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Properties

Label 1596.2.a
Level $1596$
Weight $2$
Character orbit 1596.a
Rep. character $\chi_{1596}(1,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $10$
Sturm bound $640$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1596 = 2^{2} \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1596.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(640\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1596))\).

Total New Old
Modular forms 332 16 316
Cusp forms 309 16 293
Eisenstein series 23 0 23

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

\(2\)\(3\)\(7\)\(19\)FrickeDim
\(-\)\(+\)\(+\)\(+\)$-$\(1\)
\(-\)\(+\)\(+\)\(-\)$+$\(3\)
\(-\)\(+\)\(-\)\(+\)$+$\(2\)
\(-\)\(+\)\(-\)\(-\)$-$\(2\)
\(-\)\(-\)\(+\)\(+\)$+$\(2\)
\(-\)\(-\)\(+\)\(-\)$-$\(2\)
\(-\)\(-\)\(-\)\(+\)$-$\(3\)
\(-\)\(-\)\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(8\)
Minus space\(-\)\(8\)

Trace form

\( 16 q - 8 q^{5} + 16 q^{9} + O(q^{10}) \) \( 16 q - 8 q^{5} + 16 q^{9} + 8 q^{11} + 8 q^{23} - 24 q^{29} + 8 q^{33} - 16 q^{39} - 8 q^{41} - 8 q^{45} - 8 q^{47} + 16 q^{49} + 8 q^{53} - 16 q^{55} - 4 q^{57} - 16 q^{59} - 8 q^{67} + 8 q^{69} + 24 q^{71} + 16 q^{73} + 16 q^{75} + 8 q^{79} + 16 q^{81} - 16 q^{85} + 16 q^{87} - 40 q^{89} - 8 q^{91} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1596))\) 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 3 7 19
1596.2.a.a 1596.a 1.a $1$ $12.744$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
1596.2.a.b 1596.a 1.a $1$ $12.744$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
1596.2.a.c 1596.a 1.a $1$ $12.744$ \(\Q\) None \(0\) \(1\) \(-2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
1596.2.a.d 1596.a 1.a $1$ $12.744$ \(\Q\) None \(0\) \(1\) \(-2\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
1596.2.a.e 1596.a 1.a $1$ $12.744$ \(\Q\) None \(0\) \(1\) \(2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots\)
1596.2.a.f 1596.a 1.a $2$ $12.744$ \(\Q(\sqrt{7}) \) None \(0\) \(-2\) \(-2\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta )q^{5}-q^{7}+q^{9}-2\beta q^{11}+\cdots\)
1596.2.a.g 1596.a 1.a $2$ $12.744$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}-2q^{11}+\cdots\)
1596.2.a.h 1596.a 1.a $2$ $12.744$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+q^{7}+q^{9}+2q^{11}+2\beta q^{13}+\cdots\)
1596.2.a.i 1596.a 1.a $2$ $12.744$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta )q^{5}-q^{7}+q^{9}-2\beta q^{11}+\cdots\)
1596.2.a.j 1596.a 1.a $3$ $12.744$ 3.3.1016.1 None \(0\) \(3\) \(0\) \(3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}+2q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1596))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1596)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(399))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(532))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(798))\)\(^{\oplus 2}\)