Properties

Label 2016.2.k
Level 2016
Weight 2
Character orbit k
Rep. character \(\chi_{2016}(1889,\cdot)\)
Character field \(\Q\)
Dimension 32
Newform subspaces 2
Sturm bound 768
Trace bound 25

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2016.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(768\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2016, [\chi])\).

Total New Old
Modular forms 416 32 384
Cusp forms 352 32 320
Eisenstein series 64 0 64

Trace form

\( 32q + O(q^{10}) \) \( 32q + 32q^{37} + 32q^{85} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2016, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2016.2.k.a \(16\) \(16.098\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}-\beta _{6}q^{7}+\beta _{3}q^{11}-\beta _{13}q^{13}+\cdots\)
2016.2.k.b \(16\) \(16.098\) 16.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{4}q^{11}+\beta _{9}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2016, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( ( 1 + 12 T^{2} + 78 T^{4} + 300 T^{6} + 625 T^{8} )^{4} \))(\( ( 1 + 8 T^{2} + 38 T^{4} + 200 T^{6} + 625 T^{8} )^{4} \))
$7$ (\( ( 1 + 4 T^{2} + 70 T^{4} + 196 T^{6} + 2401 T^{8} )^{2} \))(\( ( 1 - 4 T^{2} - 10 T^{4} - 196 T^{6} + 2401 T^{8} )^{2} \))
$11$ (\( ( 1 - 24 T^{2} + 314 T^{4} - 2904 T^{6} + 14641 T^{8} )^{4} \))(\( ( 1 - 28 T^{2} + 410 T^{4} - 3388 T^{6} + 14641 T^{8} )^{4} \))
$13$ (\( ( 1 - 36 T^{2} + 630 T^{4} - 6084 T^{6} + 28561 T^{8} )^{4} \))(\( ( 1 - 12 T^{2} + 262 T^{4} - 2028 T^{6} + 28561 T^{8} )^{4} \))
$17$ (\( ( 1 + 28 T^{2} + 382 T^{4} + 8092 T^{6} + 83521 T^{8} )^{4} \))(\( ( 1 + 56 T^{2} + 1334 T^{4} + 16184 T^{6} + 83521 T^{8} )^{4} \))
$19$ (\( ( 1 - 12 T^{2} - 42 T^{4} - 4332 T^{6} + 130321 T^{8} )^{4} \))(\( ( 1 - 36 T^{2} + 934 T^{4} - 12996 T^{6} + 130321 T^{8} )^{4} \))
$23$ (\( ( 1 - 40 T^{2} + 810 T^{4} - 21160 T^{6} + 279841 T^{8} )^{4} \))(\( ( 1 - 76 T^{2} + 2474 T^{4} - 40204 T^{6} + 279841 T^{8} )^{4} \))
$29$ (\( ( 1 - 56 T^{2} + 841 T^{4} )^{8} \))(\( ( 1 + 1234 T^{4} + 707281 T^{8} )^{4} \))
$31$ (\( ( 1 - 60 T^{2} + 2694 T^{4} - 57660 T^{6} + 923521 T^{8} )^{4} \))(\( ( 1 - 44 T^{2} + 1958 T^{4} - 42284 T^{6} + 923521 T^{8} )^{4} \))
$37$ (\( ( 1 + 66 T^{2} + 1369 T^{4} )^{8} \))(\( ( 1 - 4 T + 50 T^{2} - 148 T^{3} + 1369 T^{4} )^{8} \))
$41$ (\( ( 1 + 28 T^{2} + 3166 T^{4} + 47068 T^{6} + 2825761 T^{8} )^{4} \))(\( ( 1 + 88 T^{2} + 3926 T^{4} + 147928 T^{6} + 2825761 T^{8} )^{4} \))
$43$ (\( ( 1 + 20 T^{2} + 3510 T^{4} + 36980 T^{6} + 3418801 T^{8} )^{4} \))(\( ( 1 + 140 T^{2} + 8486 T^{4} + 258860 T^{6} + 3418801 T^{8} )^{4} \))
$47$ (\( ( 1 + 60 T^{2} + 2118 T^{4} + 132540 T^{6} + 4879681 T^{8} )^{4} \))(\( ( 1 - 20 T^{2} + 4070 T^{4} - 44180 T^{6} + 4879681 T^{8} )^{4} \))
$53$ (\( ( 1 - 176 T^{2} + 13234 T^{4} - 494384 T^{6} + 7890481 T^{8} )^{4} \))(\( ( 1 - 88 T^{2} + 2809 T^{4} )^{8} \))
$59$ (\( ( 1 + 108 T^{2} + 9366 T^{4} + 375948 T^{6} + 12117361 T^{8} )^{4} \))(\( ( 1 + 76 T^{2} + 6614 T^{4} + 264556 T^{6} + 12117361 T^{8} )^{4} \))
$61$ (\( ( 1 - 84 T^{2} + 9078 T^{4} - 312564 T^{6} + 13845841 T^{8} )^{4} \))(\( ( 1 - 36 T^{2} + 7318 T^{4} - 133956 T^{6} + 13845841 T^{8} )^{4} \))
$67$ (\( ( 1 + 60 T^{2} - 490 T^{4} + 269340 T^{6} + 20151121 T^{8} )^{4} \))(\( ( 1 + 62 T^{2} + 4489 T^{4} )^{8} \))
$71$ (\( ( 1 - 40 T^{2} + 10410 T^{4} - 201640 T^{6} + 25411681 T^{8} )^{4} \))(\( ( 1 - 252 T^{2} + 25706 T^{4} - 1270332 T^{6} + 25411681 T^{8} )^{4} \))
$73$ (\( ( 1 - 148 T^{2} + 13542 T^{4} - 788692 T^{6} + 28398241 T^{8} )^{4} \))(\( ( 1 - 12 T^{2} + 5206 T^{4} - 63948 T^{6} + 28398241 T^{8} )^{4} \))
$79$ (\( ( 1 - 20 T^{2} + 6310 T^{4} - 124820 T^{6} + 38950081 T^{8} )^{4} \))(\( ( 1 + 86 T^{2} + 6241 T^{4} )^{8} \))
$83$ (\( ( 1 + 76 T^{2} - 266 T^{4} + 523564 T^{6} + 47458321 T^{8} )^{4} \))(\( ( 1 + 124 T^{2} + 17174 T^{4} + 854236 T^{6} + 47458321 T^{8} )^{4} \))
$89$ (\( ( 1 + 28 T^{2} - 3170 T^{4} + 221788 T^{6} + 62742241 T^{8} )^{4} \))(\( ( 1 + 248 T^{2} + 31190 T^{4} + 1964408 T^{6} + 62742241 T^{8} )^{4} \))
$97$ (\( ( 1 - 308 T^{2} + 42502 T^{4} - 2897972 T^{6} + 88529281 T^{8} )^{4} \))(\( ( 1 - 172 T^{2} + 17142 T^{4} - 1618348 T^{6} + 88529281 T^{8} )^{4} \))
show more
show less