Space of modular forms of level 8384, weight 2, and trivial character

• Label: 8384.2.a
• Level: $8384$
• Weight: $2$
• Character orbit: 8384.a
• Rep. character: $\chi_{8384}(1,\cdot)$
• Character field: $\Q$
• Dimension: $260$
• Newform subspaces: $56$
• Sturm bound: $2112$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 8384 = 2^{6} \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8384.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 56 \)
Sturm bound:			\(2112\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8384))\).

	Total	New	Old
Modular forms	1068	260	808
Cusp forms	1045	260	785
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.

\(2\)	\(131\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(58\)
\(+\)	\(-\)	$-$	\(73\)
\(-\)	\(+\)	$-$	\(72\)
\(-\)	\(-\)	$+$	\(57\)
Plus space		\(+\)	\(115\)
Minus space		\(-\)	\(145\)

Trace form

\( 260 q + 260 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8384))\) 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	131
8384.2.a.a	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-2\)	\(-2\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}-q^{7}+q^{9}-6q^{11}+\cdots\)
8384.2.a.b	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
8384.2.a.c	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}+3q^{7}+q^{9}-6q^{11}+\cdots\)
8384.2.a.d	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-3q^{7}-2q^{9}-q^{13}+\cdots\)
8384.2.a.e	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}-2q^{9}+3q^{13}+\cdots\)
8384.2.a.f	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}-2q^{9}+4q^{11}+\cdots\)
8384.2.a.g	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-3q^{7}-3q^{9}-6q^{11}+6q^{13}+\cdots\)
8384.2.a.h	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+3q^{7}-3q^{9}+6q^{11}+6q^{13}+\cdots\)
8384.2.a.i	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(0\)	\(0\)	\(-5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{7}-3q^{9}-2q^{11}+2q^{13}-6q^{17}+\cdots\)
8384.2.a.j	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{7}-3q^{9}+2q^{11}+2q^{13}-6q^{17}+\cdots\)
8384.2.a.k	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(2\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}-2q^{9}-4q^{11}+\cdots\)
8384.2.a.l	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}-2q^{9}+3q^{13}+\cdots\)
8384.2.a.m	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(2\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+3q^{7}-2q^{9}-q^{13}+\cdots\)
8384.2.a.n	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+q^{7}+q^{9}+6q^{11}+\cdots\)
8384.2.a.o	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}-3q^{7}+q^{9}+6q^{11}+\cdots\)
8384.2.a.p	$8384$	$2$	8384.a	1.a	$1$	$1$	$1$	$66.947$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}+q^{7}+q^{9}-2q^{11}+\cdots\)
8384.2.a.q	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}-\beta q^{5}+\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
8384.2.a.r	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(1\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+\beta q^{5}-\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
8384.2.a.s	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(2-\beta )q^{5}+(2+\beta )q^{7}+\cdots\)
8384.2.a.t	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(5\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(2+\beta )q^{5}+(2-\beta )q^{7}+\cdots\)
8384.2.a.u	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+(-1-\beta )q^{5}+(-2+\cdots)q^{7}+\cdots\)
8384.2.a.v	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1+\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
8384.2.a.w	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(5\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(3-\beta )q^{5}+(-1-\beta )q^{7}+\beta q^{9}+\cdots\)
8384.2.a.x	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-2+\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
8384.2.a.y	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-2-\beta )q^{5}+(1-\beta )q^{7}-q^{9}+\cdots\)
8384.2.a.z	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1+\beta )q^{5}+(1+\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
8384.2.a.ba	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(5\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(3-\beta )q^{5}+(1+\beta )q^{7}+\beta q^{9}+\cdots\)
8384.2.a.bb	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-1+\beta )q^{5}+(2+\beta )q^{7}+\cdots\)
8384.2.a.bc	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-\beta q^{5}-\beta q^{7}+(-1+3\beta )q^{9}+\cdots\)
8384.2.a.bd	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(3\)	\(1\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+\beta q^{5}+\beta q^{7}+(-1+3\beta )q^{9}+\cdots\)
8384.2.a.be	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(3\)	\(3\)	\(-5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(2-\beta )q^{5}+(-2-\beta )q^{7}+\cdots\)
8384.2.a.bf	$8384$	$2$	8384.a	1.a	$1$	$2$	$2$	$66.947$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(3\)	\(5\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(2+\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
8384.2.a.bg	$8384$	$2$	8384.a	1.a	$1$	$3$	$3$	$66.947$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-7\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
