Properties

Label 592.2.a
Level $592$
Weight $2$
Character orbit 592.a
Rep. character $\chi_{592}(1,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $10$
Sturm bound $152$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 592 = 2^{4} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 592.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(152\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(592))\).

Total New Old
Modular forms 82 18 64
Cusp forms 71 18 53
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.

\(2\)\(37\)FrickeDim.
\(+\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(8\)
Minus space\(-\)\(10\)

Trace form

\( 18 q + 14 q^{9} + O(q^{10}) \) \( 18 q + 14 q^{9} - 4 q^{15} - 4 q^{17} - 2 q^{19} - 8 q^{21} + 6 q^{23} + 10 q^{25} - 12 q^{27} - 8 q^{29} - 14 q^{31} - 8 q^{33} + 12 q^{35} + 4 q^{39} + 4 q^{41} - 10 q^{43} - 8 q^{45} + 10 q^{49} + 28 q^{51} - 8 q^{53} + 12 q^{55} - 16 q^{57} + 2 q^{59} + 8 q^{61} + 36 q^{63} - 16 q^{65} + 12 q^{67} - 8 q^{69} + 8 q^{71} - 20 q^{73} + 20 q^{75} - 24 q^{77} - 6 q^{79} + 2 q^{81} - 8 q^{83} + 16 q^{85} - 4 q^{89} - 28 q^{91} + 8 q^{93} + 28 q^{95} - 12 q^{97} + 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(592))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 37
592.2.a.a 592.a 1.a $1$ $4.727$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}-2q^{9}-3q^{11}-4q^{13}+\cdots\)
592.2.a.b 592.a 1.a $1$ $4.727$ \(\Q\) None \(0\) \(1\) \(-4\) \(3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}+3q^{7}-2q^{9}-5q^{11}+\cdots\)
592.2.a.c 592.a 1.a $1$ $4.727$ \(\Q\) None \(0\) \(1\) \(-2\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-q^{7}-2q^{9}-q^{11}-6q^{13}+\cdots\)
592.2.a.d 592.a 1.a $1$ $4.727$ \(\Q\) None \(0\) \(1\) \(0\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{7}-2q^{9}+3q^{11}+2q^{17}+\cdots\)
592.2.a.e 592.a 1.a $1$ $4.727$ \(\Q\) None \(0\) \(3\) \(-2\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-2q^{5}+q^{7}+6q^{9}+5q^{11}+\cdots\)
592.2.a.f 592.a 1.a $2$ $4.727$ \(\Q(\sqrt{13}) \) None \(0\) \(-3\) \(-1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}-\beta q^{5}+(-2+2\beta )q^{7}+\cdots\)
592.2.a.g 592.a 1.a $2$ $4.727$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(1\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+3\beta )q^{5}+2\beta q^{7}+(-2+\cdots)q^{9}+\cdots\)
592.2.a.h 592.a 1.a $2$ $4.727$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(4\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2q^{5}-\beta q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots\)
592.2.a.i 592.a 1.a $3$ $4.727$ 3.3.229.1 None \(0\) \(-2\) \(-1\) \(-7\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+\beta _{2}q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
592.2.a.j 592.a 1.a $4$ $4.727$ 4.4.48389.1 None \(0\) \(-2\) \(5\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(1-\beta _{3})q^{5}+(\beta _{2}-\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(592))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(592)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 2}\)