68 T^{2} - 369 T^{3} + 1681 T^{4}$$)($$1 + 41 T^{2} + 1681 T^{4}$$)($$1 + 9 T + 68 T^{2} + 369 T^{3} + 1681 T^{4}$$)($$1 + 41 T^{2} + 1681 T^{4}$$)($$1 + 41 T^{2} + 1681 T^{4}$$)($$1 + 9 T + 68 T^{2} + 369 T^{3} + 1681 T^{4}$$)
$43$ ($$1 - 6 T + 55 T^{2} - 258 T^{3} + 1849 T^{4}$$)($$1 + 15 T + 118 T^{2} + 645 T^{3} + 1849 T^{4}$$)($$1 - 15 T + 118 T^{2} - 645 T^{3} + 1849 T^{4}$$)($$1 + 6 T + 55 T^{2} + 258 T^{3} + 1849 T^{4}$$)($$1 - 15 T + 118 T^{2} - 645 T^{3} + 1849 T^{4}$$)($$1 - 6 T + 55 T^{2} - 258 T^{3} + 1849 T^{4}$$)($$1 + 6 T + 55 T^{2} + 258 T^{3} + 1849 T^{4}$$)($$1 + 15 T + 118 T^{2} + 645 T^{3} + 1849 T^{4}$$)
$47$ ($$1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4}$$)($$1 + 3 T - 38 T^{2} + 141 T^{3} + 2209 T^{4}$$)($$1 - 3 T - 38 T^{2} - 141 T^{3} + 2209 T^{4}$$)($$1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4}$$)($$1 + 3 T - 38 T^{2} + 141 T^{3} + 2209 T^{4}$$)($$1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4}$$)($$1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4}$$)($$1 - 3 T - 38 T^{2} - 141 T^{3} + 2209 T^{4}$$)
$53$ ($$( 1 - 6 T + 53 T^{2} )^{2}$$)($$( 1 - 6 T + 53 T^{2} )^{2}$$)($$( 1 - 6 T + 53 T^{2} )^{2}$$)($$( 1 - 6 T + 53 T^{2} )^{2}$$)($$( 1 - 6 T + 53 T^{2} )^{2}$$)($$( 1 - 6 T + 53 T^{2} )^{2}$$)($$( 1 - 6 T + 53 T^{2} )^{2}$$)($$( 1 - 6 T + 53 T^{2} )^{2}$$)
$59$ ($$1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4}$$)($$1 - 3 T - 50 T^{2} - 177 T^{3} + 3481 T^{4}$$)($$1 + 3 T - 50 T^{2} + 177 T^{3} + 3481 T^{4}$$)($$1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4}$$)($$1 - 3 T - 50 T^{2} - 177 T^{3} + 3481 T^{4}$$)($$1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4}$$)($$1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4}$$)($$1 + 3 T - 50 T^{2} + 177 T^{3} + 3481 T^{4}$$)
$61$ ($$1 - 3 T + 64 T^{2} - 183 T^{3} + 3721 T^{4}$$)($$1 - 3 T + 64 T^{2} - 183 T^{3} + 3721 T^{4}$$)($$1 - 3 T + 64 T^{2} - 183 T^{3} + 3721 T^{4}$$)($$1 - 3 T + 64 T^{2} - 183 T^{3} + 3721 T^{4}$$)($$1 + 3 T + 64 T^{2} + 183 T^{3} + 3721 T^{4}$$)($$1 + 3 T + 64 T^{2} + 183 T^{3} + 3721 T^{4}$$)($$1 + 3 T + 64 T^{2} + 183 T^{3} + 3721 T^{4}$$)($$1 + 3 T + 64 T^{2} + 183 T^{3} + 3721 T^{4}$$)
