Properties

Label 532.2.a
Level $532$
Weight $2$
Character orbit 532.a
Rep. character $\chi_{532}(1,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $5$
Sturm bound $160$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 532.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(160\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(532))\).

Total New Old
Modular forms 86 10 76
Cusp forms 75 10 65
Eisenstein series 11 0 11

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

\(2\)\(7\)\(19\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(4\)
Minus space\(-\)\(6\)

Trace form

\( 10 q - 4 q^{3} + 6 q^{9} + O(q^{10}) \) \( 10 q - 4 q^{3} + 6 q^{9} - 4 q^{11} + 8 q^{13} - 4 q^{21} - 8 q^{23} + 14 q^{25} - 4 q^{27} + 8 q^{29} - 8 q^{31} - 12 q^{33} + 4 q^{35} - 8 q^{37} + 20 q^{39} + 4 q^{41} + 12 q^{45} + 12 q^{47} + 10 q^{49} + 4 q^{51} + 4 q^{53} + 4 q^{55} + 4 q^{57} + 4 q^{59} + 8 q^{61} - 4 q^{65} - 8 q^{67} - 20 q^{69} - 24 q^{71} - 12 q^{73} + 8 q^{75} + 8 q^{77} - 20 q^{79} - 14 q^{81} + 32 q^{83} + 28 q^{85} - 44 q^{87} - 20 q^{89} - 4 q^{91} - 8 q^{93} + 8 q^{97} - 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(532))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7 19
532.2.a.a $1$ $4.248$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $-$ $-$ $-$ \(q-2q^{5}+q^{7}-3q^{9}+4q^{11}+4q^{13}+\cdots\)
532.2.a.b $2$ $4.248$ \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(-2\) \(2\) $-$ $-$ $+$ \(q+(-1-\beta )q^{3}-q^{5}+q^{7}+(-1+3\beta )q^{9}+\cdots\)
532.2.a.c $2$ $4.248$ \(\Q(\sqrt{21}) \) None \(0\) \(-1\) \(6\) \(2\) $-$ $-$ $-$ \(q-\beta q^{3}+3q^{5}+q^{7}+(2+\beta )q^{9}+(-1+\cdots)q^{11}+\cdots\)
532.2.a.d $2$ $4.248$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-4\) \(-2\) $-$ $+$ $-$ \(q+\beta q^{3}+(-1-2\beta )q^{5}-q^{7}+(-2+\cdots)q^{9}+\cdots\)
532.2.a.e $3$ $4.248$ 3.3.733.1 None \(0\) \(-1\) \(2\) \(-3\) $-$ $+$ $+$ \(q-\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2})q^{5}-q^{7}+(2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(532))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(532)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 2}\)