Properties

Label 8032.2.a
Level 8032
Weight 2
Character orbit a
Rep. character \(\chi_{8032}(1,\cdot)\)
Character field \(\Q\)
Dimension 250
Newform subspaces 12
Sturm bound 2016
Trace bound 11

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Defining parameters

Level: \( N \) \(=\) \( 8032 = 2^{5} \cdot 251 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8032.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(2016\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8032))\).

Total New Old
Modular forms 1016 250 766
Cusp forms 1001 250 751
Eisenstein series 15 0 15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(251\)FrickeDim.
\(+\)\(+\)\(+\)\(59\)
\(+\)\(-\)\(-\)\(66\)
\(-\)\(+\)\(-\)\(66\)
\(-\)\(-\)\(+\)\(59\)
Plus space\(+\)\(118\)
Minus space\(-\)\(132\)

Trace form

\( 250q + 4q^{5} + 250q^{9} + O(q^{10}) \) \( 250q + 4q^{5} + 250q^{9} - 12q^{13} - 12q^{17} + 238q^{25} + 20q^{29} + 4q^{37} - 12q^{41} + 36q^{45} + 234q^{49} + 20q^{53} - 16q^{57} + 20q^{61} - 24q^{65} + 48q^{69} - 28q^{73} + 48q^{77} + 202q^{81} + 56q^{85} - 44q^{89} + 48q^{93} - 12q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8032))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 251
8032.2.a.a \(1\) \(64.136\) \(\Q\) None \(0\) \(0\) \(1\) \(-3\) \(-\) \(+\) \(q+q^{5}-3q^{7}-3q^{9}-6q^{11}-6q^{13}+\cdots\)
8032.2.a.b \(1\) \(64.136\) \(\Q\) None \(0\) \(0\) \(1\) \(-3\) \(+\) \(+\) \(q+q^{5}-3q^{7}-3q^{9}+2q^{11}+2q^{13}+\cdots\)
8032.2.a.c \(1\) \(64.136\) \(\Q\) None \(0\) \(0\) \(1\) \(3\) \(+\) \(-\) \(q+q^{5}+3q^{7}-3q^{9}-2q^{11}+2q^{13}+\cdots\)
8032.2.a.d \(1\) \(64.136\) \(\Q\) None \(0\) \(0\) \(1\) \(3\) \(-\) \(-\) \(q+q^{5}+3q^{7}-3q^{9}+6q^{11}-6q^{13}+\cdots\)
8032.2.a.e \(28\) \(64.136\) None \(0\) \(-3\) \(-13\) \(7\) \(+\) \(+\)
8032.2.a.f \(28\) \(64.136\) None \(0\) \(3\) \(-13\) \(-7\) \(-\) \(-\)
8032.2.a.g \(30\) \(64.136\) None \(0\) \(-9\) \(0\) \(-5\) \(-\) \(-\)
8032.2.a.h \(30\) \(64.136\) None \(0\) \(-3\) \(0\) \(-13\) \(+\) \(+\)
8032.2.a.i \(30\) \(64.136\) None \(0\) \(3\) \(0\) \(13\) \(+\) \(-\)
8032.2.a.j \(30\) \(64.136\) None \(0\) \(9\) \(0\) \(5\) \(-\) \(+\)
8032.2.a.k \(35\) \(64.136\) None \(0\) \(-3\) \(13\) \(7\) \(-\) \(+\)
8032.2.a.l \(35\) \(64.136\) None \(0\) \(3\) \(13\) \(-7\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8032))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8032)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(251))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(502))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1004))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2008))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4016))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))
$5$ (\( 1 - T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))
$7$ (\( 1 + 3 T + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))(\( 1 - 3 T + 7 T^{2} \))(\( 1 - 3 T + 7 T^{2} \))
$11$ (\( 1 + 6 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))
$13$ (\( 1 + 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))
$17$ (\( 1 + T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))(\( 1 + T + 17 T^{2} \))
$19$ (\( 1 + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))
$23$ (\( 1 - 3 T + 23 T^{2} \))(\( 1 + 5 T + 23 T^{2} \))(\( 1 - 5 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))
$29$ (\( 1 - 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))
$31$ (\( 1 + 3 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 - 3 T + 31 T^{2} \))
$37$ (\( 1 + 2 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))
$41$ (\( 1 + 11 T + 41 T^{2} \))(\( 1 - 5 T + 41 T^{2} \))(\( 1 - 5 T + 41 T^{2} \))(\( 1 + 11 T + 41 T^{2} \))
$43$ (\( 1 - 6 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))
$47$ (\( 1 - 6 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))
$53$ (\( 1 - 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))
$59$ (\( 1 - 6 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))
$61$ (\( 1 + 10 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))
$67$ (\( 1 - 3 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 + 3 T + 67 T^{2} \))
$71$ (\( 1 + 12 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))
$73$ (\( 1 + 9 T + 73 T^{2} \))(\( 1 + T + 73 T^{2} \))(\( 1 + T + 73 T^{2} \))(\( 1 + 9 T + 73 T^{2} \))
$79$ (\( 1 - 9 T + 79 T^{2} \))(\( 1 - T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 + 9 T + 79 T^{2} \))
$83$ (\( 1 + 15 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 - 15 T + 83 T^{2} \))
$89$ (\( 1 - 10 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))
$97$ (\( 1 + 97 T^{2} \))(\( 1 + 4 T + 97 T^{2} \))(\( 1 + 4 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))
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