Space of modular forms of level 9016, weight 2, and trivial character

• Label: 9016.2.a
• Level: $9016$
• Weight: $2$
• Character orbit: 9016.a
• Rep. character: $\chi_{9016}(1,\cdot)$
• Character field: $\Q$
• Dimension: $226$
• Newform subspaces: $47$
• Sturm bound: $2688$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 9016 = 2^{3} \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9016.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 47 \)
Sturm bound:			\(2688\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9016))\).

	Total	New	Old
Modular forms	1376	226	1150
Cusp forms	1313	226	1087
Eisenstein series	63	0	63

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

\(2\)	\(7\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(27\)
\(+\)	\(+\)	\(-\)	$-$	\(31\)
\(+\)	\(-\)	\(+\)	$-$	\(29\)
\(+\)	\(-\)	\(-\)	$+$	\(26\)
\(-\)	\(+\)	\(+\)	$-$	\(29\)
\(-\)	\(+\)	\(-\)	$+$	\(25\)
\(-\)	\(-\)	\(+\)	$+$	\(28\)
\(-\)	\(-\)	\(-\)	$-$	\(31\)
Plus space			\(+\)	\(106\)
Minus space			\(-\)	\(120\)

Trace form

\( 226 q + 4 q^{3} - 2 q^{5} + 222 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9016))\) 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	23
9016.2.a.a	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-2q^{5}+6q^{9}+2q^{11}+q^{13}+\cdots\)
9016.2.a.b	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+6q^{9}+5q^{13}+6q^{17}-6q^{19}+\cdots\)
9016.2.a.c	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-4q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
9016.2.a.d	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
9016.2.a.e	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{9}+4q^{11}-6q^{13}+q^{23}+\cdots\)
9016.2.a.f	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}+q^{9}-4q^{11}-4q^{15}+\cdots\)
9016.2.a.g	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{9}-6q^{11}+3q^{13}+q^{23}+\cdots\)
9016.2.a.h	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-3q^{9}+4q^{13}+4q^{17}+2q^{19}+\cdots\)
9016.2.a.i	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{9}+6q^{11}+2q^{13}-6q^{17}+6q^{19}+\cdots\)
9016.2.a.j	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-2q^{9}-2q^{11}-7q^{13}+\cdots\)
9016.2.a.k	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}-2q^{9}-4q^{11}+5q^{13}+\cdots\)
9016.2.a.l	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+q^{9}-4q^{11}-4q^{15}+\cdots\)
9016.2.a.m	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{9}+6q^{17}-6q^{19}+q^{23}+\cdots\)
9016.2.a.n	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+6q^{9}-6q^{11}-q^{13}+q^{23}+\cdots\)
9016.2.a.o	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+4q^{5}+6q^{9}+2q^{11}-5q^{13}+\cdots\)
9016.2.a.p	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+2\beta q^{5}-q^{9}-4q^{11}+3\beta q^{13}+\cdots\)
9016.2.a.q	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+2\beta q^{5}-q^{9}-4q^{11}+\beta q^{13}+\cdots\)
9016.2.a.r	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{9}+3\beta q^{13}-2\beta q^{17}+2\beta q^{19}+\cdots\)
9016.2.a.s	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+\beta q^{5}-q^{9}+2q^{11}-4\beta q^{13}+\cdots\)
9016.2.a.t	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-\beta q^{5}-q^{9}+6q^{11}-2q^{15}+\cdots\)
9016.2.a.u	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{3}+\beta q^{5}+5q^{9}-4q^{11}-4\beta q^{13}+\cdots\)
9016.2.a.v	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(2-\beta )q^{5}-q^{9}+2q^{11}+2\beta q^{13}+\cdots\)
9016.2.a.w	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2q^{5}+(1+\beta )q^{9}+2\beta q^{11}+\cdots\)
9016.2.a.x	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+2q^{5}+(1+\beta )q^{9}+2\beta q^{11}+\cdots\)
9016.2.a.y	$9016$	$2$	9016.a	1.a	$1$	$3$	$3$	$71.993$	3.3.568.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots\)
