Space of modular forms of level 8112, weight 2, and trivial character

• Label: 8112.2.a
• Level: $8112$
• Weight: $2$
• Character orbit: 8112.a
• Rep. character: $\chi_{8112}(1,\cdot)$
• Character field: $\Q$
• Dimension: $155$
• Newform subspaces: $75$
• Sturm bound: $2912$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 8112 = 2^{4} \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8112.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 75 \)
Sturm bound:			\(2912\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8112))\).

	Total	New	Old
Modular forms	1540	155	1385
Cusp forms	1373	155	1218
Eisenstein series	167	0	167

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

\(2\)	\(3\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(18\)
\(+\)	\(+\)	\(-\)	$-$	\(21\)
\(+\)	\(-\)	\(+\)	$-$	\(23\)
\(+\)	\(-\)	\(-\)	$+$	\(15\)
\(-\)	\(+\)	\(+\)	$-$	\(18\)
\(-\)	\(+\)	\(-\)	$+$	\(21\)
\(-\)	\(-\)	\(+\)	$+$	\(18\)
\(-\)	\(-\)	\(-\)	$-$	\(21\)
Plus space			\(+\)	\(72\)
Minus space			\(-\)	\(83\)

Trace form

\( 155 q - q^{3} + 2 q^{5} - 4 q^{7} + 155 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8112))\) 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	3	13
8112.2.a.a	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-4\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
8112.2.a.b	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{9}+3q^{15}-q^{17}+\cdots\)
8112.2.a.c	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
8112.2.a.d	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots\)
8112.2.a.e	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-2\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
8112.2.a.f	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+2q^{15}+2q^{17}+\cdots\)
8112.2.a.g	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{15}+\cdots\)
8112.2.a.h	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+6q^{11}+2q^{17}-4q^{23}+\cdots\)
8112.2.a.i	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-6q^{17}+2q^{19}+\cdots\)
8112.2.a.j	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-2q^{7}+q^{9}-2q^{15}+\cdots\)
8112.2.a.k	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
8112.2.a.l	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots\)
8112.2.a.m	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-2q^{7}+q^{9}-6q^{11}+\cdots\)
8112.2.a.n	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{9}-3q^{15}-q^{17}+\cdots\)
8112.2.a.o	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(4\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots\)
8112.2.a.p	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
8112.2.a.q	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+q^{9}-2q^{11}-4q^{15}+\cdots\)
8112.2.a.r	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
8112.2.a.s	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
8112.2.a.t	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}+6q^{11}-2q^{15}+\cdots\)
8112.2.a.u	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}-2q^{15}+\cdots\)
8112.2.a.v	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
8112.2.a.w	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}+q^{9}+2q^{11}-q^{15}+\cdots\)
8112.2.a.x	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}-q^{15}+\cdots\)
8112.2.a.y	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}+q^{9}-2q^{11}-6q^{17}+\cdots\)
8112.2.a.z	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{17}+\cdots\)
8112.2.a.ba	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}+2q^{11}-2q^{17}+\cdots\)
8112.2.a.bb	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}+q^{15}+\cdots\)
8112.2.a.bc	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}+q^{15}+\cdots\)
8112.2.a.bd	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(2\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}+q^{9}-2q^{11}+2q^{15}+\cdots\)
8112.2.a.be	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{15}+\cdots\)
8112.2.a.bf	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}+2q^{15}+\cdots\)
8112.2.a.bg	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+4q^{7}+q^{9}+2q^{15}+\cdots\)
8112.2.a.bh	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
8112.2.a.bi	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(4\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
8112.2.a.bj	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
8112.2.a.bk	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-3\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots\)
8112.2.a.bl	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(-1+\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
8112.2.a.bm	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}-2q^{11}+\cdots\)
8112.2.a.bn	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
8112.2.a.bo	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+(-2+\beta )q^{7}+q^{9}+\cdots\)
8112.2.a.bp	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(2+\beta )q^{5}+(1+\beta )q^{7}+q^{9}+\cdots\)
8112.2.a.bq	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+(-3+\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
