Space of modular forms of level 2850, weight 2, and trivial character

• Label: 2850.2.a
• Level: $2850$
• Weight: $2$
• Character orbit: 2850.a
• Rep. character: $\chi_{2850}(1,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $40$
• Sturm bound: $1200$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2850.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 40 \)
Sturm bound:			\(1200\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2850))\).

	Total	New	Old
Modular forms	624	56	568
Cusp forms	577	56	521
Eisenstein series	47	0	47

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

\(2\)	\(3\)	\(5\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(4\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(2\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(4\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(5\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(5\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(5\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(1\)
Plus space				\(+\)	\(22\)
Minus space				\(-\)	\(34\)

Trace form

56 * q - 2 * q^2 + 56 * q^4 - 2 * q^6 - 8 * q^7 - 2 * q^8 + 56 * q^9 + 4 * q^11 + 4 * q^13 + 56 * q^16 - 2 * q^18 - 2 * q^19 - 4 * q^22 + 4 * q^23 - 2 * q^24 + 28 * q^26 - 8 * q^28 + 12 * q^29 - 12 * q^31 - 2 * q^32 + 4 * q^33 + 20 * q^34 + 56 * q^36 - 20 * q^37 - 8 * q^39 + 4 * q^41 + 24 * q^43 + 4 * q^44 + 4 * q^47 + 24 * q^49 + 4 * q^52 + 12 * q^53 - 2 * q^54 + 2 * q^57 - 8 * q^58 - 16 * q^62 - 8 * q^63 + 56 * q^64 - 12 * q^66 + 32 * q^67 - 8 * q^69 - 2 * q^72 + 24 * q^73 + 36 * q^74 - 2 * q^76 + 8 * q^78 - 44 * q^79 + 56 * q^81 + 8 * q^82 + 60 * q^83 - 24 * q^86 - 12 * q^87 - 4 * q^88 + 28 * q^89 - 32 * q^91 + 4 * q^92 - 8 * q^93 - 8 * q^94 - 2 * q^96 - 24 * q^97 + 14 * q^98 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2850))\) 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	19
2850.2.a.a	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.a.m	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots\)
2850.2.a.b	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.a.j	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
2850.2.a.c	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.a.k	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
2850.2.a.d	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓	✓			2850.2.a.d	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
2850.2.a.e	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.a.l	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
2850.2.a.f	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓	✓			2850.2.a.f	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots\)
2850.2.a.g	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				114.2.a.c	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots\)
2850.2.a.h	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.a.i	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-4q^{7}-q^{8}+\cdots\)
2850.2.a.i	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.d.a	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
2850.2.a.j	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				114.2.a.b	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
2850.2.a.k	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.d.b	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
2850.2.a.l	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓	✓			2850.2.a.l	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
2850.2.a.m	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.a.g	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
2850.2.a.n	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.a.h	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
2850.2.a.o	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓	✓			2850.2.a.o	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
2850.2.a.p	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.a.d	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
2850.2.a.q	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.a.f	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
2850.2.a.r	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓	✓			2850.2.a.o	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
2850.2.a.s	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.d.b	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
2850.2.a.t	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.d.a	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
2850.2.a.u	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓	✓			2850.2.a.l	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
2850.2.a.v	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.a.e	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+4q^{7}+q^{8}+\cdots\)
2850.2.a.w	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓	✓	✓	✓	2850.2.a.f	$1$	$1$	\(1\)	\(1\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)
2850.2.a.x	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				114.2.a.a	$1$	$0$	\(1\)	\(1\)	\(0\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)
2850.2.a.y	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.a.b	$1$	$1$	\(1\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
2850.2.a.z	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓	✓			2850.2.a.d	$1$	$1$	\(1\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
2850.2.a.ba	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.a.c	$1$	$0$	\(1\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
2850.2.a.bb	$2850$	$2$	2850.a	1.a	$1$	$1$	$1$	$22.757$	\(\Q\)	None	✓				570.2.a.a	$1$	$0$	\(1\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
2850.2.a.bc	$2850$	$2$	2850.a	1.a	$1$	$2$	$2$	$22.757$	\(\Q(\sqrt{6}) \)	None	✓	✓	✓	✓	2850.2.a.bc	$1$	$1$	\(-2\)	\(-2\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+(-2+\beta )q^{7}+\cdots\)
2850.2.a.bd	$2850$	$2$	2850.a	1.a	$1$	$2$	$2$	$22.757$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓		2850.2.a.bd	$1$	$1$	\(-2\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+(-1+\beta )q^{7}+\cdots\)
2850.2.a.be	$2850$	$2$	2850.a	1.a	$1$	$2$	$2$	$22.757$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓		2850.2.a.be	$1$	$1$	\(-2\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+(-1+\beta )q^{7}+\cdots\)
2850.2.a.bf	$2850$	$2$	2850.a	1.a	$1$	$2$	$2$	$22.757$	\(\Q(\sqrt{10}) \)	None	✓	✓	✓		2850.2.a.bf	$1$	$1$	\(-2\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+\beta q^{7}-q^{8}+\cdots\)
2850.2.a.bg	$2850$	$2$	2850.a	1.a	$1$	$2$	$2$	$22.757$	\(\Q(\sqrt{10}) \)	None	✓	✓	✓		2850.2.a.bf	$1$	$0$	\(2\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+\beta q^{7}+q^{8}+\cdots\)
2850.2.a.bh	$2850$	$2$	2850.a	1.a	$1$	$2$	$2$	$22.757$	\(\Q(\sqrt{3}) \)	None	✓	✓			2850.2.a.be	$1$	$0$	\(2\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+(1+\beta )q^{7}+\cdots\)
2850.2.a.bi	$2850$	$2$	2850.a	1.a	$1$	$2$	$2$	$22.757$	\(\Q(\sqrt{3}) \)	None	✓	✓			2850.2.a.bd	$1$	$0$	\(2\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+(1+\beta )q^{7}+\cdots\)
2850.2.a.bj	$2850$	$2$	2850.a	1.a	$1$	$2$	$2$	$22.757$	\(\Q(\sqrt{6}) \)	None	✓	✓	✓		2850.2.a.bc	$1$	$0$	\(2\)	\(2\)	\(0\)	\(4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+(2+\beta )q^{7}+\cdots\)
2850.2.a.bk	$2850$	$2$	2850.a	1.a	$1$	$3$	$3$	$22.757$	3.3.148.1	None	✓		✓		570.2.d.d	$1$	$0$	\(-3\)	\(-3\)	\(0\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-\beta _{2}q^{7}-q^{8}+\cdots\)
2850.2.a.bl	$2850$	$2$	2850.a	1.a	$1$	$3$	$3$	$22.757$	3.3.148.1	None	✓		✓		570.2.d.c	$1$	$0$	\(-3\)	\(3\)	\(0\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-\beta _{2}q^{7}-q^{8}+\cdots\)
2850.2.a.bm	$2850$	$2$	2850.a	1.a	$1$	$3$	$3$	$22.757$	3.3.148.1	None	✓		✓		570.2.d.c	$1$	$0$	\(3\)	\(-3\)	\(0\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+\beta _{2}q^{7}+q^{8}+\cdots\)
2850.2.a.bn	$2850$	$2$	2850.a	1.a	$1$	$3$	$3$	$22.757$	3.3.148.1	None	✓		✓		570.2.d.d	$1$	$0$	\(3\)	\(3\)	\(0\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+\beta _{2}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2850))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2850)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(570))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(950))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1425))\)\(^{\oplus 2}\)