Space of modular forms of level 4032, weight 2, and trivial character

• Label: 4032.2.a
• Level: $4032$
• Weight: $2$
• Character orbit: 4032.a
• Rep. character: $\chi_{4032}(1,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $50$
• Sturm bound: $1536$
• Trace bound: $13$

Defining parameters

Level:	$N$	$=$	$4032 = 2^{6} \cdot 3^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	4032.a (trivial)
Character field:			$\Q$
Newform subspaces:			$50$
Sturm bound:			$1536$
Trace bound:			$13$
Distinguishing $T_p$:			$5$, $11$, $13$, $17$, $19$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(4032))$.

	Total	New	Old
Modular forms	816	60	756
Cusp forms	721	60	661
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.

$2$	$3$	$7$	Fricke	Dim
$+$	$+$	$+$	$+$	$6$
$+$	$+$	$-$	$-$	$8$
$+$	$-$	$+$	$-$	$9$
$+$	$-$	$-$	$+$	$8$
$-$	$+$	$+$	$-$	$6$
$-$	$+$	$-$	$+$	$4$
$-$	$-$	$+$	$+$	$9$
$-$	$-$	$-$	$-$	$10$
Plus space			$+$	$27$
Minus space			$-$	$33$

Trace form

$60 q - 8 q^{17} + 52 q^{25} - 8 q^{29} - 8 q^{37} + 8 q^{41} + 60 q^{49} - 56 q^{53} + 32 q^{61} + 8 q^{73} - 8 q^{77} + 32 q^{85} + 8 q^{89} - 8 q^{97}+O(q^{100})$

