# Properties

 Label 2100.2.ce Level 2100 Weight 2 Character orbit ce Rep. character $$\chi_{2100}(157,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 96 Newform subspaces 5 Sturm bound 960 Trace bound 21

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2100.ce (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$5$$ Sturm bound: $$960$$ Trace bound: $$21$$ Distinguishing $$T_p$$: $$11$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2100, [\chi])$$.

Total New Old
Modular forms 2064 96 1968
Cusp forms 1776 96 1680
Eisenstein series 288 0 288

## Trace form

 $$96q + O(q^{10})$$ $$96q - 16q^{11} - 4q^{21} - 16q^{23} - 48q^{31} - 12q^{33} - 20q^{37} + 24q^{43} - 12q^{47} + 16q^{51} - 40q^{53} + 16q^{57} - 12q^{61} + 12q^{63} + 32q^{71} + 60q^{73} + 84q^{77} + 48q^{81} + 48q^{87} + 20q^{91} - 8q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2100, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2100.2.ce.a $$8$$ $$16.769$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{24}^{3}-\zeta_{24}^{7})q^{3}+(-3\zeta_{24}^{3}+\zeta_{24}^{7})q^{7}+\cdots$$
2100.2.ce.b $$8$$ $$16.769$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}q^{3}+(-3\zeta_{24}+2\zeta_{24}^{5})q^{7}+\cdots$$
2100.2.ce.c $$24$$ $$16.769$$ None $$0$$ $$0$$ $$0$$ $$0$$
2100.2.ce.d $$24$$ $$16.769$$ None $$0$$ $$0$$ $$0$$ $$0$$
2100.2.ce.e $$32$$ $$16.769$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2100, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2100, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(420, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(700, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1050, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ ($$1 - T^{4} + T^{8}$$)($$1 - T^{4} + T^{8}$$)
$5$ 1
$7$ ($$1 + 23 T^{4} + 2401 T^{8}$$)($$1 + 23 T^{4} + 2401 T^{8}$$)
$11$ ($$( 1 + 2 T - 16 T^{2} - 4 T^{3} + 235 T^{4} - 44 T^{5} - 1936 T^{6} + 2662 T^{7} + 14641 T^{8} )^{2}$$)($$( 1 + 2 T - 16 T^{2} - 4 T^{3} + 235 T^{4} - 44 T^{5} - 1936 T^{6} + 2662 T^{7} + 14641 T^{8} )^{2}$$)
$13$ ($$( 1 + 287 T^{4} + 28561 T^{8} )^{2}$$)($$( 1 + 287 T^{4} + 28561 T^{8} )^{2}$$)
$17$ ($$1 + 60 T^{2} + 2042 T^{4} + 50520 T^{6} + 972243 T^{8} + 14600280 T^{10} + 170549882 T^{12} + 1448254140 T^{14} + 6975757441 T^{16}$$)($$1 - 60 T^{2} + 2042 T^{4} - 50520 T^{6} + 972243 T^{8} - 14600280 T^{10} + 170549882 T^{12} - 1448254140 T^{14} + 6975757441 T^{16}$$)
$19$ ($$( 1 + 10 T + 49 T^{2} + 130 T^{3} + 340 T^{4} + 2470 T^{5} + 17689 T^{6} + 68590 T^{7} + 130321 T^{8} )^{2}$$)($$( 1 - 10 T + 49 T^{2} - 130 T^{3} + 340 T^{4} - 2470 T^{5} + 17689 T^{6} - 68590 T^{7} + 130321 T^{8} )^{2}$$)
$23$ ($$1 - 96 T^{2} + 4574 T^{4} - 144192 T^{6} + 3601251 T^{8} - 76277568 T^{10} + 1279992734 T^{12} - 14211445344 T^{14} + 78310985281 T^{16}$$)($$1 + 96 T^{2} + 4574 T^{4} + 144192 T^{6} + 3601251 T^{8} + 76277568 T^{10} + 1279992734 T^{12} + 14211445344 T^{14} + 78310985281 T^{16}$$)
$29$ ($$( 1 - 10 T^{2} + 841 T^{4} )^{4}$$)($$( 1 - 10 T^{2} + 841 T^{4} )^{4}$$)
$31$ ($$( 1 + 58 T^{2} + 2403 T^{4} + 55738 T^{6} + 923521 T^{8} )^{2}$$)($$( 1 + 58 T^{2} + 2403 T^{4} + 55738 T^{6} + 923521 T^{8} )^{2}$$)
