Space of modular forms of level 8700, weight 2, and trivial character

• Label: 8700.2.a
• Level: $8700$
• Weight: $2$
• Character orbit: 8700.a
• Rep. character: $\chi_{8700}(1,\cdot)$
• Character field: $\Q$
• Dimension: $88$
• Newform subspaces: $38$
• Sturm bound: $3600$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 8700 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8700.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 38 \)
Sturm bound:			\(3600\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8700))\).

	Total	New	Old
Modular forms	1836	88	1748
Cusp forms	1765	88	1677
Eisenstein series	71	0	71

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

\(2\)	\(3\)	\(5\)	\(29\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(102\)	\(0\)	\(102\)		\(97\)	\(0\)	\(97\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(129\)	\(0\)	\(129\)		\(123\)	\(0\)	\(123\)		\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(126\)	\(0\)	\(126\)		\(120\)	\(0\)	\(120\)		\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(105\)	\(0\)	\(105\)		\(99\)	\(0\)	\(99\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(120\)	\(0\)	\(120\)		\(114\)	\(0\)	\(114\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(111\)	\(0\)	\(111\)		\(105\)	\(0\)	\(105\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(108\)	\(0\)	\(108\)		\(102\)	\(0\)	\(102\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(123\)	\(0\)	\(123\)		\(117\)	\(0\)	\(117\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(114\)	\(10\)	\(104\)		\(111\)	\(10\)	\(101\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(114\)	\(10\)	\(104\)		\(111\)	\(10\)	\(101\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(117\)	\(12\)	\(105\)		\(114\)	\(12\)	\(102\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(111\)	\(12\)	\(99\)		\(108\)	\(12\)	\(96\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(123\)	\(11\)	\(112\)		\(120\)	\(11\)	\(109\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(105\)	\(11\)	\(94\)		\(102\)	\(11\)	\(91\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(108\)	\(11\)	\(97\)		\(105\)	\(11\)	\(94\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(120\)	\(11\)	\(109\)		\(117\)	\(11\)	\(106\)		\(3\)	\(0\)	\(3\)
Plus space				\(+\)		\(900\)	\(44\)	\(856\)		\(865\)	\(44\)	\(821\)		\(35\)	\(0\)	\(35\)
Minus space				\(-\)		\(936\)	\(44\)	\(892\)		\(900\)	\(44\)	\(856\)		\(36\)	\(0\)	\(36\)

