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Properties

Label 936.2.a
Level $936$
Weight $2$
Character orbit 936.a
Rep. character $\chi_{936}(1,\cdot)$
Character field $\Q$
Dimension $15$
Newform subspaces $12$
Sturm bound $336$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 936.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(336\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(936))\).

Total New Old
Modular forms 184 15 169
Cusp forms 153 15 138
Eisenstein series 31 0 31

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

\(2\)\(3\)\(13\)FrickeDim
\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(-\)$-$\(2\)
\(+\)\(-\)\(+\)$-$\(3\)
\(+\)\(-\)\(-\)$+$\(1\)
\(-\)\(+\)\(+\)$-$\(1\)
\(-\)\(+\)\(-\)$+$\(2\)
\(-\)\(-\)\(+\)$+$\(2\)
\(-\)\(-\)\(-\)$-$\(3\)
Plus space\(+\)\(6\)
Minus space\(-\)\(9\)

Trace form

\( 15 q - 2 q^{5} - 4 q^{7} + O(q^{10}) \) \( 15 q - 2 q^{5} - 4 q^{7} + 4 q^{11} + q^{13} + 8 q^{17} - 12 q^{23} + 19 q^{25} + 14 q^{29} - 4 q^{31} - 10 q^{35} - 14 q^{37} - 2 q^{41} + 14 q^{43} + 20 q^{47} + 33 q^{49} + 10 q^{53} + 16 q^{59} - 2 q^{61} - 4 q^{65} + 4 q^{67} + 4 q^{71} - 6 q^{73} - 24 q^{77} + 12 q^{79} + 4 q^{83} + 8 q^{85} + 22 q^{89} - 6 q^{91} + 20 q^{95} - 18 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(936))\) 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 13
936.2.a.a 936.a 1.a $1$ $7.474$ \(\Q\) None \(0\) \(0\) \(-4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{5}+2q^{11}-q^{13}-2q^{17}+8q^{19}+\cdots\)
936.2.a.b 936.a 1.a $1$ $7.474$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{13}-2q^{17}-4q^{19}-q^{25}+\cdots\)
936.2.a.c 936.a 1.a $1$ $7.474$ \(\Q\) None \(0\) \(0\) \(-2\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}-4q^{11}-q^{13}-2q^{19}+\cdots\)
936.2.a.d 936.a 1.a $1$ $7.474$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{7}+2q^{11}-q^{13}+6q^{17}-4q^{19}+\cdots\)
936.2.a.e 936.a 1.a $1$ $7.474$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-6q^{11}-q^{13}-2q^{17}-4q^{23}-5q^{25}+\cdots\)
936.2.a.f 936.a 1.a $1$ $7.474$ \(\Q\) None \(0\) \(0\) \(1\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+5q^{7}+2q^{11}-q^{13}+3q^{17}+\cdots\)
936.2.a.g 936.a 1.a $1$ $7.474$ \(\Q\) None \(0\) \(0\) \(2\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}+4q^{11}-q^{13}-2q^{19}+\cdots\)
936.2.a.h 936.a 1.a $1$ $7.474$ \(\Q\) None \(0\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}+q^{13}-2q^{17}+8q^{19}+\cdots\)
936.2.a.i 936.a 1.a $1$ $7.474$ \(\Q\) None \(0\) \(0\) \(4\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{5}-4q^{7}+2q^{11}-q^{13}+6q^{17}+\cdots\)
936.2.a.j 936.a 1.a $2$ $7.474$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-3\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+(-1+\beta )q^{7}+(2-2\beta )q^{11}+\cdots\)
936.2.a.k 936.a 1.a $2$ $7.474$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(-2-\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
936.2.a.l 936.a 1.a $2$ $7.474$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(-2+\beta )q^{7}+(2-\beta )q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(936))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(936)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(468))\)\(^{\oplus 2}\)