Properties

Label 8092.2.a
Level $8092$
Weight $2$
Character orbit 8092.a
Rep. character $\chi_{8092}(1,\cdot)$
Character field $\Q$
Dimension $136$
Newform subspaces $26$
Sturm bound $2448$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 8092 = 2^{2} \cdot 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8092.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(2448\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8092))\).

Total New Old
Modular forms 1278 136 1142
Cusp forms 1171 136 1035
Eisenstein series 107 0 107

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

\(2\)\(7\)\(17\)FrickeDim
\(-\)\(+\)\(+\)$-$\(32\)
\(-\)\(+\)\(-\)$+$\(36\)
\(-\)\(-\)\(+\)$+$\(32\)
\(-\)\(-\)\(-\)$-$\(36\)
Plus space\(+\)\(68\)
Minus space\(-\)\(68\)

Trace form

\( 136 q + 4 q^{3} + 4 q^{5} + 140 q^{9} + O(q^{10}) \) \( 136 q + 4 q^{3} + 4 q^{5} + 140 q^{9} - 4 q^{11} - 12 q^{15} - 8 q^{23} + 152 q^{25} + 16 q^{27} + 4 q^{29} + 4 q^{31} - 8 q^{33} + 4 q^{35} + 8 q^{37} + 4 q^{39} - 4 q^{41} + 8 q^{43} - 16 q^{45} - 16 q^{47} + 136 q^{49} + 4 q^{53} + 8 q^{55} - 4 q^{57} + 16 q^{59} - 4 q^{61} - 8 q^{63} - 24 q^{65} + 12 q^{67} + 8 q^{71} - 4 q^{73} - 24 q^{75} + 4 q^{79} + 128 q^{81} - 20 q^{83} + 12 q^{87} + 40 q^{89} - 4 q^{91} - 8 q^{93} + 12 q^{95} + 28 q^{97} + 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8092))\) 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 7 17
8092.2.a.a 8092.a 1.a $1$ $64.615$ \(\Q\) None \(0\) \(-3\) \(-2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{5}-q^{7}+6q^{9}+4q^{13}+\cdots\)
8092.2.a.b 8092.a 1.a $1$ $64.615$ \(\Q\) None \(0\) \(-2\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}+q^{7}+q^{9}+4q^{13}+\cdots\)
8092.2.a.c 8092.a 1.a $1$ $64.615$ \(\Q\) None \(0\) \(-1\) \(-2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{7}-2q^{9}-4q^{11}+\cdots\)
8092.2.a.d 8092.a 1.a $1$ $64.615$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}-2q^{9}-6q^{11}-4q^{13}+\cdots\)
8092.2.a.e 8092.a 1.a $1$ $64.615$ \(\Q\) None \(0\) \(0\) \(-4\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{5}+q^{7}-3q^{9}-4q^{11}-2q^{19}+\cdots\)
8092.2.a.f 8092.a 1.a $1$ $64.615$ \(\Q\) None \(0\) \(0\) \(4\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-q^{7}-3q^{9}+4q^{11}-2q^{19}+\cdots\)
8092.2.a.g 8092.a 1.a $1$ $64.615$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}-2q^{9}+6q^{11}-4q^{13}+\cdots\)
8092.2.a.h 8092.a 1.a $1$ $64.615$ \(\Q\) None \(0\) \(1\) \(2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-q^{7}-2q^{9}+4q^{11}+\cdots\)
8092.2.a.i 8092.a 1.a $1$ $64.615$ \(\Q\) None \(0\) \(2\) \(-2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}-q^{7}+q^{9}+4q^{13}+\cdots\)
8092.2.a.j 8092.a 1.a $1$ $64.615$ \(\Q\) None \(0\) \(3\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{5}+q^{7}+6q^{9}+4q^{13}+\cdots\)
8092.2.a.k 8092.a 1.a $2$ $64.615$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{5}-q^{7}+\beta q^{9}+(4+\cdots)q^{13}+\cdots\)
8092.2.a.l 8092.a 1.a $2$ $64.615$ \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(-1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+\beta )q^{5}+q^{7}+\beta q^{9}+\cdots\)
8092.2.a.m 8092.a 1.a $2$ $64.615$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots\)
8092.2.a.n 8092.a 1.a $2$ $64.615$ \(\Q(\sqrt{13}) \) None \(0\) \(3\) \(3\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2-\beta )q^{5}-q^{7}+(1+3\beta )q^{9}+\cdots\)
8092.2.a.o 8092.a 1.a $3$ $64.615$ 3.3.788.1 None \(0\) \(-1\) \(4\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(1+\beta _{2})q^{5}+q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
8092.2.a.p 8092.a 1.a $3$ $64.615$ 3.3.788.1 None \(0\) \(1\) \(-4\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(-1-\beta _{2})q^{5}-q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
8092.2.a.q 8092.a 1.a $4$ $64.615$ 4.4.1957.1 None \(0\) \(-4\) \(-2\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2})q^{3}+(-1+\beta _{3})q^{5}+q^{7}+\cdots\)
8092.2.a.r 8092.a 1.a $4$ $64.615$ 4.4.1957.1 None \(0\) \(4\) \(2\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{3}+(1-\beta _{3})q^{5}-q^{7}+(2+\cdots)q^{9}+\cdots\)
8092.2.a.s 8092.a 1.a $8$ $64.615$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-4\) \(-4\) \(8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(-1-\beta _{1})q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots\)
8092.2.a.t 8092.a 1.a $8$ $64.615$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(4\) \(4\) \(-8\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(1+\beta _{1})q^{5}-q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)
8092.2.a.u 8092.a 1.a $12$ $64.615$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-12\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{7}q^{5}-q^{7}+(1+\beta _{6}+\beta _{8}+\cdots)q^{9}+\cdots\)
8092.2.a.v 8092.a 1.a $12$ $64.615$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-12\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{10}q^{5}-q^{7}+(1-\beta _{3}+\beta _{8}+\cdots)q^{9}+\cdots\)
8092.2.a.w 8092.a 1.a $12$ $64.615$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(12\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{10}q^{5}+q^{7}+(1-\beta _{3}+\beta _{8}+\cdots)q^{9}+\cdots\)
8092.2.a.x 8092.a 1.a $12$ $64.615$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(12\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{7}q^{5}+q^{7}+(1+\beta _{6}+\beta _{8}+\cdots)q^{9}+\cdots\)
8092.2.a.y 8092.a 1.a $20$ $64.615$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-8\) \(-8\) \(-20\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{12}q^{5}-q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
8092.2.a.z 8092.a 1.a $20$ $64.615$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(8\) \(8\) \(20\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{12}q^{5}+q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8092))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8092)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2023))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4046))\)\(^{\oplus 2}\)