Properties

Label 8752.2.a
Level $8752$
Weight $2$
Character orbit 8752.a
Rep. character $\chi_{8752}(1,\cdot)$
Character field $\Q$
Dimension $273$
Newform subspaces $26$
Sturm bound $2192$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 8752 = 2^{4} \cdot 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8752.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(2192\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8752))\).

Total New Old
Modular forms 1102 273 829
Cusp forms 1091 273 818
Eisenstein series 11 0 11

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

\(2\)\(547\)FrickeDim
\(+\)\(+\)$+$\(64\)
\(+\)\(-\)$-$\(73\)
\(-\)\(+\)$-$\(68\)
\(-\)\(-\)$+$\(68\)
Plus space\(+\)\(132\)
Minus space\(-\)\(141\)

Trace form

\( 273 q - 2 q^{5} + 273 q^{9} + O(q^{10}) \) \( 273 q - 2 q^{5} + 273 q^{9} + 6 q^{11} - 2 q^{13} + 8 q^{15} + 2 q^{17} - 2 q^{19} + 12 q^{23} + 267 q^{25} + 12 q^{27} - 2 q^{29} - 8 q^{31} - 8 q^{33} + 24 q^{35} - 10 q^{37} + 24 q^{39} - 6 q^{41} - 10 q^{45} + 2 q^{47} + 257 q^{49} + 8 q^{51} - 10 q^{53} + 36 q^{55} - 16 q^{57} - 2 q^{61} - 20 q^{63} - 12 q^{65} + 30 q^{67} + 16 q^{69} + 36 q^{71} + 2 q^{73} + 12 q^{75} - 8 q^{77} - 8 q^{79} + 257 q^{81} + 4 q^{83} - 12 q^{85} + 24 q^{87} + 2 q^{89} - 16 q^{93} + 10 q^{97} + 42 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8752))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 547
8752.2.a.a 8752.a 1.a $1$ $69.885$ \(\Q\) None \(0\) \(-2\) \(0\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
8752.2.a.b 8752.a 1.a $1$ $69.885$ \(\Q\) None \(0\) \(-2\) \(0\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
8752.2.a.c 8752.a 1.a $1$ $69.885$ \(\Q\) None \(0\) \(-2\) \(0\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{7}+q^{9}+3q^{11}+q^{13}+\cdots\)
8752.2.a.d 8752.a 1.a $1$ $69.885$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{9}+5q^{11}+q^{13}+2q^{17}+\cdots\)
8752.2.a.e 8752.a 1.a $1$ $69.885$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{7}-3q^{9}+3q^{11}-2q^{13}+2q^{17}+\cdots\)
8752.2.a.f 8752.a 1.a $1$ $69.885$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{7}-3q^{9}+5q^{11}+7q^{13}+2q^{17}+\cdots\)
8752.2.a.g 8752.a 1.a $1$ $69.885$ \(\Q\) None \(0\) \(0\) \(2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}-3q^{9}+3q^{11}+5q^{13}+\cdots\)
8752.2.a.h 8752.a 1.a $1$ $69.885$ \(\Q\) None \(0\) \(0\) \(4\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-4q^{7}-3q^{9}-q^{11}-2q^{13}+\cdots\)
8752.2.a.i 8752.a 1.a $1$ $69.885$ \(\Q\) None \(0\) \(2\) \(-2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}+4q^{7}+q^{9}+3q^{11}+\cdots\)
8752.2.a.j 8752.a 1.a $1$ $69.885$ \(\Q\) None \(0\) \(2\) \(2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}+4q^{7}+q^{9}+q^{13}+\cdots\)
8752.2.a.k 8752.a 1.a $1$ $69.885$ \(\Q\) None \(0\) \(2\) \(4\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{5}+2q^{7}+q^{9}+5q^{11}+\cdots\)
8752.2.a.l 8752.a 1.a $2$ $69.885$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(-8\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(-1-\beta )q^{5}-4q^{7}+\cdots\)
8752.2.a.m 8752.a 1.a $2$ $69.885$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-2+\beta )q^{5}-q^{9}+(-3+\beta )q^{11}+\cdots\)
8752.2.a.n 8752.a 1.a $2$ $69.885$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+\beta q^{5}-2q^{7}-q^{9}+(5-\beta )q^{11}+\cdots\)
8752.2.a.o 8752.a 1.a $7$ $69.885$ 7.7.195805801.1 None \(0\) \(0\) \(0\) \(5\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{3})q^{3}+(-\beta _{1}-\beta _{4})q^{5}+(1+\cdots)q^{7}+\cdots\)
8752.2.a.p 8752.a 1.a $7$ $69.885$ 7.7.100069857.1 None \(0\) \(8\) \(-4\) \(9\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
8752.2.a.q 8752.a 1.a $13$ $69.885$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(-1\) \(7\) \(-11\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{4})q^{5}+(-1-\beta _{5})q^{7}+\cdots\)
8752.2.a.r 8752.a 1.a $15$ $69.885$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(-9\) \(-1\) \(-11\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-\beta _{3}q^{5}+(-1-\beta _{4}+\cdots)q^{7}+\cdots\)
8752.2.a.s 8752.a 1.a $18$ $69.885$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(10\) \(-27\) \(11\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{9})q^{3}+(-2-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
8752.2.a.t 8752.a 1.a $19$ $69.885$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(0\) \(8\) \(-1\) \(9\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{7}q^{5}-\beta _{4}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
8752.2.a.u 8752.a 1.a $23$ $69.885$ None \(0\) \(-12\) \(-3\) \(-5\) $-$ $-$ $\mathrm{SU}(2)$
8752.2.a.v 8752.a 1.a $25$ $69.885$ None \(0\) \(-8\) \(29\) \(-5\) $-$ $+$ $\mathrm{SU}(2)$
8752.2.a.w 8752.a 1.a $27$ $69.885$ None \(0\) \(4\) \(-5\) \(2\) $+$ $+$ $\mathrm{SU}(2)$
8752.2.a.x 8752.a 1.a $31$ $69.885$ None \(0\) \(8\) \(-11\) \(10\) $+$ $-$ $\mathrm{SU}(2)$
8752.2.a.y 8752.a 1.a $34$ $69.885$ None \(0\) \(-9\) \(4\) \(-20\) $+$ $+$ $\mathrm{SU}(2)$
8752.2.a.z 8752.a 1.a $37$ $69.885$ None \(0\) \(3\) \(6\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8752))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8752)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(547))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1094))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2188))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4376))\)\(^{\oplus 2}\)