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Properties

Label 8372.2.a
Level $8372$
Weight $2$
Character orbit 8372.a
Rep. character $\chi_{8372}(1,\cdot)$
Character field $\Q$
Dimension $132$
Newform subspaces $16$
Sturm bound $2688$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 8372 = 2^{2} \cdot 7 \cdot 13 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8372.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(2688\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8372))\).

Total New Old
Modular forms 1356 132 1224
Cusp forms 1333 132 1201
Eisenstein series 23 0 23

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

\(2\)\(7\)\(13\)\(23\)FrickeDim
\(-\)\(+\)\(+\)\(+\)$-$\(17\)
\(-\)\(+\)\(+\)\(-\)$+$\(16\)
\(-\)\(+\)\(-\)\(+\)$+$\(12\)
\(-\)\(+\)\(-\)\(-\)$-$\(21\)
\(-\)\(-\)\(+\)\(+\)$+$\(16\)
\(-\)\(-\)\(+\)\(-\)$-$\(17\)
\(-\)\(-\)\(-\)\(+\)$-$\(21\)
\(-\)\(-\)\(-\)\(-\)$+$\(12\)
Plus space\(+\)\(56\)
Minus space\(-\)\(76\)

Trace form

\( 132 q - 8 q^{3} + 124 q^{9} + O(q^{10}) \) \( 132 q - 8 q^{3} + 124 q^{9} - 8 q^{11} - 8 q^{17} - 24 q^{19} + 132 q^{25} - 32 q^{27} + 16 q^{31} + 16 q^{37} - 8 q^{47} + 132 q^{49} - 48 q^{51} + 8 q^{53} + 16 q^{55} + 16 q^{57} - 72 q^{59} + 56 q^{61} - 8 q^{67} - 24 q^{71} - 8 q^{73} - 24 q^{75} - 32 q^{79} + 132 q^{81} + 40 q^{83} + 40 q^{85} + 32 q^{87} - 16 q^{89} + 48 q^{93} + 24 q^{95} - 16 q^{97} - 56 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8372))\) 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 23
8372.2.a.a 8372.a 1.a $1$ $66.851$ \(\Q\) None \(0\) \(-2\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{7}+q^{9}-3q^{11}+q^{13}+\cdots\)
8372.2.a.b 8372.a 1.a $1$ $66.851$ \(\Q\) None \(0\) \(-2\) \(2\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}+\cdots\)
8372.2.a.c 8372.a 1.a $1$ $66.851$ \(\Q\) None \(0\) \(-2\) \(4\) \(1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{5}+q^{7}+q^{9}+5q^{11}+\cdots\)
8372.2.a.d 8372.a 1.a $1$ $66.851$ \(\Q\) None \(0\) \(-1\) \(1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}-2q^{9}-3q^{11}+q^{13}+\cdots\)
8372.2.a.e 8372.a 1.a $1$ $66.851$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}-3q^{9}-q^{13}+6q^{17}-4q^{19}+\cdots\)
8372.2.a.f 8372.a 1.a $1$ $66.851$ \(\Q\) None \(0\) \(1\) \(-3\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}+q^{7}-2q^{9}+3q^{11}+\cdots\)
8372.2.a.g 8372.a 1.a $1$ $66.851$ \(\Q\) None \(0\) \(1\) \(3\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}+q^{7}-2q^{9}-3q^{11}+\cdots\)
8372.2.a.h 8372.a 1.a $4$ $66.851$ 4.4.6224.1 None \(0\) \(-2\) \(-2\) \(-4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{3}+(\beta _{2}-\beta _{3})q^{5}-q^{7}+\cdots\)
8372.2.a.i 8372.a 1.a $8$ $66.851$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(2\) \(-1\) \(-8\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{4}q^{5}-q^{7}+(\beta _{2}+\beta _{5}+\beta _{6}+\cdots)q^{9}+\cdots\)
8372.2.a.j 8372.a 1.a $9$ $66.851$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-2\) \(-7\) \(9\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
8372.2.a.k 8372.a 1.a $15$ $66.851$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(4\) \(-5\) \(-15\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{6}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots\)
8372.2.a.l 8372.a 1.a $16$ $66.851$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-4\) \(3\) \(-16\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots\)
8372.2.a.m 8372.a 1.a $16$ $66.851$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-2\) \(-3\) \(16\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{8}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
8372.2.a.n 8372.a 1.a $16$ $66.851$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(2\) \(-1\) \(16\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{5}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
8372.2.a.o 8372.a 1.a $20$ $66.851$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(1\) \(6\) \(20\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{6}q^{5}+q^{7}+(2+\beta _{2})q^{9}+\cdots\)
8372.2.a.p 8372.a 1.a $21$ $66.851$ None \(0\) \(-2\) \(3\) \(-21\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8372))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8372)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(299))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(598))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(644))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2093))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4186))\)\(^{\oplus 2}\)