Properties

Label 16.5.c
Level 16
Weight 5
Character orbit c
Rep. character \(\chi_{16}(15,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 10
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 16.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(16, [\chi])\).

Total New Old
Modular forms 11 2 9
Cusp forms 5 2 3
Eisenstein series 6 0 6

Trace form

\( 2q + 36q^{5} - 222q^{9} + O(q^{10}) \) \( 2q + 36q^{5} - 222q^{9} + 356q^{13} - 252q^{17} + 768q^{21} - 602q^{25} - 2844q^{29} + 3456q^{33} + 1060q^{37} + 324q^{41} - 3996q^{45} + 3266q^{49} + 1188q^{53} - 11136q^{57} + 1252q^{61} + 6408q^{65} + 20736q^{69} - 13372q^{73} - 6912q^{77} - 6462q^{81} - 4536q^{85} + 16452q^{89} - 9216q^{93} - 3196q^{97} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(16, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
16.5.c.a \(2\) \(1.654\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(36\) \(0\) \(q-\zeta_{6}q^{3}+18q^{5}+2\zeta_{6}q^{7}-111q^{9}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(16, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(16, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 3}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 + 30 T^{2} + 6561 T^{4} \)
$5$ \( ( 1 - 18 T + 625 T^{2} )^{2} \)
$7$ \( ( 1 - 94 T + 2401 T^{2} )( 1 + 94 T + 2401 T^{2} ) \)
$11$ \( 1 - 13730 T^{2} + 214358881 T^{4} \)
$13$ \( ( 1 - 178 T + 28561 T^{2} )^{2} \)
$17$ \( ( 1 + 126 T + 83521 T^{2} )^{2} \)
$19$ \( 1 - 99170 T^{2} + 16983563041 T^{4} \)
$23$ \( 1 + 190 T^{2} + 78310985281 T^{4} \)
$29$ \( ( 1 + 1422 T + 707281 T^{2} )^{2} \)
$31$ \( 1 - 1736450 T^{2} + 852891037441 T^{4} \)
$37$ \( ( 1 - 530 T + 1874161 T^{2} )^{2} \)
$41$ \( ( 1 - 162 T + 2825761 T^{2} )^{2} \)
$43$ \( 1 - 4471970 T^{2} + 11688200277601 T^{4} \)
$47$ \( 1 + 2433406 T^{2} + 23811286661761 T^{4} \)
$53$ \( ( 1 - 594 T + 7890481 T^{2} )^{2} \)
$59$ \( 1 - 18620450 T^{2} + 146830437604321 T^{4} \)
$61$ \( ( 1 - 626 T + 13845841 T^{2} )^{2} \)
$67$ \( 1 - 39103970 T^{2} + 406067677556641 T^{4} \)
$71$ \( 1 + 8958526 T^{2} + 645753531245761 T^{4} \)
$73$ \( ( 1 + 6686 T + 28398241 T^{2} )^{2} \)
$79$ \( 1 - 75980162 T^{2} + 1517108809906561 T^{4} \)
$83$ \( 1 - 73625954 T^{2} + 2252292232139041 T^{4} \)
$89$ \( ( 1 - 8226 T + 62742241 T^{2} )^{2} \)
$97$ \( ( 1 + 1598 T + 88529281 T^{2} )^{2} \)
show more
show less