Properties

Label 112.10.a
Level $112$
Weight $10$
Character orbit 112.a
Rep. character $\chi_{112}(1,\cdot)$
Character field $\Q$
Dimension $27$
Newform subspaces $11$
Sturm bound $160$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 112.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(160\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(112))\).

Total New Old
Modular forms 150 27 123
Cusp forms 138 27 111
Eisenstein series 12 0 12

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

\(2\)\(7\)FrickeDim
\(+\)\(+\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(7\)
\(-\)\(+\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(13\)
Minus space\(-\)\(14\)

Trace form

\( 27 q + 718 q^{5} - 2401 q^{7} + 204887 q^{9} + 54916 q^{11} + 86158 q^{13} - 81528 q^{15} - 344210 q^{17} + 480888 q^{19} - 812552 q^{23} + 11407757 q^{25} + 5798016 q^{27} + 746738 q^{29} - 6344712 q^{31}+ \cdots + 409926388 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(112))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7
112.10.a.a 112.a 1.a $1$ $57.684$ \(\Q\) None 14.10.a.b \(0\) \(-170\) \(544\) \(2401\) $-$ $-$ $\mathrm{SU}(2)$ \(q-170q^{3}+544q^{5}+7^{4}q^{7}+9217q^{9}+\cdots\)
112.10.a.b 112.a 1.a $1$ $57.684$ \(\Q\) None 14.10.a.a \(0\) \(6\) \(560\) \(2401\) $-$ $-$ $\mathrm{SU}(2)$ \(q+6q^{3}+560q^{5}+7^{4}q^{7}-19647q^{9}+\cdots\)
112.10.a.c 112.a 1.a $2$ $57.684$ \(\Q(\sqrt{2305}) \) None 14.10.a.c \(0\) \(14\) \(-2730\) \(-4802\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(7+5\beta )q^{3}+(-1365-21\beta )q^{5}+\cdots\)
112.10.a.d 112.a 1.a $2$ $57.684$ \(\Q(\sqrt{11209}) \) None 28.10.a.b \(0\) \(70\) \(1554\) \(4802\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(35-\beta )q^{3}+(777+19\beta )q^{5}+7^{4}q^{7}+\cdots\)
112.10.a.e 112.a 1.a $2$ $57.684$ \(\Q(\sqrt{193}) \) None 7.10.a.a \(0\) \(86\) \(-2238\) \(4802\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(43+11\beta )q^{3}+(-1119+95\beta )q^{5}+\cdots\)
112.10.a.f 112.a 1.a $2$ $57.684$ \(\Q(\sqrt{4561}) \) None 28.10.a.a \(0\) \(224\) \(1596\) \(-4802\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(112-\beta )q^{3}+(798-9\beta )q^{5}-7^{4}q^{7}+\cdots\)
112.10.a.g 112.a 1.a $3$ $57.684$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 56.10.a.b \(0\) \(-84\) \(-2958\) \(-7203\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-28+\beta _{1})q^{3}+(-986+5\beta _{1}-\beta _{2})q^{5}+\cdots\)
112.10.a.h 112.a 1.a $3$ $57.684$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 7.10.a.b \(0\) \(-84\) \(1554\) \(-7203\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-28+\beta _{1})q^{3}+(518-6\beta _{1}+7\beta _{2})q^{5}+\cdots\)
112.10.a.i 112.a 1.a $3$ $57.684$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 56.10.a.a \(0\) \(92\) \(274\) \(7203\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(31+\beta _{1})q^{3}+(92+\beta _{1}-\beta _{2})q^{5}+\cdots\)
112.10.a.j 112.a 1.a $4$ $57.684$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 56.10.a.d \(0\) \(-84\) \(1540\) \(9604\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-21+\beta _{1})q^{3}+(385-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
112.10.a.k 112.a 1.a $4$ $57.684$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 56.10.a.c \(0\) \(-70\) \(1022\) \(-9604\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-17+\beta _{1})q^{3}+(255-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(112))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(112)) \simeq \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 2}\)