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Properties

Label 1932.2.a
Level $1932$
Weight $2$
Character orbit 1932.a
Rep. character $\chi_{1932}(1,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $10$
Sturm bound $768$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1932.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(768\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1932))\).

Total New Old
Modular forms 396 20 376
Cusp forms 373 20 353
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.

\(2\)\(3\)\(7\)\(23\)FrickeDim
\(-\)\(+\)\(+\)\(+\)$-$\(3\)
\(-\)\(+\)\(+\)\(-\)$+$\(2\)
\(-\)\(+\)\(-\)\(+\)$+$\(2\)
\(-\)\(+\)\(-\)\(-\)$-$\(3\)
\(-\)\(-\)\(+\)\(+\)$+$\(2\)
\(-\)\(-\)\(+\)\(-\)$-$\(3\)
\(-\)\(-\)\(-\)\(+\)$-$\(3\)
\(-\)\(-\)\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(8\)
Minus space\(-\)\(12\)

Trace form

\( 20 q - 8 q^{5} + 20 q^{9} + O(q^{10}) \) \( 20 q - 8 q^{5} + 20 q^{9} - 8 q^{13} - 8 q^{17} + 4 q^{25} - 24 q^{29} + 8 q^{31} + 8 q^{33} - 16 q^{41} + 16 q^{43} - 8 q^{45} - 8 q^{47} + 20 q^{49} + 8 q^{51} + 24 q^{53} + 24 q^{55} + 16 q^{57} + 8 q^{59} + 8 q^{61} + 24 q^{65} + 16 q^{67} - 8 q^{71} + 24 q^{73} + 16 q^{75} + 16 q^{77} - 32 q^{79} + 20 q^{81} + 40 q^{83} + 24 q^{85} - 8 q^{87} - 32 q^{89} - 8 q^{93} + 32 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1932))\) 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 23
1932.2.a.a 1932.a 1.a $1$ $15.427$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}-5q^{11}-6q^{13}+\cdots\)
1932.2.a.b 1932.a 1.a $1$ $15.427$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots\)
1932.2.a.c 1932.a 1.a $2$ $15.427$ \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(-5\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-2-\beta )q^{5}-q^{7}+q^{9}+(3+\cdots)q^{11}+\cdots\)
1932.2.a.d 1932.a 1.a $2$ $15.427$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(1\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}-q^{7}+q^{9}+(-1-2\beta )q^{11}+\cdots\)
1932.2.a.e 1932.a 1.a $2$ $15.427$ \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(1\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+q^{7}+q^{9}+(1-2\beta )q^{11}+\cdots\)
1932.2.a.f 1932.a 1.a $2$ $15.427$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-5\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-2-\beta )q^{5}+q^{7}+q^{9}-q^{11}+\cdots\)
1932.2.a.g 1932.a 1.a $2$ $15.427$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-1\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}-q^{7}+q^{9}-3q^{11}+(-1+\cdots)q^{13}+\cdots\)
1932.2.a.h 1932.a 1.a $2$ $15.427$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(1\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+3\beta )q^{5}+q^{7}+q^{9}+3q^{11}+\cdots\)
1932.2.a.i 1932.a 1.a $3$ $15.427$ 3.3.1509.1 None \(0\) \(-3\) \(-1\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{1}q^{5}+q^{7}+q^{9}+(1-2\beta _{1}+\cdots)q^{11}+\cdots\)
1932.2.a.j 1932.a 1.a $3$ $15.427$ 3.3.1101.1 None \(0\) \(3\) \(1\) \(-3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}+q^{11}+(-1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1932))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1932)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(644))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(966))\)\(^{\oplus 2}\)