Space of modular forms of level 3150, weight 2, and trivial character

• Label: 3150.2.a
• Level: $3150$
• Weight: $2$
• Character orbit: 3150.a
• Rep. character: $\chi_{3150}(1,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $46$
• Sturm bound: $1440$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 46 \)
Sturm bound:			\(1440\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3150))\).

	Total	New	Old
Modular forms	768	48	720
Cusp forms	673	48	625
Eisenstein series	95	0	95

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

\(2\)	\(3\)	\(5\)	\(7\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(2\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(3\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(5\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(5\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(2\)
Plus space				\(+\)	\(21\)
Minus space				\(-\)	\(27\)

Trace form

\( 48 q + 2 q^{2} + 48 q^{4} + 2 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3150))\) 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	5	7
3150.2.a.a	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}-6q^{11}+q^{13}+\cdots\)
3150.2.a.b	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}-4q^{11}-3q^{13}+\cdots\)
3150.2.a.c	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{11}+q^{13}+\cdots\)
3150.2.a.d	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{11}+6q^{13}+\cdots\)
3150.2.a.e	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}-4q^{13}+q^{14}+\cdots\)
3150.2.a.f	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{13}+q^{14}+\cdots\)
3150.2.a.g	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{13}+q^{14}+\cdots\)
3150.2.a.h	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{13}+q^{14}+\cdots\)
3150.2.a.i	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}+4q^{13}+q^{14}+\cdots\)
3150.2.a.j	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}+5q^{11}-6q^{13}+\cdots\)
3150.2.a.k	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}+6q^{11}+2q^{13}+\cdots\)
3150.2.a.l	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}-6q^{11}-2q^{13}+\cdots\)
3150.2.a.m	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{11}+2q^{13}+\cdots\)
3150.2.a.n	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}-q^{13}+\cdots\)
3150.2.a.o	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{13}-q^{14}+\cdots\)
3150.2.a.p	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}+4q^{13}-q^{14}+\cdots\)
3150.2.a.q	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}+2q^{11}+2q^{13}+\cdots\)
3150.2.a.r	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}+2q^{11}+7q^{13}+\cdots\)
3150.2.a.s	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}+4q^{11}-6q^{13}+\cdots\)
3150.2.a.t	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}+4q^{11}+2q^{13}+\cdots\)
3150.2.a.u	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}+4q^{11}+3q^{13}+\cdots\)
3150.2.a.v	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-6q^{11}+2q^{13}+\cdots\)
3150.2.a.w	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{11}+2q^{13}+\cdots\)
3150.2.a.x	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}-2q^{13}+\cdots\)
3150.2.a.y	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}+q^{13}+\cdots\)
3150.2.a.z	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{13}-q^{14}+\cdots\)
3150.2.a.ba	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{13}-q^{14}+\cdots\)
3150.2.a.bb	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{13}-q^{14}+\cdots\)
3150.2.a.bc	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots\)
3150.2.a.bd	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{11}-7q^{13}+\cdots\)
3150.2.a.be	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{11}-2q^{13}+\cdots\)
3150.2.a.bf	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}+4q^{11}-3q^{13}+\cdots\)
3150.2.a.bg	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}-6q^{11}-q^{13}+\cdots\)
3150.2.a.bh	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}-4q^{11}-6q^{13}+\cdots\)
3150.2.a.bi	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}-4q^{11}+3q^{13}+\cdots\)
3150.2.a.bj	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}-4q^{11}+6q^{13}+\cdots\)
3150.2.a.bk	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}-2q^{11}-6q^{13}+\cdots\)
3150.2.a.bl	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}-2q^{11}-q^{13}+\cdots\)
3150.2.a.bm	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{13}+q^{14}+\cdots\)
3150.2.a.bn	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{13}+q^{14}+\cdots\)
3150.2.a.bo	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}-6q^{13}+\cdots\)
3150.2.a.bp	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}+2q^{13}+\cdots\)
3150.2.a.bq	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{11}+6q^{13}+\cdots\)
3150.2.a.br	$3150$	$2$	3150.a	1.a	$1$	$1$	$1$	$25.153$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}+6q^{11}-2q^{13}+\cdots\)
3150.2.a.bs	$3150$	$2$	3150.a	1.a	$1$	$2$	$2$	$25.153$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
3150.2.a.bt	$3150$	$2$	3150.a	1.a	$1$	$2$	$2$	$25.153$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3150))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3150)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(525))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1050))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1575))\)\(^{\oplus 2}\)