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(4032))$ 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	7
4032.2.a.a	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				56.2.a.b	$1$	$1$	$0$	$0$	$-4$	$-1$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-q^{7}+2q^{17}-2q^{19}+8q^{23}+\cdots$
4032.2.a.b	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				672.2.a.a	$1$	$0$	$0$	$0$	$-4$	$-1$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-q^{7}+2q^{11}+2q^{13}-4q^{19}+\cdots$
4032.2.a.c	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				672.2.a.a	$1$	$1$	$0$	$0$	$-4$	$1$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+q^{7}-2q^{11}+2q^{13}+4q^{19}+\cdots$
4032.2.a.d	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				56.2.a.b	$1$	$1$	$0$	$0$	$-4$	$1$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+q^{7}+2q^{17}+2q^{19}-8q^{23}+\cdots$
4032.2.a.e	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				42.2.a.a	$1$	$0$	$0$	$0$	$-2$	$-1$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-4q^{11}-6q^{13}-2q^{17}+\cdots$
4032.2.a.f	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				672.2.a.b	$1$	$1$	$0$	$0$	$-2$	$-1$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-4q^{11}+6q^{13}+2q^{17}+\cdots$
4032.2.a.g	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				504.2.a.a	$1$	$1$	$0$	$0$	$-2$	$-1$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-2q^{11}-2q^{13}+6q^{17}+\cdots$
4032.2.a.h	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				21.2.a.a	$1$	$0$	$0$	$0$	$-2$	$-1$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots$
4032.2.a.i	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				504.2.a.d	$1$	$0$	$0$	$0$	$-2$	$-1$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}+6q^{11}+6q^{13}-2q^{17}+\cdots$
4032.2.a.j	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				504.2.a.d	$1$	$0$	$0$	$0$	$-2$	$1$		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-6q^{11}+6q^{13}-2q^{17}+\cdots$
4032.2.a.k	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				21.2.a.a	$1$	$0$	$0$	$0$	$-2$	$1$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-4q^{11}+2q^{13}+6q^{17}+\cdots$
4032.2.a.l	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				504.2.a.a	$1$	$1$	$0$	$0$	$-2$	$1$		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}+2q^{11}-2q^{13}+6q^{17}+\cdots$
4032.2.a.m	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				42.2.a.a	$1$	$0$	$0$	$0$	$-2$	$1$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots$
4032.2.a.n	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				672.2.a.b	$1$	$0$	$0$	$0$	$-2$	$1$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}+4q^{11}+6q^{13}+2q^{17}+\cdots$
4032.2.a.o	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				2016.2.a.c	$1$	$0$	$0$	$0$	$0$	$-1$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-4q^{11}-2q^{13}-4q^{17}+4q^{23}+\cdots$
4032.2.a.p	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				224.2.a.a	$1$	$1$	$0$	$0$	$0$	$-1$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-4q^{11}+4q^{13}+2q^{17}+6q^{19}+\cdots$
4032.2.a.q	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				672.2.a.c	$1$	$0$	$0$	$0$	$0$	$-1$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-2q^{11}+2q^{13}-4q^{17}+4q^{19}+\cdots$
4032.2.a.r	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				14.2.a.a	$1$	$1$	$0$	$0$	$0$	$-1$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+4q^{13}-6q^{17}+2q^{19}-5q^{25}+\cdots$
4032.2.a.s	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				2016.2.a.c	$1$	$0$	$0$	$0$	$0$	$-1$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+4q^{11}-2q^{13}+4q^{17}-4q^{23}+\cdots$
4032.2.a.t	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				84.2.a.b	$1$	$1$	$0$	$0$	$0$	$-1$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+6q^{11}-2q^{13}-4q^{19}-6q^{23}+\cdots$
4032.2.a.u	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				84.2.a.b	$1$	$1$	$0$	$0$	$0$	$1$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-6q^{11}-2q^{13}+4q^{19}+6q^{23}+\cdots$
4032.2.a.v	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				2016.2.a.c	$1$	$1$	$0$	$0$	$0$	$1$		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-4q^{11}-2q^{13}+4q^{17}+4q^{23}+\cdots$
4032.2.a.w	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				14.2.a.a	$1$	$1$	$0$	$0$	$0$	$1$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+4q^{13}-6q^{17}-2q^{19}-5q^{25}+\cdots$
4032.2.a.x	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				672.2.a.c	$1$	$1$	$0$	$0$	$0$	$1$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+2q^{11}+2q^{13}-4q^{17}-4q^{19}+\cdots$
4032.2.a.y	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				2016.2.a.c	$1$	$1$	$0$	$0$	$0$	$1$		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+4q^{11}-2q^{13}-4q^{17}-4q^{23}+\cdots$
4032.2.a.z	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				224.2.a.a	$1$	$0$	$0$	$0$	$0$	$1$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+4q^{11}+4q^{13}+2q^{17}-6q^{19}+\cdots$
4032.2.a.ba	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				504.2.a.d	$1$	$0$	$0$	$0$	$2$	$-1$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}-6q^{11}+6q^{13}+2q^{17}+\cdots$
4032.2.a.bb	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				56.2.a.a	$1$	$0$	$0$	$0$	$2$	$-1$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots$
4032.2.a.bc	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				168.2.a.a	$1$	$1$	$0$	$0$	$2$	$-1$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}-6q^{13}+2q^{17}+4q^{19}+\cdots$
4032.2.a.bd	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				672.2.a.d	$1$	$1$	$0$	$0$	$2$	$-1$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}-2q^{13}-2q^{17}-4q^{19}+\cdots$