8112.2.a.br	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+(-1-\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
8112.2.a.bs	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+\beta q^{15}+\cdots\)
8112.2.a.bt	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+2\beta q^{7}+q^{9}-2\beta q^{11}+\cdots\)
8112.2.a.bu	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2\beta q^{5}-\beta q^{7}+q^{9}+2\beta q^{11}+\cdots\)
8112.2.a.bv	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{7}+q^{9}-\beta q^{11}+6q^{17}+\cdots\)
8112.2.a.bw	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+(1-\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
8112.2.a.bx	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+(3+\beta )q^{7}+q^{9}+(3+\beta )q^{11}+\cdots\)
8112.2.a.by	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-4\)	\(10\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{1})q^{5}+(3+\beta _{1})q^{7}+\cdots\)
8112.2.a.bz	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.ca	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.cb	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
8112.2.a.cc	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-2\beta _{1}+\beta _{2})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.cd	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-2\beta _{1}+\beta _{2})q^{5}+(3-2\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.ce	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{1}+\beta _{2})q^{5}+(\beta _{1}-2\beta _{2})q^{7}+\cdots\)
8112.2.a.cf	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(4\)	\(-10\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{1})q^{5}+(-3-\beta _{1})q^{7}+\cdots\)
8112.2.a.cg	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-6\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+\beta _{1}+\beta _{2})q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
8112.2.a.ch	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(-6\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.ci	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{2})q^{5}+(1-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
8112.2.a.cj	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(9\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-3\beta _{1}+\beta _{2})q^{5}+(4-\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.ck	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	3.3.837.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-3\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{2}q^{5}+(-1+\beta _{1})q^{7}+q^{9}+\cdots\)
8112.2.a.cl	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	3.3.837.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(3\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{2}q^{5}+(1-\beta _{1})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
8112.2.a.cm	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(1\)	\(-9\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-\beta _{1}-2\beta _{2})q^{5}+(-2-2\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.cn	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{1}+2\beta _{2})q^{7}+\cdots\)
8112.2.a.co	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(2\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}+(3-\beta _{1}+2\beta _{2})q^{7}+\cdots\)
8112.2.a.cp	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(6\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(2-\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
8112.2.a.cq	$8112$	$2$	8112.a	1.a	$1$	$4$	$4$	$64.775$	4.4.25488.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(-4\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.cr	$8112$	$2$	8112.a	1.a	$1$	$4$	$4$	$64.775$	\(\Q(\sqrt{3}, \sqrt{43})\)	None	✓	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
8112.2.a.cs	$8112$	$2$	8112.a	1.a	$1$	$4$	$4$	$64.775$	4.4.25488.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(4\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.ct	$8112$	$2$	8112.a	1.a	$1$	$6$	$6$	$64.775$	6.6.27700337.1	None	✓	$1$	$1$	\(0\)	\(-6\)	\(-1\)	\(-5\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
8112.2.a.cu	$8112$	$2$	8112.a	1.a	$1$	$6$	$6$	$64.775$	6.6.27700337.1	None	✓	$1$	$0$	\(0\)	\(-6\)	\(1\)	\(5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(1-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
8112.2.a.cv	$8112$	$2$	8112.a	1.a	$1$	$6$	$6$	$64.775$	6.6.27700337.1	None	✓	$1$	$0$	\(0\)	\(6\)	\(-1\)	\(7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{5}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
8112.2.a.cw	$8112$	$2$	8112.a	1.a	$1$	$6$	$6$	$64.775$	6.6.27700337.1	None	✓	$1$	$1$	\(0\)	\(6\)	\(1\)	\(-7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{5}q^{5}+(-1-\beta _{1})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8112))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8112)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(676))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1014))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2028))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4056))\)\(^{\oplus 2}\)