Properties

Label 2016.2.i
Level 2016
Weight 2
Character orbit i
Rep. character \(\chi_{2016}(881,\cdot)\)
Character field \(\Q\)
Dimension 32
Newform subspaces 2
Sturm bound 768
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2016.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 168 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(768\)
Trace bound: \(1\)
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

\( 32q + O(q^{10}) \) \( 32q - 32q^{25} - 16q^{49} + 16q^{79} + O(q^{100}) \)

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.i.a \(8\) \(16.098\) 8.0.157351936.1 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{7}+(-\beta _{4}-\beta _{7})q^{11}+(\beta _{5}+\beta _{6}+\cdots)q^{23}+\cdots\)
2016.2.i.b \(24\) \(16.098\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( ( 1 - 5 T^{2} )^{8} \))
$7$ (\( ( 1 - 7 T^{2} )^{4} \))
$11$ (\( ( 1 - 206 T^{4} + 14641 T^{8} )^{2} \))
$13$ (\( ( 1 + 13 T^{2} )^{8} \))
$17$ (\( ( 1 + 17 T^{2} )^{8} \))
$19$ (\( ( 1 + 19 T^{2} )^{8} \))
$23$ (\( ( 1 - 734 T^{4} + 279841 T^{8} )^{2} \))
$29$ (\( ( 1 + 1234 T^{4} + 707281 T^{8} )^{2} \))
$31$ (\( ( 1 - 31 T^{2} )^{8} \))
$37$ (\( ( 1 - 38 T^{2} + 1369 T^{4} )^{4} \))
$41$ (\( ( 1 + 41 T^{2} )^{8} \))
$43$ (\( ( 1 + 58 T^{2} + 1849 T^{4} )^{4} \))
$47$ (\( ( 1 + 47 T^{2} )^{8} \))
$53$ (\( ( 1 - 5582 T^{4} + 7890481 T^{8} )^{2} \))
$59$ (\( ( 1 - 59 T^{2} )^{8} \))
$61$ (\( ( 1 + 61 T^{2} )^{8} \))
$67$ (\( ( 1 - 4 T + 67 T^{2} )^{4}( 1 + 4 T + 67 T^{2} )^{4} \))
$71$ (\( ( 1 + 2914 T^{4} + 25411681 T^{8} )^{2} \))
$73$ (\( ( 1 - 73 T^{2} )^{8} \))
$79$ (\( ( 1 - 8 T + 79 T^{2} )^{8} \))
$83$ (\( ( 1 - 83 T^{2} )^{8} \))
$89$ (\( ( 1 + 89 T^{2} )^{8} \))
$97$ (\( ( 1 - 97 T^{2} )^{8} \))
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