$67$ ($$1 - 12 T + 115 T^{2} - 804 T^{3} + 4489 T^{4}$$)($$1 - 15 T + 142 T^{2} - 1005 T^{3} + 4489 T^{4}$$)($$1 + 15 T + 142 T^{2} + 1005 T^{3} + 4489 T^{4}$$)($$1 + 12 T + 115 T^{2} + 804 T^{3} + 4489 T^{4}$$)($$1 + 15 T + 142 T^{2} + 1005 T^{3} + 4489 T^{4}$$)($$1 - 12 T + 115 T^{2} - 804 T^{3} + 4489 T^{4}$$)($$1 + 12 T + 115 T^{2} + 804 T^{3} + 4489 T^{4}$$)($$1 - 15 T + 142 T^{2} - 1005 T^{3} + 4489 T^{4}$$)
$71$ ($$1 + 5 T^{2} + 5041 T^{4}$$)($$1 - 130 T^{2} + 5041 T^{4}$$)($$1 - 130 T^{2} + 5041 T^{4}$$)($$1 + 5 T^{2} + 5041 T^{4}$$)($$1 - 130 T^{2} + 5041 T^{4}$$)($$1 + 5 T^{2} + 5041 T^{4}$$)($$1 + 5 T^{2} + 5041 T^{4}$$)($$1 - 130 T^{2} + 5041 T^{4}$$)
$73$ ($$1 - 98 T^{2} + 5329 T^{4}$$)($$1 - 98 T^{2} + 5329 T^{4}$$)($$1 - 98 T^{2} + 5329 T^{4}$$)($$1 - 98 T^{2} + 5329 T^{4}$$)($$1 - 98 T^{2} + 5329 T^{4}$$)($$1 - 98 T^{2} + 5329 T^{4}$$)($$1 - 98 T^{2} + 5329 T^{4}$$)($$1 - 98 T^{2} + 5329 T^{4}$$)
$79$ ($$1 + 27 T + 322 T^{2} + 2133 T^{3} + 6241 T^{4}$$)($$( 1 - 13 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} )$$)($$( 1 - 4 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} )$$)($$1 - 27 T + 322 T^{2} - 2133 T^{3} + 6241 T^{4}$$)($$( 1 - 4 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} )$$)($$1 + 27 T + 322 T^{2} + 2133 T^{3} + 6241 T^{4}$$)($$1 - 27 T + 322 T^{2} - 2133 T^{3} + 6241 T^{4}$$)($$( 1 - 13 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} )$$)
$83$ ($$1 - 83 T^{2} + 6889 T^{4}$$)($$1 - 9 T - 2 T^{2} - 747 T^{3} + 6889 T^{4}$$)($$1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4}$$)($$1 - 83 T^{2} + 6889 T^{4}$$)($$1 - 9 T - 2 T^{2} - 747 T^{3} + 6889 T^{4}$$)($$1 - 83 T^{2} + 6889 T^{4}$$)($$1 - 83 T^{2} + 6889 T^{4}$$)($$1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4}$$)
$89$ ($$1 + 14 T^{2} + 7921 T^{4}$$)($$1 - 130 T^{2} + 7921 T^{4}$$)($$1 - 130 T^{2} + 7921 T^{4}$$)($$1 + 14 T^{2} + 7921 T^{4}$$)($$1 - 130 T^{2} + 7921 T^{4}$$)($$1 + 14 T^{2} + 7921 T^{4}$$)($$1 + 14 T^{2} + 7921 T^{4}$$)($$1 - 130 T^{2} + 7921 T^{4}$$)
$97$ ($$1 + 18 T + 205 T^{2} + 1746 T^{3} + 9409 T^{4}$$)($$( 1 - 5 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} )$$)($$( 1 - 5 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} )$$)($$1 + 18 T + 205 T^{2} + 1746 T^{3} + 9409 T^{4}$$)($$( 1 - 14 T + 97 T^{2} )( 1 + 5 T + 97 T^{2} )$$)($$1 - 18 T + 205 T^{2} - 1746 T^{3} + 9409 T^{4}$$)($$1 - 18 T + 205 T^{2} - 1746 T^{3} + 9409 T^{4}$$)($$( 1 - 14 T + 97 T^{2} )( 1 + 5 T + 97 T^{2} )$$)