Properties

Label 5096.2.a
Level $5096$
Weight $2$
Character orbit 5096.a
Rep. character $\chi_{5096}(1,\cdot)$
Character field $\Q$
Dimension $123$
Newform subspaces $33$
Sturm bound $1568$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 5096 = 2^{3} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5096.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 33 \)
Sturm bound: \(1568\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5096))\).

Total New Old
Modular forms 816 123 693
Cusp forms 753 123 630
Eisenstein series 63 0 63

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

\(2\)\(7\)\(13\)FrickeDim
\(+\)\(+\)\(+\)$+$\(14\)
\(+\)\(+\)\(-\)$-$\(18\)
\(+\)\(-\)\(+\)$-$\(18\)
\(+\)\(-\)\(-\)$+$\(12\)
\(-\)\(+\)\(+\)$-$\(15\)
\(-\)\(+\)\(-\)$+$\(13\)
\(-\)\(-\)\(+\)$+$\(15\)
\(-\)\(-\)\(-\)$-$\(18\)
Plus space\(+\)\(54\)
Minus space\(-\)\(69\)

Trace form

\( 123 q + 2 q^{3} - 2 q^{5} + 113 q^{9} + O(q^{10}) \) \( 123 q + 2 q^{3} - 2 q^{5} + 113 q^{9} - 4 q^{11} - q^{13} - 16 q^{15} - 8 q^{17} + 12 q^{19} + 12 q^{23} + 127 q^{25} - 10 q^{27} + 10 q^{29} - 4 q^{31} - 4 q^{33} - 14 q^{37} - 14 q^{41} - 2 q^{43} - 22 q^{45} - 4 q^{47} + 10 q^{51} - 2 q^{53} - 32 q^{57} + 28 q^{59} + 2 q^{61} + 4 q^{65} + 4 q^{67} - 4 q^{69} - 12 q^{71} + 2 q^{73} + 32 q^{75} - 20 q^{79} + 107 q^{81} + 16 q^{83} + 32 q^{85} + 56 q^{87} - 6 q^{89} + 68 q^{95} - 10 q^{97} + 104 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5096))\) 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 13
5096.2.a.a 5096.a 1.a $1$ $40.692$ \(\Q\) None \(0\) \(-2\) \(-3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-3q^{5}+q^{9}+q^{13}+6q^{15}+\cdots\)
5096.2.a.b 5096.a 1.a $1$ $40.692$ \(\Q\) None \(0\) \(-1\) \(-3\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}-2q^{9}-3q^{11}-q^{13}+\cdots\)
5096.2.a.c 5096.a 1.a $1$ $40.692$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{9}-2q^{11}+q^{13}+\cdots\)
5096.2.a.d 5096.a 1.a $1$ $40.692$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{9}+5q^{11}+q^{13}+\cdots\)
5096.2.a.e 5096.a 1.a $1$ $40.692$ \(\Q\) None \(0\) \(-1\) \(3\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-2q^{9}-q^{11}-q^{13}+\cdots\)
5096.2.a.f 5096.a 1.a $1$ $40.692$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}+2q^{11}-q^{13}+7q^{19}+\cdots\)
5096.2.a.g 5096.a 1.a $1$ $40.692$ \(\Q\) None \(0\) \(1\) \(-3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}-2q^{9}-q^{11}+q^{13}+\cdots\)
5096.2.a.h 5096.a 1.a $1$ $40.692$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{9}+5q^{11}-q^{13}+\cdots\)
5096.2.a.i 5096.a 1.a $1$ $40.692$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{9}+3q^{11}+q^{13}-4q^{17}+\cdots\)
5096.2.a.j 5096.a 1.a $1$ $40.692$ \(\Q\) None \(0\) \(1\) \(3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}-2q^{9}-3q^{11}+q^{13}+\cdots\)
5096.2.a.k 5096.a 1.a $1$ $40.692$ \(\Q\) None \(0\) \(2\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+q^{9}+4q^{11}+q^{13}+\cdots\)
5096.2.a.l 5096.a 1.a $2$ $40.692$ \(\Q(\sqrt{7}) \) None \(0\) \(-4\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}+(-2+\beta )q^{11}+q^{13}+\cdots\)
5096.2.a.m 5096.a 1.a $2$ $40.692$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{9}-2\beta q^{11}+\cdots\)
5096.2.a.n 5096.a 1.a $2$ $40.692$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{5}+(1+\beta )q^{9}+(2+\beta )q^{11}+\cdots\)
5096.2.a.o 5096.a 1.a $2$ $40.692$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-\beta q^{5}+(1+2\beta )q^{9}+(-1+\cdots)q^{11}+\cdots\)
5096.2.a.p 5096.a 1.a $2$ $40.692$ \(\Q(\sqrt{7}) \) None \(0\) \(4\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{9}+(-2-\beta )q^{11}-q^{13}+\cdots\)
5096.2.a.q 5096.a 1.a $2$ $40.692$ \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}+(1+\beta )q^{5}+(3+4\beta )q^{9}+\cdots\)
5096.2.a.r 5096.a 1.a $4$ $40.692$ 4.4.23252.1 None \(0\) \(-1\) \(-3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
5096.2.a.s 5096.a 1.a $4$ $40.692$ 4.4.64268.1 None \(0\) \(-1\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(3+\beta _{1}+\beta _{3})q^{9}+\cdots\)
5096.2.a.t 5096.a 1.a $4$ $40.692$ 4.4.183064.1 None \(0\) \(-1\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(2+\beta _{2})q^{9}+\beta _{1}q^{11}+\cdots\)
5096.2.a.u 5096.a 1.a $4$ $40.692$ 4.4.20308.1 None \(0\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
5096.2.a.v 5096.a 1.a $4$ $40.692$ 4.4.20308.1 None \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
5096.2.a.w 5096.a 1.a $4$ $40.692$ 4.4.23252.1 None \(0\) \(1\) \(3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{3})q^{5}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
5096.2.a.x 5096.a 1.a $5$ $40.692$ 5.5.2398996.1 None \(0\) \(-1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(\beta _{2}-\beta _{3})q^{9}+(\beta _{3}+\cdots)q^{11}+\cdots\)
5096.2.a.y 5096.a 1.a $5$ $40.692$ 5.5.2398996.1 None \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{2}-\beta _{3})q^{9}+(\beta _{3}+\cdots)q^{11}+\cdots\)
5096.2.a.z 5096.a 1.a $7$ $40.692$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-2\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{4}q^{5}+(1+\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
5096.2.a.ba 5096.a 1.a $7$ $40.692$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(2\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{4}q^{5}+(1+\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
5096.2.a.bb 5096.a 1.a $8$ $40.692$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-2\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{6}q^{5}+(2-\beta _{2}-\beta _{4}+\beta _{7})q^{9}+\cdots\)
5096.2.a.bc 5096.a 1.a $8$ $40.692$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-2\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(1+\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
5096.2.a.bd 5096.a 1.a $8$ $40.692$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(2\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(1+\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
5096.2.a.be 5096.a 1.a $8$ $40.692$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(2\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{6}q^{5}+(2-\beta _{2}-\beta _{4}+\beta _{7})q^{9}+\cdots\)
5096.2.a.bf 5096.a 1.a $10$ $40.692$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-2\) \(-6\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{9})q^{5}+(2+\beta _{8}-\beta _{9})q^{9}+\cdots\)
5096.2.a.bg 5096.a 1.a $10$ $40.692$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(2\) \(6\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{9})q^{5}+(2+\beta _{8}-\beta _{9})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5096))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5096)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1274))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2548))\)\(^{\oplus 2}\)