$37$ ($$1 + 216 T^{2} + 22057 T^{4} + 1405080 T^{6} + 61731552 T^{8} + 1923554520 T^{10} + 41338369177 T^{12} + 554196904344 T^{14} + 3512479453921 T^{16}$$)($$1 - 216 T^{2} + 22057 T^{4} - 1405080 T^{6} + 61731552 T^{8} - 1923554520 T^{10} + 41338369177 T^{12} - 554196904344 T^{14} + 3512479453921 T^{16}$$)
$41$ ($$( 1 - 108 T^{2} + 6170 T^{4} - 181548 T^{6} + 2825761 T^{8} )^{2}$$)($$( 1 - 108 T^{2} + 6170 T^{4} - 181548 T^{6} + 2825761 T^{8} )^{2}$$)
$43$ ($$1 + 868 T^{4} - 3308250 T^{8} + 2967519268 T^{12} + 11688200277601 T^{16}$$)($$1 + 868 T^{4} - 3308250 T^{8} + 2967519268 T^{12} + 11688200277601 T^{16}$$)
$47$ ($$1 - 180 T^{2} + 16154 T^{4} - 963720 T^{6} + 47642835 T^{8} - 2128857480 T^{10} + 78826366874 T^{12} - 1940258759220 T^{14} + 23811286661761 T^{16}$$)($$1 + 180 T^{2} + 16154 T^{4} + 963720 T^{6} + 47642835 T^{8} + 2128857480 T^{10} + 78826366874 T^{12} + 1940258759220 T^{14} + 23811286661761 T^{16}$$)
$53$ ($$1 + 84 T^{2} + 5642 T^{4} + 276360 T^{6} + 9540387 T^{8} + 776295240 T^{10} + 44518093802 T^{12} + 1861806334836 T^{14} + 62259690411361 T^{16}$$)($$1 - 84 T^{2} + 5642 T^{4} - 276360 T^{6} + 9540387 T^{8} - 776295240 T^{10} + 44518093802 T^{12} - 1861806334836 T^{14} + 62259690411361 T^{16}$$)
$59$ ($$( 1 - 22 T + 248 T^{2} - 2596 T^{3} + 23659 T^{4} - 153164 T^{5} + 863288 T^{6} - 4518338 T^{7} + 12117361 T^{8} )^{2}$$)($$( 1 + 22 T + 248 T^{2} + 2596 T^{3} + 23659 T^{4} + 153164 T^{5} + 863288 T^{6} + 4518338 T^{7} + 12117361 T^{8} )^{2}$$)
$61$ ($$( 1 + 6 T + 73 T^{2} + 366 T^{3} + 732 T^{4} + 22326 T^{5} + 271633 T^{6} + 1361886 T^{7} + 13845841 T^{8} )^{2}$$)($$( 1 + 6 T + 73 T^{2} + 366 T^{3} + 732 T^{4} + 22326 T^{5} + 271633 T^{6} + 1361886 T^{7} + 13845841 T^{8} )^{2}$$)
$67$ ($$1 + 1753 T^{4} - 17078112 T^{8} + 35324915113 T^{12} + 406067677556641 T^{16}$$)($$1 + 1753 T^{4} - 17078112 T^{8} + 35324915113 T^{12} + 406067677556641 T^{16}$$)
$71$ ($$( 1 + 8 T + 71 T^{2} )^{8}$$)($$( 1 + 8 T + 71 T^{2} )^{8}$$)
$73$ ($$1 - 360 T^{2} + 64489 T^{4} - 7664040 T^{6} + 655036080 T^{8} - 40841669160 T^{10} + 1831374163849 T^{12} - 54480321464040 T^{14} + 806460091894081 T^{16}$$)($$1 + 360 T^{2} + 64489 T^{4} + 7664040 T^{6} + 655036080 T^{8} + 40841669160 T^{10} + 1831374163849 T^{12} + 54480321464040 T^{14} + 806460091894081 T^{16}$$)
$79$ ($$( 1 - 6 T + 157 T^{2} - 870 T^{3} + 15732 T^{4} - 68730 T^{5} + 979837 T^{6} - 2958234 T^{7} + 38950081 T^{8} )^{2}$$)($$( 1 + 6 T + 157 T^{2} + 870 T^{3} + 15732 T^{4} + 68730 T^{5} + 979837 T^{6} + 2958234 T^{7} + 38950081 T^{8} )^{2}$$)
$83$ ($$1 + 20092 T^{4} + 185593446 T^{8} + 953532585532 T^{12} + 2252292232139041 T^{16}$$)($$1 + 20092 T^{4} + 185593446 T^{8} + 953532585532 T^{12} + 2252292232139041 T^{16}$$)
$89$ ($$( 1 + 18 T + 68 T^{2} + 1404 T^{3} + 28779 T^{4} + 124956 T^{5} + 538628 T^{6} + 12689442 T^{7} + 62742241 T^{8} )^{2}$$)($$( 1 - 18 T + 68 T^{2} - 1404 T^{3} + 28779 T^{4} - 124956 T^{5} + 538628 T^{6} - 12689442 T^{7} + 62742241 T^{8} )^{2}$$)
$97$ ($$1 + 2446 T^{4} + 12136179 T^{8} + 216542621326 T^{12} + 7837433594376961 T^{16}$$)($$1 + 2446 T^{4} + 12136179 T^{8} + 216542621326 T^{12} + 7837433594376961 T^{16}$$)