8384.2.a.bh	$8384$	$2$	8384.a	1.a	$1$	$3$	$3$	$66.947$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(7\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
8384.2.a.bi	$8384$	$2$	8384.a	1.a	$1$	$4$	$4$	$66.947$	4.4.3981.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-2\)	\(7\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{3}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)
8384.2.a.bj	$8384$	$2$	8384.a	1.a	$1$	$4$	$4$	$66.947$	4.4.123336.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1-\beta _{1})q^{5}-\beta _{3}q^{7}+(3+\beta _{3})q^{9}+\cdots\)
8384.2.a.bk	$8384$	$2$	8384.a	1.a	$1$	$4$	$4$	$66.947$	4.4.123336.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{1})q^{5}+\beta _{3}q^{7}+(3+\beta _{3})q^{9}+\cdots\)
8384.2.a.bl	$8384$	$2$	8384.a	1.a	$1$	$4$	$4$	$66.947$	4.4.3981.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-2\)	\(-7\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{3})q^{3}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)
8384.2.a.bm	$8384$	$2$	8384.a	1.a	$1$	$5$	$5$	$66.947$	5.5.592456.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(1+\beta _{4})q^{7}+\cdots\)
8384.2.a.bn	$8384$	$2$	8384.a	1.a	$1$	$5$	$5$	$66.947$	5.5.703228.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+(-\beta _{2}-\beta _{4})q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots\)
8384.2.a.bo	$8384$	$2$	8384.a	1.a	$1$	$5$	$5$	$66.947$	5.5.703228.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+(-\beta _{2}-\beta _{4})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
8384.2.a.bp	$8384$	$2$	8384.a	1.a	$1$	$5$	$5$	$66.947$	5.5.592456.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(-1-\beta _{4})q^{7}+\cdots\)
8384.2.a.bq	$8384$	$2$	8384.a	1.a	$1$	$8$	$8$	$66.947$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{3}+(-1+\beta _{4})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
8384.2.a.br	$8384$	$2$	8384.a	1.a	$1$	$8$	$8$	$66.947$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{5}q^{3}+(-1+\beta _{4})q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
8384.2.a.bs	$8384$	$2$	8384.a	1.a	$1$	$10$	$10$	$66.947$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-2\)	\(11\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{9}q^{5}+(1+\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots\)
8384.2.a.bt	$8384$	$2$	8384.a	1.a	$1$	$10$	$10$	$66.947$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(1\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots\)
8384.2.a.bu	$8384$	$2$	8384.a	1.a	$1$	$10$	$10$	$66.947$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(-1\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)
8384.2.a.bv	$8384$	$2$	8384.a	1.a	$1$	$10$	$10$	$66.947$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(-11\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{9}q^{5}+(-1-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
8384.2.a.bw	$8384$	$2$	8384.a	1.a	$1$	$11$	$11$	$66.947$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-5\)	\(6\)	\(10\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1-\beta _{9})q^{5}+(1-\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
8384.2.a.bx	$8384$	$2$	8384.a	1.a	$1$	$11$	$11$	$66.947$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(5\)	\(6\)	\(-10\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{9})q^{5}+(-1+\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
8384.2.a.by	$8384$	$2$	8384.a	1.a	$1$	$15$	$15$	$66.947$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-7\)	\(3\)	\(7\)		$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{10}q^{5}+(1+\beta _{7}-\beta _{10}+\cdots)q^{7}+\cdots\)
8384.2.a.bz	$8384$	$2$	8384.a	1.a	$1$	$15$	$15$	$66.947$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(9\)	\(-5\)		$+$	$+$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1-\beta _{3})q^{5}-\beta _{7}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
8384.2.a.ca	$8384$	$2$	8384.a	1.a	$1$	$15$	$15$	$66.947$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(9\)	\(5\)		$+$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{3})q^{5}+\beta _{7}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
8384.2.a.cb	$8384$	$2$	8384.a	1.a	$1$	$15$	$15$	$66.947$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(7\)	\(3\)	\(-7\)		$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{10}q^{5}+(-1-\beta _{7}+\beta _{10}+\cdots)q^{7}+\cdots\)
8384.2.a.cc	$8384$	$2$	8384.a	1.a	$1$	$16$	$16$	$66.947$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-6\)	\(-12\)	\(0\)		$+$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{8})q^{5}-\beta _{11}q^{7}+\cdots\)
8384.2.a.cd	$8384$	$2$	8384.a	1.a	$1$	$16$	$16$	$66.947$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(6\)	\(-12\)	\(0\)		$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{8})q^{5}+\beta _{11}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8384))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8384)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(131))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(262))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(524))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1048))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2096))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4192))\)\(^{\oplus 2}\)