# Properties

 Label 3024.2.cz Level 3024 Weight 2 Character orbit cz Rep. character $$\chi_{3024}(1279,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 96 Newform subspaces 9 Sturm bound 1152 Trace bound 7

# Related objects

## Defining parameters

 Level: $$N$$ = $$3024 = 2^{4} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 3024.cz (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$252$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$9$$ Sturm bound: $$1152$$ Trace bound: $$7$$ 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

 $$96q + O(q^{10})$$ $$96q + 48q^{25} + 12q^{29} + 48q^{65} + 24q^{77} - 36q^{89} + O(q^{100})$$

## 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.cz.a $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-1$$ $$q+(-2+3\zeta_{6})q^{7}+(4-2\zeta_{6})q^{11}+(-2+\cdots)q^{13}+\cdots$$
3024.2.cz.b $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$1$$ $$q+(2-3\zeta_{6})q^{7}+(-4+2\zeta_{6})q^{11}+(-2+\cdots)q^{13}+\cdots$$
3024.2.cz.c $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$-4$$ $$q+(1+\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+(6-3\zeta_{6})q^{11}+\cdots$$
3024.2.cz.d $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$4$$ $$q+(1+\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+(-6+3\zeta_{6})q^{11}+\cdots$$
3024.2.cz.e $$4$$ $$24.147$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$-6$$ $$-4$$ $$q+(-2-\beta _{1}+\beta _{3})q^{5}+(-1+\beta _{2})q^{7}+\cdots$$
3024.2.cz.f $$4$$ $$24.147$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$-6$$ $$4$$ $$q+(-2-\beta _{1}+\beta _{3})q^{5}+(1-\beta _{2})q^{7}+\cdots$$
3024.2.cz.g $$24$$ $$24.147$$ None $$0$$ $$0$$ $$3$$ $$-4$$
3024.2.cz.h $$24$$ $$24.147$$ None $$0$$ $$0$$ $$3$$ $$4$$
3024.2.cz.i $$32$$ $$24.147$$ 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
$5$ ($$1 + 5 T^{2} + 25 T^{4}$$)($$1 + 5 T^{2} + 25 T^{4}$$)($$1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4}$$)($$1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4}$$)($$( 1 + 2 T^{2} + 25 T^{4} )( 1 + 6 T + 17 T^{2} + 30 T^{3} + 25 T^{4} )$$)($$( 1 + 2 T^{2} + 25 T^{4} )( 1 + 6 T + 17 T^{2} + 30 T^{3} + 25 T^{4} )$$)
$7$ ($$1 + T + 7 T^{2}$$)($$1 - T + 7 T^{2}$$)($$1 + 4 T + 7 T^{2}$$)($$1 - 4 T + 7 T^{2}$$)($$( 1 + 2 T + 7 T^{2} )^{2}$$)($$( 1 - 2 T + 7 T^{2} )^{2}$$)
