Properties

Label 792.2.a
Level $792$
Weight $2$
Character orbit 792.a
Rep. character $\chi_{792}(1,\cdot)$
Character field $\Q$
Dimension $13$
Newform subspaces $10$
Sturm bound $288$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 792.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(288\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(792))\).

Total New Old
Modular forms 160 13 147
Cusp forms 129 13 116
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.

\(2\)\(3\)\(11\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(5\)
Minus space\(-\)\(8\)

Trace form

\( 13 q - 4 q^{5} + 4 q^{7} + O(q^{10}) \) \( 13 q - 4 q^{5} + 4 q^{7} + 3 q^{11} + 2 q^{13} - 2 q^{17} + 4 q^{19} - 6 q^{23} + 13 q^{25} + 14 q^{29} - 6 q^{31} - 4 q^{35} + 2 q^{41} - 8 q^{43} - 4 q^{47} + 29 q^{49} + 10 q^{53} + 30 q^{59} + 18 q^{61} + 28 q^{65} - 14 q^{67} - 2 q^{71} - 10 q^{73} - 4 q^{77} + 28 q^{79} + 8 q^{83} - 16 q^{89} - 8 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(792))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 11
792.2.a.a 792.a 1.a $1$ $6.324$ \(\Q\) None 264.2.a.d \(0\) \(0\) \(-4\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}-2q^{7}+q^{11}+6q^{17}+4q^{19}+\cdots\)
792.2.a.b 792.a 1.a $1$ $6.324$ \(\Q\) None 264.2.a.a \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{11}+2q^{13}-6q^{17}-4q^{23}+\cdots\)
792.2.a.c 792.a 1.a $1$ $6.324$ \(\Q\) None 792.2.a.c \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-q^{11}-6q^{13}+6q^{17}-2q^{19}+\cdots\)
792.2.a.d 792.a 1.a $1$ $6.324$ \(\Q\) None 792.2.a.c \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}+q^{11}-6q^{13}-6q^{17}-2q^{19}+\cdots\)
792.2.a.e 792.a 1.a $1$ $6.324$ \(\Q\) None 264.2.a.c \(0\) \(0\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-q^{11}+2q^{17}+8q^{19}+2q^{23}+\cdots\)
792.2.a.f 792.a 1.a $1$ $6.324$ \(\Q\) None 264.2.a.b \(0\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}+q^{11}+6q^{13}-6q^{17}+\cdots\)
792.2.a.g 792.a 1.a $1$ $6.324$ \(\Q\) None 88.2.a.a \(0\) \(0\) \(3\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{5}-2q^{7}+q^{11}+6q^{17}+4q^{19}+\cdots\)
792.2.a.h 792.a 1.a $2$ $6.324$ \(\Q(\sqrt{17}) \) None 88.2.a.b \(0\) \(0\) \(-3\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+(-2+2\beta )q^{7}+q^{11}+\cdots\)
792.2.a.i 792.a 1.a $2$ $6.324$ \(\Q(\sqrt{2}) \) None 792.2.a.i \(0\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(2-\beta )q^{7}-q^{11}+(2+\beta )q^{13}+\cdots\)
792.2.a.j 792.a 1.a $2$ $6.324$ \(\Q(\sqrt{2}) \) None 792.2.a.i \(0\) \(0\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(2+\beta )q^{7}+q^{11}+(2-\beta )q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(792))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(792)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 2}\)