9016.2.a.z	$9016$	$2$	9016.a	1.a	$1$	$3$	$3$	$71.993$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-2+2\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
9016.2.a.ba	$9016$	$2$	9016.a	1.a	$1$	$4$	$4$	$71.993$	\(\Q(\zeta_{24})^+\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+2\beta _{3}q^{5}+(-1+\beta _{2})q^{9}+\cdots\)
9016.2.a.bb	$9016$	$2$	9016.a	1.a	$1$	$4$	$4$	$71.993$	4.4.9248.1	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{9}+\cdots\)
9016.2.a.bc	$9016$	$2$	9016.a	1.a	$1$	$4$	$4$	$71.993$	4.4.34196.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{1}q^{5}+(1+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
9016.2.a.bd	$9016$	$2$	9016.a	1.a	$1$	$4$	$4$	$71.993$	4.4.170528.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(2+\beta _{2})q^{9}+2q^{11}+\cdots\)
9016.2.a.be	$9016$	$2$	9016.a	1.a	$1$	$4$	$4$	$71.993$	\(\Q(\sqrt{7}, \sqrt{15})\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(2-\beta _{3})q^{9}-2q^{11}-\beta _{1}q^{13}+\cdots\)
9016.2.a.bf	$9016$	$2$	9016.a	1.a	$1$	$4$	$4$	$71.993$	4.4.8468.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(\beta _{2}-\beta _{3})q^{5}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
9016.2.a.bg	$9016$	$2$	9016.a	1.a	$1$	$5$	$5$	$71.993$	5.5.3385684.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{3}-\beta _{1}q^{5}+(3-\beta _{4})q^{9}+\cdots\)
9016.2.a.bh	$9016$	$2$	9016.a	1.a	$1$	$6$	$6$	$71.993$	6.6.79480832.1	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{1}q^{5}+(1+\beta _{2}-\beta _{3})q^{9}+\cdots\)
9016.2.a.bi	$9016$	$2$	9016.a	1.a	$1$	$6$	$6$	$71.993$	6.6.1229312.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{9}+(2+\beta _{5})q^{11}+\cdots\)
9016.2.a.bj	$9016$	$2$	9016.a	1.a	$1$	$8$	$8$	$71.993$	8.8.\(\cdots\).1	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q-\beta _{6}q^{3}-\beta _{4}q^{5}-\beta _{3}q^{9}+(-1-\beta _{3}+\cdots)q^{11}+\cdots\)
9016.2.a.bk	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{10}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
9016.2.a.bl	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
9016.2.a.bm	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-7\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(1+\beta _{1}+\beta _{7}+\cdots)q^{9}+\cdots\)
9016.2.a.bn	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(9\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1-\beta _{5})q^{5}+(1+\beta _{4}-\beta _{5}+\cdots)q^{9}+\cdots\)
9016.2.a.bo	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-9\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{5})q^{5}+(1+\beta _{4}-\beta _{5}+\cdots)q^{9}+\cdots\)
9016.2.a.bp	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(7\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{3})q^{5}+(1+\beta _{1}+\beta _{7}+\cdots)q^{9}+\cdots\)
9016.2.a.bq	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(4\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
9016.2.a.br	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(4\)	\(3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{10}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
9016.2.a.bs	$9016$	$2$	9016.a	1.a	$1$	$14$	$14$	$71.993$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{7})q^{5}+(1+\beta _{4}+\cdots)q^{9}+\cdots\)
9016.2.a.bt	$9016$	$2$	9016.a	1.a	$1$	$18$	$18$	$71.993$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{10}q^{5}+(1+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
9016.2.a.bu	$9016$	$2$	9016.a	1.a	$1$	$18$	$18$	$71.993$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2^{8}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{10}q^{5}+(2+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9016))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9016)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(644))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1127))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2254))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4508))\)\(^{\oplus 2}\)