$11$ ($$1 - 6 T + 23 T^{2} - 66 T^{3} + 121 T^{4}$$)($$1 + 6 T + 23 T^{2} + 66 T^{3} + 121 T^{4}$$)($$1 - 9 T + 38 T^{2} - 99 T^{3} + 121 T^{4}$$)($$1 + 9 T + 38 T^{2} + 99 T^{3} + 121 T^{4}$$)($$( 1 + 3 T + 14 T^{2} + 33 T^{3} + 121 T^{4} )^{2}$$)($$( 1 - 3 T + 14 T^{2} - 33 T^{3} + 121 T^{4} )^{2}$$)
$13$ ($$( 1 - 2 T + 13 T^{2} )( 1 + 5 T + 13 T^{2} )$$)($$( 1 - 2 T + 13 T^{2} )( 1 + 5 T + 13 T^{2} )$$)($$( 1 - 7 T + 13 T^{2} )( 1 - 2 T + 13 T^{2} )$$)($$( 1 - 7 T + 13 T^{2} )( 1 - 2 T + 13 T^{2} )$$)($$1 + 6 T + 35 T^{2} + 138 T^{3} + 516 T^{4} + 1794 T^{5} + 5915 T^{6} + 13182 T^{7} + 28561 T^{8}$$)($$1 + 6 T + 35 T^{2} + 138 T^{3} + 516 T^{4} + 1794 T^{5} + 5915 T^{6} + 13182 T^{7} + 28561 T^{8}$$)
$17$ ($$1 + 3 T + 20 T^{2} + 51 T^{3} + 289 T^{4}$$)($$1 + 3 T + 20 T^{2} + 51 T^{3} + 289 T^{4}$$)($$1 + 3 T + 20 T^{2} + 51 T^{3} + 289 T^{4}$$)($$1 + 3 T + 20 T^{2} + 51 T^{3} + 289 T^{4}$$)($$1 + 6 T + 25 T^{2} + 78 T^{3} + 84 T^{4} + 1326 T^{5} + 7225 T^{6} + 29478 T^{7} + 83521 T^{8}$$)($$1 + 6 T + 25 T^{2} + 78 T^{3} + 84 T^{4} + 1326 T^{5} + 7225 T^{6} + 29478 T^{7} + 83521 T^{8}$$)
$19$ ($$1 + 5 T + 6 T^{2} + 95 T^{3} + 361 T^{4}$$)($$1 - 5 T + 6 T^{2} - 95 T^{3} + 361 T^{4}$$)($$( 1 - 8 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} )$$)($$( 1 - 7 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} )$$)($$( 1 - 7 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2}$$)($$( 1 - 8 T + 19 T^{2} )^{2}( 1 + 7 T + 19 T^{2} )^{2}$$)
$23$ ($$1 + 6 T + 35 T^{2} + 138 T^{3} + 529 T^{4}$$)($$1 - 6 T + 35 T^{2} - 138 T^{3} + 529 T^{4}$$)($$1 + 3 T + 26 T^{2} + 69 T^{3} + 529 T^{4}$$)($$1 - 3 T + 26 T^{2} - 69 T^{3} + 529 T^{4}$$)($$1 + 18 T + 175 T^{2} + 1206 T^{3} + 6444 T^{4} + 27738 T^{5} + 92575 T^{6} + 219006 T^{7} + 279841 T^{8}$$)($$1 - 18 T + 175 T^{2} - 1206 T^{3} + 6444 T^{4} - 27738 T^{5} + 92575 T^{6} - 219006 T^{7} + 279841 T^{8}$$)
$29$ ($$1 - 3 T - 20 T^{2} - 87 T^{3} + 841 T^{4}$$)($$1 - 3 T - 20 T^{2} - 87 T^{3} + 841 T^{4}$$)($$1 - 9 T + 52 T^{2} - 261 T^{3} + 841 T^{4}$$)($$1 - 9 T + 52 T^{2} - 261 T^{3} + 841 T^{4}$$)($$1 - 6 T - 13 T^{2} + 54 T^{3} + 516 T^{4} + 1566 T^{5} - 10933 T^{6} - 146334 T^{7} + 707281 T^{8}$$)($$1 - 6 T - 13 T^{2} + 54 T^{3} + 516 T^{4} + 1566 T^{5} - 10933 T^{6} - 146334 T^{7} + 707281 T^{8}$$)
$31$ ($$( 1 - T + 31 T^{2} )^{2}$$)($$( 1 + T + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{2}$$)($$( 1 - 8 T + 31 T^{2} )^{2}$$)($$( 1 + 4 T + 31 T^{2} )^{4}$$)($$( 1 - 4 T + 31 T^{2} )^{4}$$)
