Space of modular forms of level 112, weight 14, and trivial character

• Label: 112.14.a
• Level: $112$
• Weight: $14$
• Character orbit: 112.a
• Rep. character: $\chi_{112}(1,\cdot)$
• Character field: $\Q$
• Dimension: $39$
• Newform subspaces: $12$
• Sturm bound: $224$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	112.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(112))\).

	Total	New	Old
Modular forms	214	39	175
Cusp forms	202	39	163
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.

\(2\)	\(7\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(10\)
\(+\)	\(-\)	$-$	\(10\)
\(-\)	\(+\)	$-$	\(10\)
\(-\)	\(-\)	$+$	\(9\)
Plus space		\(+\)	\(19\)
Minus space		\(-\)	\(20\)

Trace form

\( 39 q - 33802 q^{5} - 117649 q^{7} + 21380675 q^{9} + O(q^{10}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(112))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7
112.14.a.a	$112$	$14$	112.a	1.a	$1$	$1$	$1$	$120.099$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1626\)	\(-36400\)	\(117649\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-1626q^{3}-36400q^{5}+7^{6}q^{7}+1049553q^{9}+\cdots\)
112.14.a.b	$112$	$14$	112.a	1.a	$1$	$1$	$1$	$120.099$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1026\)	\(4320\)	\(-117649\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+1026q^{3}+4320q^{5}-7^{6}q^{7}-541647q^{9}+\cdots\)
112.14.a.c	$112$	$14$	112.a	1.a	$1$	$2$	$2$	$120.099$	\(\Q(\sqrt{78985}) \)	None	✓	$1$	$1$	\(0\)	\(-1106\)	\(75530\)	\(235298\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-553-5\beta )q^{3}+(37765+39\beta )q^{5}+\cdots\)
112.14.a.d	$112$	$14$	112.a	1.a	$1$	$2$	$2$	$120.099$	\(\Q(\sqrt{100129}) \)	None	✓	$1$	$0$	\(0\)	\(-952\)	\(32004\)	\(-235298\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-476-\beta )q^{3}+(16002+63\beta )q^{5}+\cdots\)
112.14.a.e	$112$	$14$	112.a	1.a	$1$	$3$	$3$	$120.099$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(76\)	\(-2174\)	\(352947\)		$-$	$-$	$+$	$2^{5}\cdot 7$	$\mathrm{SU}(2)$	\(q+(5^{2}+\beta _{1})q^{3}+(-725+2\beta _{1}+\beta _{2})q^{5}+\cdots\)
112.14.a.f	$112$	$14$	112.a	1.a	$1$	$3$	$3$	$120.099$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(860\)	\(-47646\)	\(-352947\)		$-$	$+$	$-$	$2^{4}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	\(q+(287-\beta _{1})q^{3}+(-15881-4\beta _{1}+\cdots)q^{5}+\cdots\)
112.14.a.g	$112$	$14$	112.a	1.a	$1$	$3$	$3$	$120.099$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(1796\)	\(-24086\)	\(352947\)		$-$	$-$	$+$	$2^{9}\cdot 7$	$\mathrm{SU}(2)$	\(q+(599+\beta _{1})q^{3}+(-8037-23\beta _{1}+\cdots)q^{5}+\cdots\)
112.14.a.h	$112$	$14$	112.a	1.a	$1$	$4$	$4$	$120.099$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-336\)	\(24192\)	\(-470596\)		$-$	$+$	$-$	$2^{12}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-84-\beta _{2})q^{3}+(6048+2\beta _{1}-6\beta _{2}+\cdots)q^{5}+\cdots\)
112.14.a.i	$112$	$14$	112.a	1.a	$1$	$4$	$4$	$120.099$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(690\)	\(-40106\)	\(-470596\)		$+$	$+$	$+$	$2^{13}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q+(172-\beta _{2})q^{3}+(-10024+5\beta _{2}+\cdots)q^{5}+\cdots\)
112.14.a.j	$112$	$14$	112.a	1.a	$1$	$5$	$5$	$120.099$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(170\)	\(48892\)	\(588245\)		$+$	$-$	$-$	$2^{22}\cdot 3^{2}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+(34+\beta _{1})q^{3}+(9778+2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
112.14.a.k	$112$	$14$	112.a	1.a	$1$	$5$	$5$	$120.099$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(690\)	\(-31788\)	\(588245\)		$+$	$-$	$-$	$2^{20}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q+(138+\beta _{1})q^{3}+(-6358+15\beta _{1}+\cdots)q^{5}+\cdots\)
112.14.a.l	$112$	$14$	112.a	1.a	$1$	$6$	$6$	$120.099$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-1288\)	\(-36540\)	\(-705894\)		$+$	$+$	$+$	$2^{29}\cdot 3^{3}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+(-215-\beta _{1})q^{3}+(-6090-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(112))\) into lower level spaces

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