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

Downloads

Learn more about

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