Trace form

88 * q + 4 * q^7 + 88 * q^9 - 8 * q^11 - 4 * q^13 - 20 * q^19 - 12 * q^21 - 12 * q^23 - 12 * q^31 - 8 * q^37 - 12 * q^39 - 8 * q^41 - 8 * q^47 + 80 * q^49 + 8 * q^51 + 12 * q^53 - 12 * q^57 + 24 * q^59 - 4 * q^61 + 4 * q^63 - 4 * q^67 - 12 * q^71 + 16 * q^73 - 8 * q^77 + 8 * q^79 + 88 * q^81 - 24 * q^91 - 20 * q^93 - 32 * q^97 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8700))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	29
8700.2.a.a	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓	✓			8700.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-3\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{7}+q^{9}-6q^{11}-q^{13}+\cdots\)
8700.2.a.b	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				1740.2.a.h	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
8700.2.a.c	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				348.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}+q^{11}+3q^{13}+3q^{17}+\cdots\)
8700.2.a.d	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				1740.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}-3q^{11}+q^{13}-3q^{17}+\cdots\)
8700.2.a.e	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓	✓			8700.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}-2q^{11}-5q^{13}+\cdots\)
8700.2.a.f	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				1740.2.g.a	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
8700.2.a.g	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				1740.2.g.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}+5q^{11}-4q^{17}+\cdots\)
8700.2.a.h	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				1740.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(3\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
8700.2.a.i	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				348.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(3\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{7}+q^{9}-q^{11}+3q^{13}+\cdots\)
8700.2.a.j	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				1740.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(5\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+5q^{7}+q^{9}+5q^{11}+5q^{13}+\cdots\)
8700.2.a.k	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				1740.2.a.d	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{7}+q^{9}+3q^{11}-3q^{13}+\cdots\)
8700.2.a.l	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				1740.2.a.c	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
8700.2.a.m	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				1740.2.g.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
8700.2.a.n	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				1740.2.g.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}+5q^{11}+4q^{17}+\cdots\)
8700.2.a.o	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓	✓			8700.2.a.e	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}-2q^{11}+5q^{13}+\cdots\)
8700.2.a.p	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				348.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}+3q^{11}-5q^{13}+\cdots\)
8700.2.a.q	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				1740.2.a.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-6q^{11}-6q^{13}-4q^{17}+\cdots\)
8700.2.a.r	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				1740.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots\)
8700.2.a.s	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓	✓			8700.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{7}+q^{9}-6q^{11}+q^{13}+\cdots\)
8700.2.a.t	$8700$	$2$	8700.a	1.a	$1$	$1$	$1$	$69.470$	\(\Q\)	None	✓				348.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{7}+q^{9}-3q^{11}+3q^{13}+\cdots\)
8700.2.a.u	$8700$	$2$	8700.a	1.a	$1$	$2$	$2$	$69.470$	\(\Q(\sqrt{57}) \)	None	✓				1740.2.a.n	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots\)
8700.2.a.v	$8700$	$2$	8700.a	1.a	$1$	$2$	$2$	$69.470$	\(\Q(\sqrt{17}) \)	None	✓				1740.2.a.m	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
8700.2.a.w	$8700$	$2$	8700.a	1.a	$1$	$2$	$2$	$69.470$	\(\Q(\sqrt{33}) \)	None	✓				1740.2.a.l	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{7}+q^{9}+(2-\beta )q^{11}+(2+\cdots)q^{13}+\cdots\)
8700.2.a.x	$8700$	$2$	8700.a	1.a	$1$	$2$	$2$	$69.470$	\(\Q(\sqrt{17}) \)	None	✓				1740.2.a.j	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{7}+q^{9}+(-1+2\beta )q^{11}+\cdots\)
8700.2.a.y	$8700$	$2$	8700.a	1.a	$1$	$2$	$2$	$69.470$	\(\Q(\sqrt{33}) \)	None	✓				1740.2.a.i	$1$	$0$	\(0\)	\(2\)	\(0\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{7}+q^{9}+(2+\beta )q^{11}+(2+\cdots)q^{13}+\cdots\)
8700.2.a.z	$8700$	$2$	8700.a	1.a	$1$	$2$	$2$	$69.470$	\(\Q(\sqrt{17}) \)	None	✓				1740.2.a.k	$1$	$1$	\(0\)	\(2\)	\(0\)	\(5\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(3-\beta )q^{7}+q^{9}+(-1+\beta )q^{11}+\cdots\)
8700.2.a.ba	$8700$	$2$	8700.a	1.a	$1$	$3$	$3$	$69.470$	3.3.321.1	None	✓	✓	✓		8700.2.a.ba	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+2\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
8700.2.a.bb	$8700$	$2$	8700.a	1.a	$1$	$3$	$3$	$69.470$	3.3.257.1	None	✓	✓	✓		8700.2.a.bb	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{7}+q^{9}-\beta _{2}q^{11}+\cdots\)
8700.2.a.bc	$8700$	$2$	8700.a	1.a	$1$	$3$	$3$	$69.470$	3.3.257.1	None	✓	✓			8700.2.a.bb	$1$	$1$	\(0\)	\(3\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{1})q^{7}+q^{9}-\beta _{2}q^{11}+\cdots\)
8700.2.a.bd	$8700$	$2$	8700.a	1.a	$1$	$3$	$3$	$69.470$	3.3.321.1	None	✓	✓			8700.2.a.ba	$1$	$0$	\(0\)	\(3\)	\(0\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-2\beta _{1}-\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
8700.2.a.be	$8700$	$2$	8700.a	1.a	$1$	$5$	$5$	$69.470$	5.5.8524696.1	None	✓	✓			8700.2.a.be	$1$	$1$	\(0\)	\(-5\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{4}q^{7}+q^{9}+(-2+\beta _{3})q^{11}+\cdots\)
8700.2.a.bf	$8700$	$2$	8700.a	1.a	$1$	$5$	$5$	$69.470$	5.5.40563468.1	None	✓	✓			8700.2.a.bf	$1$	$0$	\(0\)	\(-5\)	\(0\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{7}+q^{9}-\beta _{2}q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots\)
8700.2.a.bg	$8700$	$2$	8700.a	1.a	$1$	$5$	$5$	$69.470$	5.5.8524696.1	None	✓	✓	✓		8700.2.a.be	$1$	$1$	\(0\)	\(5\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{4}q^{7}+q^{9}+(-2+\beta _{3})q^{11}+\cdots\)
8700.2.a.bh	$8700$	$2$	8700.a	1.a	$1$	$5$	$5$	$69.470$	5.5.40563468.1	None	✓	✓	✓		8700.2.a.bf	$1$	$0$	\(0\)	\(5\)	\(0\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{7}+q^{9}-\beta _{2}q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots\)
8700.2.a.bi	$8700$	$2$	8700.a	1.a	$1$	$6$	$6$	$69.470$	6.6.41017664.1	None	✓		✓		1740.2.g.c	$1$	$1$	\(0\)	\(-6\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{3}q^{7}+q^{9}+(-\beta _{3}-\beta _{4})q^{11}+\cdots\)
8700.2.a.bj	$8700$	$2$	8700.a	1.a	$1$	$6$	$6$	$69.470$	6.6.71480896.1	None	✓		✓		1740.2.g.d	$1$	$0$	\(0\)	\(-6\)	\(0\)	\(6\)		$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{2})q^{7}+q^{9}+(\beta _{4}+\beta _{5})q^{11}+\cdots\)
8700.2.a.bk	$8700$	$2$	8700.a	1.a	$1$	$6$	$6$	$69.470$	6.6.71480896.1	None	✓		✓		1740.2.g.d	$1$	$1$	\(0\)	\(6\)	\(0\)	\(-6\)		$-$	$-$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{2})q^{7}+q^{9}+(\beta _{4}+\beta _{5})q^{11}+\cdots\)
8700.2.a.bl	$8700$	$2$	8700.a	1.a	$1$	$6$	$6$	$69.470$	6.6.41017664.1	None	✓		✓		1740.2.g.c	$1$	$0$	\(0\)	\(6\)	\(0\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{3}q^{7}+q^{9}+(-\beta _{3}-\beta _{4})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8700))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8700)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(174))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(290))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(348))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(435))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(580))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(725))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(870))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1450))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1740))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2175))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2900))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4350))\)\(^{\oplus 2}\)