4032.2.a.be	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				168.2.a.b	$1$	$0$	$0$	$0$	$2$	$-1$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}+2q^{13}-6q^{17}+4q^{19}+\cdots$
4032.2.a.bf	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				504.2.a.a	$1$	$1$	$0$	$0$	$2$	$-1$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}+2q^{11}-2q^{13}-6q^{17}+\cdots$
4032.2.a.bg	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				504.2.a.a	$1$	$1$	$0$	$0$	$2$	$1$		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-2q^{11}-2q^{13}-6q^{17}+\cdots$
4032.2.a.bh	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				168.2.a.a	$1$	$1$	$0$	$0$	$2$	$1$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-6q^{13}+2q^{17}-4q^{19}+\cdots$
4032.2.a.bi	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				672.2.a.d	$1$	$0$	$0$	$0$	$2$	$1$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-2q^{13}-2q^{17}+4q^{19}+\cdots$
4032.2.a.bj	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				168.2.a.b	$1$	$0$	$0$	$0$	$2$	$1$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}+2q^{13}-6q^{17}-4q^{19}+\cdots$
4032.2.a.bk	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				56.2.a.a	$1$	$0$	$0$	$0$	$2$	$1$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots$
4032.2.a.bl	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				504.2.a.d	$1$	$0$	$0$	$0$	$2$	$1$		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}+6q^{11}+6q^{13}+2q^{17}+\cdots$
4032.2.a.bm	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				84.2.a.a	$1$	$0$	$0$	$0$	$4$	$-1$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-q^{7}+2q^{11}+6q^{13}+4q^{17}+\cdots$
4032.2.a.bn	$4032$	$2$	4032.a	1.a	$1$	$1$	$1$	$32.196$	$\Q$	None	✓				84.2.a.a	$1$	$0$	$0$	$0$	$4$	$1$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+q^{7}-2q^{11}+6q^{13}+4q^{17}+\cdots$
4032.2.a.bo	$4032$	$2$	4032.a	1.a	$1$	$2$	$2$	$32.196$	$\Q(\sqrt{5})$	None	✓				2016.2.a.p	$1$	$1$	$0$	$0$	$-2$	$-2$		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}-q^{7}+(1+\beta )q^{11}-2\beta q^{13}+\cdots$
4032.2.a.bp	$4032$	$2$	4032.a	1.a	$1$	$2$	$2$	$32.196$	$\Q(\sqrt{5})$	None	✓				2016.2.a.p	$1$	$0$	$0$	$0$	$-2$	$2$		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+q^{7}+(-1-\beta )q^{11}+\cdots$
4032.2.a.bq	$4032$	$2$	4032.a	1.a	$1$	$2$	$2$	$32.196$	$\Q(\sqrt{3})$	None	✓		✓		63.2.a.b	$2$	$0$	$0$	$0$	$0$	$-2$		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}-q^{7}+\beta q^{11}-2q^{13}+\beta q^{17}+\cdots$
4032.2.a.br	$4032$	$2$	4032.a	1.a	$1$	$2$	$2$	$32.196$	$\Q(\sqrt{3})$	None	✓		✓		672.2.a.i	$1$	$1$	$0$	$0$	$0$	$-2$		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}-q^{7}+(2-\beta )q^{11}-2q^{13}+\cdots$
4032.2.a.bs	$4032$	$2$	4032.a	1.a	$1$	$2$	$2$	$32.196$	$\Q(\sqrt{3})$	None	✓		✓		672.2.a.i	$1$	$0$	$0$	$0$	$0$	$2$		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}+q^{7}+(-2+\beta )q^{11}-2q^{13}+\cdots$
4032.2.a.bt	$4032$	$2$	4032.a	1.a	$1$	$2$	$2$	$32.196$	$\Q(\sqrt{3})$	None	✓				63.2.a.b	$2$	$0$	$0$	$0$	$0$	$2$		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}+q^{7}-\beta q^{11}-2q^{13}+\beta q^{17}+\cdots$
4032.2.a.bu	$4032$	$2$	4032.a	1.a	$1$	$2$	$2$	$32.196$	$\Q(\sqrt{5})$	None	✓				2016.2.a.p	$1$	$1$	$0$	$0$	$2$	$-2$		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-q^{7}+(-1-\beta )q^{11}-2\beta q^{13}+\cdots$
4032.2.a.bv	$4032$	$2$	4032.a	1.a	$1$	$2$	$2$	$32.196$	$\Q(\sqrt{5})$	None	✓		✓		224.2.a.c	$1$	$0$	$0$	$0$	$2$	$-2$		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-q^{7}+(2+2\beta )q^{11}+(-3+\cdots)q^{13}+\cdots$
4032.2.a.bw	$4032$	$2$	4032.a	1.a	$1$	$2$	$2$	$32.196$	$\Q(\sqrt{5})$	None	✓		✓		224.2.a.c	$1$	$1$	$0$	$0$	$2$	$2$		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+q^{7}+(-2-2\beta )q^{11}+\cdots$
4032.2.a.bx	$4032$	$2$	4032.a	1.a	$1$	$2$	$2$	$32.196$	$\Q(\sqrt{5})$	None	✓				2016.2.a.p	$1$	$0$	$0$	$0$	$2$	$2$		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+q^{7}+(1+\beta )q^{11}-2\beta q^{13}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(4032))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_0(4032)) \simeq$ $S_{2}^{\mathrm{new}}(\Gamma_0(14))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(21))$$^{\oplus 14}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(24))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(32))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(36))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(42))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(48))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(56))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(63))$$^{\oplus 7}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(64))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(72))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(84))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(96))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(112))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(126))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(144))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(168))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(192))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(224))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(252))$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(288))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(336))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(448))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(504))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(576))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(672))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(1008))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(1344))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(2016))$$^{\oplus 2}$