Space of modular forms of level 9464, weight 2, and trivial character

• Label: 9464.2.a
• Level: $9464$
• Weight: $2$
• Character orbit: 9464.a
• Rep. character: $\chi_{9464}(1,\cdot)$
• Character field: $\Q$
• Dimension: $232$
• Newform subspaces: $45$
• Sturm bound: $2912$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 9464 = 2^{3} \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9464.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 45 \)
Sturm bound:			\(2912\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9464))\).

	Total	New	Old
Modular forms	1512	232	1280
Cusp forms	1401	232	1169
Eisenstein series	111	0	111

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

\(2\)	\(7\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(29\)
\(+\)	\(+\)	\(-\)	$-$	\(30\)
\(+\)	\(-\)	\(+\)	$-$	\(34\)
\(+\)	\(-\)	\(-\)	$+$	\(24\)
\(-\)	\(+\)	\(+\)	$-$	\(30\)
\(-\)	\(+\)	\(-\)	$+$	\(27\)
\(-\)	\(-\)	\(+\)	$+$	\(25\)
\(-\)	\(-\)	\(-\)	$-$	\(33\)
Plus space			\(+\)	\(105\)
Minus space			\(-\)	\(127\)

Trace form

\( 232 q + 2 q^{3} + 2 q^{5} + 224 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9464))\) 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	13
9464.2.a.a	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{15}+\cdots\)
9464.2.a.b	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}-2q^{9}-3q^{11}+4q^{17}+\cdots\)
9464.2.a.c	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}-3q^{9}+4q^{11}-6q^{17}+\cdots\)
9464.2.a.d	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-3q^{9}-2q^{11}+7q^{19}+\cdots\)
9464.2.a.e	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-3q^{5}-q^{7}+q^{9}-6q^{15}+\cdots\)
9464.2.a.f	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}-2q^{15}+\cdots\)
9464.2.a.g	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{7}+q^{9}+2q^{11}+2q^{15}+\cdots\)
9464.2.a.h	$9464$	$2$	9464.a	1.a	$1$	$1$	$1$	$75.570$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+4q^{5}-q^{7}+q^{9}+8q^{15}+\cdots\)
9464.2.a.i	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-4\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+\beta q^{5}-q^{7}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
9464.2.a.j	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-4\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-\beta q^{5}+q^{7}+q^{9}+(2-2\beta )q^{11}+\cdots\)
9464.2.a.k	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{3}+(1-\beta )q^{5}-q^{7}+(3+\cdots)q^{9}+\cdots\)
9464.2.a.l	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$2$	\(0\)	\(-2\)	\(-4\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+(-2-\beta )q^{5}-q^{7}+\cdots\)
9464.2.a.m	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-\beta q^{5}-q^{7}+(1-2\beta )q^{9}+\cdots\)
9464.2.a.n	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+\beta q^{5}+q^{7}+(1-2\beta )q^{9}+\cdots\)
9464.2.a.o	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+\beta q^{5}+q^{7}+(1-2\beta )q^{9}+\cdots\)
9464.2.a.p	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+(2+\beta )q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
9464.2.a.q	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-5\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-2-\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots\)
9464.2.a.r	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
9464.2.a.s	$9464$	$2$	9464.a	1.a	$1$	$2$	$2$	$75.570$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(5\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(2+\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots\)
9464.2.a.t	$9464$	$2$	9464.a	1.a	$1$	$3$	$3$	$75.570$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{3}+(-1+\beta _{2})q^{5}+q^{7}+\cdots\)
9464.2.a.u	$9464$	$2$	9464.a	1.a	$1$	$3$	$3$	$75.570$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{3}+(1-\beta _{2})q^{5}-q^{7}+\cdots\)
9464.2.a.v	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.27004.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-1+\beta _{3})q^{5}+q^{7}+\cdots\)
9464.2.a.w	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.27004.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(5\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(1-\beta _{3})q^{5}-q^{7}+\cdots\)
9464.2.a.x	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.122260.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-5\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{1})q^{5}-q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
9464.2.a.y	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.122260.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(5\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1+\beta _{1})q^{5}+q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
9464.2.a.z	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.64268.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)
9464.2.a.ba	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.183064.1	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots\)
9464.2.a.bb	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.21801.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-5\)	\(4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-1-\beta _{1})q^{5}+q^{7}+\cdots\)
9464.2.a.bc	$9464$	$2$	9464.a	1.a	$1$	$4$	$4$	$75.570$	4.4.21801.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(5\)	\(-4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(1+\beta _{1})q^{5}-q^{7}+(2+\cdots)q^{9}+\cdots\)
9464.2.a.bd	$9464$	$2$	9464.a	1.a	$1$	$6$	$6$	$75.570$	6.6.415174304.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{4}-\beta _{5})q^{5}-q^{7}+\cdots\)
9464.2.a.be	$9464$	$2$	9464.a	1.a	$1$	$6$	$6$	$75.570$	6.6.415174304.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{4}+\beta _{5})q^{5}+q^{7}+\cdots\)
9464.2.a.bf	$9464$	$2$	9464.a	1.a	$1$	$6$	$6$	$75.570$	6.6.7674048.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{5})q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots\)
9464.2.a.bg	$9464$	$2$	9464.a	1.a	$1$	$6$	$6$	$75.570$	6.6.7674048.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(4\)	\(6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{5})q^{5}+q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
9464.2.a.bh	$9464$	$2$	9464.a	1.a	$1$	$7$	$7$	$75.570$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(7\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
9464.2.a.bi	$9464$	$2$	9464.a	1.a	$1$	$7$	$7$	$75.570$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-7\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}-q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
9464.2.a.bj	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(12\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{7}q^{5}+q^{7}+(\beta _{5}+\beta _{6})q^{9}+\cdots\)
9464.2.a.bk	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(-12\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{7}q^{5}-q^{7}+(\beta _{5}+\beta _{6})q^{9}+\cdots\)
9464.2.a.bl	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-8\)	\(-12\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{6})q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
9464.2.a.bm	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(8\)	\(12\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{6})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
9464.2.a.bn	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-8\)	\(-12\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}-q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
9464.2.a.bo	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(8\)	\(12\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}+q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
9464.2.a.bp	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(4\)	\(-4\)	\(12\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
9464.2.a.bq	$9464$	$2$	9464.a	1.a	$1$	$12$	$12$	$75.570$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(4\)	\(4\)	\(-12\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
9464.2.a.br	$9464$	$2$	9464.a	1.a	$1$	$15$	$15$	$75.570$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-4\)	\(-15\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{6}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots\)
9464.2.a.bs	$9464$	$2$	9464.a	1.a	$1$	$15$	$15$	$75.570$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(4\)	\(15\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{6}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9464))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9464)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(676))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2366))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4732))\)\(^{\oplus 2}\)