Properties

Label 8032.2.a
Level 8032
Weight 2
Character orbit a
Rep. character \(\chi_{8032}(1,\cdot)\)
Character field \(\Q\)
Dimension 250
Newforms 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: \(\Q\)
Newforms: \( 12 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8032))\) into irreducible Hecke orbits

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

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