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Properties

Label 792.4.a
Level $792$
Weight $4$
Character orbit 792.a
Rep. character $\chi_{792}(1,\cdot)$
Character field $\Q$
Dimension $37$
Newform subspaces $17$
Sturm bound $576$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 792.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(576\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(792))\).

Total New Old
Modular forms 448 37 411
Cusp forms 416 37 379
Eisenstein series 32 0 32

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
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(20\)
Minus space\(-\)\(17\)

Trace form

\( 37 q + 24 q^{5} + 36 q^{7} - 33 q^{11} - 102 q^{13} + 86 q^{17} + 180 q^{19} - 142 q^{23} + 881 q^{25} - 194 q^{29} + 130 q^{31} - 260 q^{35} + 468 q^{37} - 574 q^{41} + 88 q^{43} + 820 q^{47} + 981 q^{49}+ \cdots - 724 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(792))\) 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
792.4.a.a 792.a 1.a $1$ $46.730$ \(\Q\) None 264.4.a.b \(0\) \(0\) \(-12\) \(22\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-12q^{5}+22q^{7}-11q^{11}-48q^{13}+\cdots\)
792.4.a.b 792.a 1.a $1$ $46.730$ \(\Q\) None 88.4.a.b \(0\) \(0\) \(-9\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-9q^{5}+2q^{7}+11q^{11}+38q^{17}+\cdots\)
792.4.a.c 792.a 1.a $1$ $46.730$ \(\Q\) None 264.4.a.c \(0\) \(0\) \(6\) \(-14\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+6q^{5}-14q^{7}-11q^{11}+6q^{13}+\cdots\)
792.4.a.d 792.a 1.a $1$ $46.730$ \(\Q\) None 264.4.a.d \(0\) \(0\) \(6\) \(-8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+6q^{5}-8q^{7}+11q^{11}-30q^{13}+\cdots\)
792.4.a.e 792.a 1.a $1$ $46.730$ \(\Q\) None 88.4.a.a \(0\) \(0\) \(7\) \(-6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+7q^{5}-6q^{7}+11q^{11}-40q^{13}+\cdots\)
792.4.a.f 792.a 1.a $1$ $46.730$ \(\Q\) None 264.4.a.a \(0\) \(0\) \(18\) \(-28\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+18q^{5}-28q^{7}-11q^{11}-18q^{13}+\cdots\)
792.4.a.g 792.a 1.a $2$ $46.730$ \(\Q(\sqrt{5}) \) None 88.4.a.c \(0\) \(0\) \(6\) \(-56\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(3+4\beta )q^{5}+(-28+\beta )q^{7}-11q^{11}+\cdots\)
792.4.a.h 792.a 1.a $2$ $46.730$ \(\Q(\sqrt{17}) \) None 264.4.a.e \(0\) \(0\) \(6\) \(10\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(3+\beta )q^{5}+(5+\beta )q^{7}-11q^{11}+(-1+\cdots)q^{13}+\cdots\)
792.4.a.i 792.a 1.a $2$ $46.730$ \(\Q(\sqrt{137}) \) None 264.4.a.f \(0\) \(0\) \(6\) \(16\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(3+\beta )q^{5}+(8+2\beta )q^{7}+11q^{11}+\cdots\)
792.4.a.j 792.a 1.a $2$ $46.730$ \(\Q(\sqrt{185}) \) None 264.4.a.g \(0\) \(0\) \(6\) \(22\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(3+\beta )q^{5}+(11-\beta )q^{7}+11q^{11}+\cdots\)
792.4.a.k 792.a 1.a $3$ $46.730$ 3.3.4364.1 None 792.4.a.k \(0\) \(0\) \(-8\) \(10\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-3-\beta _{1})q^{5}+(3-\beta _{2})q^{7}+11q^{11}+\cdots\)
792.4.a.l 792.a 1.a $3$ $46.730$ 3.3.11109.1 None 88.4.a.d \(0\) \(0\) \(-8\) \(24\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-3-\beta _{2})q^{5}+(8-\beta _{1}-\beta _{2})q^{7}+\cdots\)
792.4.a.m 792.a 1.a $3$ $46.730$ 3.3.142161.1 None 264.4.a.h \(0\) \(0\) \(-4\) \(-12\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}+(-4+\beta _{2})q^{7}+11q^{11}+\cdots\)
792.4.a.n 792.a 1.a $3$ $46.730$ 3.3.123209.1 None 264.4.a.i \(0\) \(0\) \(-4\) \(28\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}+(10+\beta _{1}+\beta _{2})q^{7}+\cdots\)
792.4.a.o 792.a 1.a $3$ $46.730$ 3.3.4364.1 None 792.4.a.k \(0\) \(0\) \(8\) \(10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(3+\beta _{1})q^{5}+(3-\beta _{2})q^{7}-11q^{11}+\cdots\)
792.4.a.p 792.a 1.a $4$ $46.730$ 4.4.8611212.1 None 792.4.a.p \(0\) \(0\) \(-8\) \(8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{1})q^{5}+(2+\beta _{2})q^{7}-11q^{11}+\cdots\)
792.4.a.q 792.a 1.a $4$ $46.730$ 4.4.8611212.1 None 792.4.a.p \(0\) \(0\) \(8\) \(8\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta _{1})q^{5}+(2+\beta _{2})q^{7}+11q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(792))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(792)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 2}\)