$37$ ($$1 + 7 T + 12 T^{2} + 259 T^{3} + 1369 T^{4}$$)($$1 + 7 T + 12 T^{2} + 259 T^{3} + 1369 T^{4}$$)($$( 1 - 10 T + 37 T^{2} )( 1 - T + 37 T^{2} )$$)($$( 1 - 10 T + 37 T^{2} )( 1 - T + 37 T^{2} )$$)($$1 + 2 T - 53 T^{2} - 34 T^{3} + 1732 T^{4} - 1258 T^{5} - 72557 T^{6} + 101306 T^{7} + 1874161 T^{8}$$)($$1 + 2 T - 53 T^{2} - 34 T^{3} + 1732 T^{4} - 1258 T^{5} - 72557 T^{6} + 101306 T^{7} + 1874161 T^{8}$$)
$41$ ($$1 - 3 T + 44 T^{2} - 123 T^{3} + 1681 T^{4}$$)($$1 - 3 T + 44 T^{2} - 123 T^{3} + 1681 T^{4}$$)($$1 + 3 T + 44 T^{2} + 123 T^{3} + 1681 T^{4}$$)($$1 + 3 T + 44 T^{2} + 123 T^{3} + 1681 T^{4}$$)($$1 - 18 T + 193 T^{2} - 1530 T^{3} + 9972 T^{4} - 62730 T^{5} + 324433 T^{6} - 1240578 T^{7} + 2825761 T^{8}$$)($$1 - 18 T + 193 T^{2} - 1530 T^{3} + 9972 T^{4} - 62730 T^{5} + 324433 T^{6} - 1240578 T^{7} + 2825761 T^{8}$$)
$43$ ($$( 1 - 8 T + 43 T^{2} )( 1 + 5 T + 43 T^{2} )$$)($$( 1 - 5 T + 43 T^{2} )( 1 + 8 T + 43 T^{2} )$$)($$1 + 15 T + 118 T^{2} + 645 T^{3} + 1849 T^{4}$$)($$1 - 15 T + 118 T^{2} - 645 T^{3} + 1849 T^{4}$$)($$1 + 6 T + 77 T^{2} + 390 T^{3} + 2892 T^{4} + 16770 T^{5} + 142373 T^{6} + 477042 T^{7} + 3418801 T^{8}$$)($$1 - 6 T + 77 T^{2} - 390 T^{3} + 2892 T^{4} - 16770 T^{5} + 142373 T^{6} - 477042 T^{7} + 3418801 T^{8}$$)
$47$ ($$( 1 - 9 T + 47 T^{2} )^{2}$$)($$( 1 + 9 T + 47 T^{2} )^{2}$$)($$( 1 + 12 T + 47 T^{2} )^{2}$$)($$( 1 - 12 T + 47 T^{2} )^{2}$$)($$( 1 + 22 T^{2} + 2209 T^{4} )^{2}$$)($$( 1 + 22 T^{2} + 2209 T^{4} )^{2}$$)
$53$ ($$1 + 9 T + 28 T^{2} + 477 T^{3} + 2809 T^{4}$$)($$1 + 9 T + 28 T^{2} + 477 T^{3} + 2809 T^{4}$$)($$1 + 3 T - 44 T^{2} + 159 T^{3} + 2809 T^{4}$$)($$1 + 3 T - 44 T^{2} + 159 T^{3} + 2809 T^{4}$$)($$1 + 6 T - 61 T^{2} - 54 T^{3} + 4692 T^{4} - 2862 T^{5} - 171349 T^{6} + 893262 T^{7} + 7890481 T^{8}$$)($$1 + 6 T - 61 T^{2} - 54 T^{3} + 4692 T^{4} - 2862 T^{5} - 171349 T^{6} + 893262 T^{7} + 7890481 T^{8}$$)
$59$ ($$( 1 - 15 T + 59 T^{2} )^{2}$$)($$( 1 + 15 T + 59 T^{2} )^{2}$$)($$( 1 - 12 T + 59 T^{2} )^{2}$$)($$( 1 + 12 T + 59 T^{2} )^{2}$$)($$( 1 - 6 T + 59 T^{2} )^{4}$$)($$( 1 + 6 T + 59 T^{2} )^{4}$$)
$61$ ($$1 - 119 T^{2} + 3721 T^{4}$$)($$1 - 119 T^{2} + 3721 T^{4}$$)($$( 1 - 61 T^{2} )^{2}$$)($$( 1 - 61 T^{2} )^{2}$$)($$( 1 - 14 T + 61 T^{2} )^{2}( 1 + 14 T + 61 T^{2} )^{2}$$)($$( 1 - 14 T + 61 T^{2} )^{2}( 1 + 14 T + 61 T^{2} )^{2}$$)
