Properties

Label 5796.2.a
Level $5796$
Weight $2$
Character orbit 5796.a
Rep. character $\chi_{5796}(1,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $22$
Sturm bound $2304$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5796.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(2304\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5796))\).

Total New Old
Modular forms 1176 56 1120
Cusp forms 1129 56 1073
Eisenstein series 47 0 47

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.
\(-\)\(+\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(10\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(10\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(24\)
Minus space\(-\)\(32\)

Trace form

\( 56 q + 4 q^{5} + O(q^{10}) \) \( 56 q + 4 q^{5} + 4 q^{13} + 12 q^{19} + 64 q^{25} + 4 q^{29} + 8 q^{31} - 4 q^{35} + 12 q^{37} + 4 q^{41} + 16 q^{43} + 24 q^{47} + 56 q^{49} - 12 q^{53} + 12 q^{55} - 32 q^{59} + 32 q^{61} - 12 q^{65} + 28 q^{67} - 4 q^{71} + 12 q^{73} - 16 q^{77} - 20 q^{79} - 8 q^{83} + 24 q^{85} + 32 q^{89} - 12 q^{91} + 36 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5796))\) 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
5796.2.a.a 5796.a 1.a $1$ $46.281$ \(\Q\) None \(0\) \(0\) \(-4\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{5}+q^{7}+2q^{13}-4q^{17}+4q^{19}+\cdots\)
5796.2.a.b 5796.a 1.a $1$ $46.281$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+3q^{11}-4q^{13}-8q^{17}+\cdots\)
5796.2.a.c 5796.a 1.a $1$ $46.281$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{7}+5q^{11}-6q^{13}-4q^{17}+7q^{19}+\cdots\)
5796.2.a.d 5796.a 1.a $1$ $46.281$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{11}+2q^{13}+5q^{19}+q^{23}+\cdots\)
5796.2.a.e 5796.a 1.a $1$ $46.281$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+2q^{11}-3q^{13}+q^{23}-5q^{25}+\cdots\)
5796.2.a.f 5796.a 1.a $1$ $46.281$ \(\Q\) None \(0\) \(0\) \(2\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}+2q^{11}-q^{13}-6q^{19}+\cdots\)
5796.2.a.g 5796.a 1.a $1$ $46.281$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-3q^{11}-4q^{13}+8q^{17}+\cdots\)
5796.2.a.h 5796.a 1.a $1$ $46.281$ \(\Q\) None \(0\) \(0\) \(4\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+q^{7}+2q^{13}+4q^{17}+4q^{19}+\cdots\)
5796.2.a.i 5796.a 1.a $2$ $46.281$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-1\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{5}-q^{7}+(1+2\beta )q^{11}+(1+\beta )q^{13}+\cdots\)
5796.2.a.j 5796.a 1.a $2$ $46.281$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-1\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-3\beta )q^{5}+q^{7}-3q^{11}+(-2+\beta )q^{13}+\cdots\)
5796.2.a.k 5796.a 1.a $2$ $46.281$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(-1\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+q^{7}+(-1+2\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
5796.2.a.l 5796.a 1.a $2$ $46.281$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}+3q^{11}+(-1+\beta )q^{13}+\cdots\)
5796.2.a.m 5796.a 1.a $2$ $46.281$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(5\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(3-\beta )q^{5}-q^{7}+(-1-2\beta )q^{11}+\cdots\)
5796.2.a.n 5796.a 1.a $2$ $46.281$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(5\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(3-\beta )q^{5}+q^{7}+q^{11}+(2-5\beta )q^{13}+\cdots\)
5796.2.a.o 5796.a 1.a $3$ $46.281$ 3.3.1101.1 None \(0\) \(0\) \(-1\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{5}-q^{7}-q^{11}+(-1+\beta _{1}-\beta _{2})q^{13}+\cdots\)
5796.2.a.p 5796.a 1.a $3$ $46.281$ 3.3.1509.1 None \(0\) \(0\) \(1\) \(3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+q^{7}+(-1+2\beta _{1})q^{11}+(1+\cdots)q^{13}+\cdots\)
5796.2.a.q 5796.a 1.a $4$ $46.281$ 4.4.140608.1 None \(0\) \(0\) \(-2\) \(4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}+q^{7}+(-1-\beta _{1})q^{11}+(1+\cdots)q^{13}+\cdots\)
5796.2.a.r 5796.a 1.a $4$ $46.281$ 4.4.140608.1 None \(0\) \(0\) \(2\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}+q^{7}+(1+\beta _{1})q^{11}+(1+\beta _{2}+\cdots)q^{13}+\cdots\)
5796.2.a.s 5796.a 1.a $5$ $46.281$ 5.5.8580816.1 None \(0\) \(0\) \(-4\) \(5\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{4})q^{5}+q^{7}+(\beta _{2}+\beta _{4})q^{11}+\cdots\)
5796.2.a.t 5796.a 1.a $5$ $46.281$ 5.5.6963152.1 None \(0\) \(0\) \(-2\) \(-5\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2}-\beta _{3})q^{5}-q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
5796.2.a.u 5796.a 1.a $6$ $46.281$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(-4\) \(-6\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}-q^{7}+(-\beta _{3}-\beta _{4}+\cdots)q^{11}+\cdots\)
5796.2.a.v 5796.a 1.a $6$ $46.281$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(4\) \(-6\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{5}-q^{7}+(\beta _{3}+\beta _{4})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5796))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5796)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(644))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(828))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(966))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1449))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1932))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2898))\)\(^{\oplus 2}\)