Properties

Label 4032.2.i
Level 4032
Weight 2
Character orbit i
Rep. character \(\chi_{4032}(1889,\cdot)\)
Character field \(\Q\)
Dimension 64
Newform subspaces 3
Sturm bound 1536
Trace bound 47

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4032.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(1536\)
Trace bound: \(47\)
Distinguishing \(T_p\): \(5\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4032, [\chi])\).

Total New Old
Modular forms 816 64 752
Cusp forms 720 64 656
Eisenstein series 96 0 96

Trace form

\( 64q + O(q^{10}) \) \( 64q - 64q^{25} + 32q^{49} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4032, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4032.2.i.a \(8\) \(32.196\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}+(-\beta _{2}+\beta _{4})q^{7}+\beta _{3}q^{11}+\cdots\)
4032.2.i.b \(8\) \(32.196\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}+(-\beta _{2}-\beta _{4})q^{7}-\beta _{3}q^{11}+\cdots\)
4032.2.i.c \(48\) \(32.196\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(4032, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4032, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( ( 1 - 4 T + 5 T^{2} )^{4}( 1 + 4 T + 5 T^{2} )^{4} \))(\( ( 1 - 4 T + 5 T^{2} )^{4}( 1 + 4 T + 5 T^{2} )^{4} \))
$7$ (\( ( 1 - 6 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 - 6 T^{2} + 49 T^{4} )^{2} \))
$11$ (\( ( 1 + 20 T^{2} + 121 T^{4} )^{4} \))(\( ( 1 + 20 T^{2} + 121 T^{4} )^{4} \))
$13$ (\( ( 1 + 13 T^{2} )^{8} \))(\( ( 1 + 13 T^{2} )^{8} \))
$17$ (\( ( 1 + 14 T^{2} + 289 T^{4} )^{4} \))(\( ( 1 + 14 T^{2} + 289 T^{4} )^{4} \))
$19$ (\( ( 1 - 2 T^{2} + 361 T^{4} )^{4} \))(\( ( 1 - 2 T^{2} + 361 T^{4} )^{4} \))
$23$ (\( ( 1 - 36 T^{2} + 529 T^{4} )^{4} \))(\( ( 1 - 36 T^{2} + 529 T^{4} )^{4} \))
$29$ (\( ( 1 + 48 T^{2} + 841 T^{4} )^{4} \))(\( ( 1 + 48 T^{2} + 841 T^{4} )^{4} \))
$31$ (\( ( 1 - 30 T^{2} + 961 T^{4} )^{4} \))(\( ( 1 - 30 T^{2} + 961 T^{4} )^{4} \))
$37$ (\( ( 1 - 54 T^{2} + 1369 T^{4} )^{4} \))(\( ( 1 - 54 T^{2} + 1369 T^{4} )^{4} \))
$41$ (\( ( 1 + 62 T^{2} + 1681 T^{4} )^{4} \))(\( ( 1 + 62 T^{2} + 1681 T^{4} )^{4} \))
$43$ (\( ( 1 - 70 T^{2} + 1849 T^{4} )^{4} \))(\( ( 1 - 70 T^{2} + 1849 T^{4} )^{4} \))
$47$ (\( ( 1 + 8 T + 47 T^{2} )^{8} \))(\( ( 1 - 8 T + 47 T^{2} )^{8} \))
$53$ (\( ( 1 + 16 T^{2} + 2809 T^{4} )^{4} \))(\( ( 1 + 16 T^{2} + 2809 T^{4} )^{4} \))
$59$ (\( ( 1 - 38 T^{2} + 3481 T^{4} )^{4} \))(\( ( 1 - 38 T^{2} + 3481 T^{4} )^{4} \))
$61$ (\( ( 1 + 50 T^{2} + 3721 T^{4} )^{4} \))(\( ( 1 + 50 T^{2} + 3721 T^{4} )^{4} \))
$67$ (\( ( 1 - 130 T^{2} + 4489 T^{4} )^{4} \))(\( ( 1 - 130 T^{2} + 4489 T^{4} )^{4} \))
$71$ (\( ( 1 - 52 T^{2} + 5041 T^{4} )^{4} \))(\( ( 1 - 52 T^{2} + 5041 T^{4} )^{4} \))
$73$ (\( ( 1 - 106 T^{2} + 5329 T^{4} )^{4} \))(\( ( 1 - 106 T^{2} + 5329 T^{4} )^{4} \))
$79$ (\( ( 1 + 78 T^{2} + 6241 T^{4} )^{4} \))(\( ( 1 + 78 T^{2} + 6241 T^{4} )^{4} \))
$83$ (\( ( 1 - 83 T^{2} )^{8} \))(\( ( 1 - 83 T^{2} )^{8} \))
$89$ (\( ( 1 - 2 T^{2} + 7921 T^{4} )^{4} \))(\( ( 1 - 2 T^{2} + 7921 T^{4} )^{4} \))
$97$ (\( ( 1 - 154 T^{2} + 9409 T^{4} )^{4} \))(\( ( 1 - 154 T^{2} + 9409 T^{4} )^{4} \))
show more
show less