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

\( 27 q + 718 q^{5} - 2401 q^{7} + 204887 q^{9} + O(q^{10}) \) \( 27 q + 718 q^{5} - 2401 q^{7} + 204887 q^{9} + 54916 q^{11} + 86158 q^{13} - 81528 q^{15} - 344210 q^{17} + 480888 q^{19} - 812552 q^{23} + 11407757 q^{25} + 5798016 q^{27} + 746738 q^{29} - 6344712 q^{31} + 9585408 q^{33} + 9003750 q^{35} - 2210198 q^{37} - 83320200 q^{39} - 5961738 q^{41} + 83940724 q^{43} + 23553990 q^{45} - 173719272 q^{47} + 155649627 q^{49} + 229586448 q^{51} + 3292082 q^{53} - 246809592 q^{55} + 58487224 q^{57} + 86244480 q^{59} - 90027306 q^{61} - 78764805 q^{63} + 154041124 q^{65} + 181960980 q^{67} - 382360176 q^{69} - 285033976 q^{71} - 471146066 q^{73} - 501618592 q^{75} - 103022108 q^{77} + 978029168 q^{79} + 1432922699 q^{81} + 28717816 q^{83} - 324885860 q^{85} + 4293732080 q^{87} - 388851410 q^{89} + 411449766 q^{91} + 1674528144 q^{93} - 181551768 q^{95} + 344333406 q^{97} + 409926388 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7
112.10.a.a \(1\) \(57.684\) \(\Q\) None \(0\) \(-170\) \(544\) \(2401\) \(-\) \(-\) \(q-170q^{3}+544q^{5}+7^{4}q^{7}+9217q^{9}+\cdots\)
112.10.a.b \(1\) \(57.684\) \(\Q\) None \(0\) \(6\) \(560\) \(2401\) \(-\) \(-\) \(q+6q^{3}+560q^{5}+7^{4}q^{7}-19647q^{9}+\cdots\)
112.10.a.c \(2\) \(57.684\) \(\Q(\sqrt{2305}) \) None \(0\) \(14\) \(-2730\) \(-4802\) \(-\) \(+\) \(q+(7+5\beta )q^{3}+(-1365-21\beta )q^{5}+\cdots\)
112.10.a.d \(2\) \(57.684\) \(\Q(\sqrt{11209}) \) None \(0\) \(70\) \(1554\) \(4802\) \(-\) \(-\) \(q+(35-\beta )q^{3}+(777+19\beta )q^{5}+7^{4}q^{7}+\cdots\)
112.10.a.e \(2\) \(57.684\) \(\Q(\sqrt{193}) \) None \(0\) \(86\) \(-2238\) \(4802\) \(-\) \(-\) \(q+(43+11\beta )q^{3}+(-1119+95\beta )q^{5}+\cdots\)
112.10.a.f \(2\) \(57.684\) \(\Q(\sqrt{4561}) \) None \(0\) \(224\) \(1596\) \(-4802\) \(-\) \(+\) \(q+(112-\beta )q^{3}+(798-9\beta )q^{5}-7^{4}q^{7}+\cdots\)
112.10.a.g \(3\) \(57.684\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-84\) \(-2958\) \(-7203\) \(+\) \(+\) \(q+(-28+\beta _{1})q^{3}+(-986+5\beta _{1}-\beta _{2})q^{5}+\cdots\)
112.10.a.h \(3\) \(57.684\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-84\) \(1554\) \(-7203\) \(-\) \(+\) \(q+(-28+\beta _{1})q^{3}+(518-6\beta _{1}+7\beta _{2})q^{5}+\cdots\)
112.10.a.i \(3\) \(57.684\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(92\) \(274\) \(7203\) \(+\) \(-\) \(q+(31+\beta _{1})q^{3}+(92+\beta _{1}-\beta _{2})q^{5}+\cdots\)
112.10.a.j \(4\) \(57.684\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-84\) \(1540\) \(9604\) \(+\) \(-\) \(q+(-21+\beta _{1})q^{3}+(385-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
112.10.a.k \(4\) \(57.684\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-70\) \(1022\) \(-9604\) \(+\) \(+\) \(q+(-17+\beta _{1})q^{3}+(255-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

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

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