$67$ ($$( 1 - 5 T + 67 T^{2} )( 1 + 5 T + 67 T^{2} )$$)($$( 1 - 5 T + 67 T^{2} )( 1 + 5 T + 67 T^{2} )$$)($$( 1 - 16 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} )$$)($$( 1 - 16 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} )$$)($$( 1 - 67 T^{2} )^{4}$$)($$( 1 - 67 T^{2} )^{4}$$)
$71$ ($$1 - 34 T^{2} + 5041 T^{4}$$)($$1 - 34 T^{2} + 5041 T^{4}$$)($$1 - 130 T^{2} + 5041 T^{4}$$)($$1 - 130 T^{2} + 5041 T^{4}$$)($$1 - 68 T^{2} + 6630 T^{4} - 342788 T^{6} + 25411681 T^{8}$$)($$1 - 68 T^{2} + 6630 T^{4} - 342788 T^{6} + 25411681 T^{8}$$)
$73$ ($$( 1 - 10 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} )$$)($$( 1 - 10 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} )$$)($$1 + 21 T + 220 T^{2} + 1533 T^{3} + 5329 T^{4}$$)($$1 + 21 T + 220 T^{2} + 1533 T^{3} + 5329 T^{4}$$)($$( 1 + 15 T + 148 T^{2} + 1095 T^{3} + 5329 T^{4} )^{2}$$)($$( 1 + 15 T + 148 T^{2} + 1095 T^{3} + 5329 T^{4} )^{2}$$)
$79$ ($$1 - 155 T^{2} + 6241 T^{4}$$)($$1 - 155 T^{2} + 6241 T^{4}$$)($$1 - 50 T^{2} + 6241 T^{4}$$)($$1 - 50 T^{2} + 6241 T^{4}$$)($$1 - 172 T^{2} + 15270 T^{4} - 1073452 T^{6} + 38950081 T^{8}$$)($$1 - 172 T^{2} + 15270 T^{4} - 1073452 T^{6} + 38950081 T^{8}$$)
$83$ ($$1 - 9 T - 2 T^{2} - 747 T^{3} + 6889 T^{4}$$)($$1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4}$$)($$1 - 9 T - 2 T^{2} - 747 T^{3} + 6889 T^{4}$$)($$1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4}$$)($$1 + 6 T - 67 T^{2} - 378 T^{3} + 732 T^{4} - 31374 T^{5} - 461563 T^{6} + 3430722 T^{7} + 47458321 T^{8}$$)($$1 - 6 T - 67 T^{2} + 378 T^{3} + 732 T^{4} + 31374 T^{5} - 461563 T^{6} - 3430722 T^{7} + 47458321 T^{8}$$)
$89$ ($$1 + 3 T + 92 T^{2} + 267 T^{3} + 7921 T^{4}$$)($$1 + 3 T + 92 T^{2} + 267 T^{3} + 7921 T^{4}$$)($$1 - 9 T + 116 T^{2} - 801 T^{3} + 7921 T^{4}$$)($$1 - 9 T + 116 T^{2} - 801 T^{3} + 7921 T^{4}$$)($$1 - 6 T - 23 T^{2} + 210 T^{3} - 5628 T^{4} + 18690 T^{5} - 182183 T^{6} - 4229814 T^{7} + 62742241 T^{8}$$)($$1 - 6 T - 23 T^{2} + 210 T^{3} - 5628 T^{4} + 18690 T^{5} - 182183 T^{6} - 4229814 T^{7} + 62742241 T^{8}$$)
$97$ ($$1 + 3 T + 100 T^{2} + 291 T^{3} + 9409 T^{4}$$)($$1 + 3 T + 100 T^{2} + 291 T^{3} + 9409 T^{4}$$)($$1 - 3 T + 100 T^{2} - 291 T^{3} + 9409 T^{4}$$)($$1 - 3 T + 100 T^{2} - 291 T^{3} + 9409 T^{4}$$)($$1 + 6 T + 185 T^{2} + 1038 T^{3} + 21684 T^{4} + 100686 T^{5} + 1740665 T^{6} + 5476038 T^{7} + 88529281 T^{8}$$)($$1 + 6 T + 185 T^{2} + 1038 T^{3} + 21684 T^{4} + 100686 T^{5} + 1740665 T^{6} + 5476038 T^{7} + 88529281 T^{8}$$)