Space of modular forms of level 4368, weight 2, and trivial character

• Label: 4368.2.a
• Level: $4368$
• Weight: $2$
• Character orbit: 4368.a
• Rep. character: $\chi_{4368}(1,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $45$
• Sturm bound: $1792$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 4368 = 2^{4} \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4368.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 45 \)
Sturm bound:			\(1792\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4368))\).

	Total	New	Old
Modular forms	920	72	848
Cusp forms	873	72	801
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.

\(2\)	\(3\)	\(7\)	\(13\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(6\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(5\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(3\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(7\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(5\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(6\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(5\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(5\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(2\)
Plus space				\(+\)	\(32\)
Minus space				\(-\)	\(40\)

Trace form

\( 72 q - 4 q^{7} + 72 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4368))\) 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	7	13
4368.2.a.a	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
4368.2.a.b	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
4368.2.a.c	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}+q^{9}-q^{13}+2q^{15}+\cdots\)
4368.2.a.d	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
4368.2.a.e	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}-q^{13}+\cdots\)
4368.2.a.f	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}+2q^{11}-q^{13}-6q^{17}+\cdots\)
4368.2.a.g	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}+2q^{11}-q^{13}-2q^{17}+\cdots\)
4368.2.a.h	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
4368.2.a.i	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
4368.2.a.j	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
4368.2.a.k	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
4368.2.a.l	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-q^{7}+q^{9}-3q^{11}+q^{13}+\cdots\)
4368.2.a.m	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-q^{7}+q^{9}-6q^{11}-q^{13}+\cdots\)
4368.2.a.n	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-q^{7}+q^{9}+5q^{11}-q^{13}+\cdots\)
4368.2.a.o	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}-q^{13}-2q^{15}+\cdots\)
4368.2.a.p	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
4368.2.a.q	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+2q^{11}+q^{13}+\cdots\)
4368.2.a.r	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-2q^{11}+q^{13}+\cdots\)
4368.2.a.s	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
4368.2.a.t	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}-2q^{11}-q^{13}-2q^{17}+\cdots\)
4368.2.a.u	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}+2q^{11}-q^{13}+4q^{17}+\cdots\)
4368.2.a.v	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-5q^{11}+q^{13}+\cdots\)
4368.2.a.w	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+6q^{11}-q^{13}+\cdots\)
4368.2.a.x	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
4368.2.a.y	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{7}+q^{9}+q^{13}+2q^{15}+\cdots\)
4368.2.a.z	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
4368.2.a.ba	$4368$	$2$	4368.a	1.a	$1$	$1$	$1$	$34.879$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(4\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}-q^{7}+q^{9}-6q^{11}-q^{13}+\cdots\)
4368.2.a.bb	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(2\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
4368.2.a.bc	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{11}-q^{13}+\cdots\)
4368.2.a.bd	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
4368.2.a.be	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4368.2.a.bf	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
4368.2.a.bg	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
4368.2.a.bh	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	\(\Q(\sqrt{57}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}-q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
4368.2.a.bi	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}+q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
4368.2.a.bj	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}-2q^{11}-q^{13}+(2+\cdots)q^{17}+\cdots\)
4368.2.a.bk	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
4368.2.a.bl	$4368$	$2$	4368.a	1.a	$1$	$2$	$2$	$34.879$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4368.2.a.bm	$4368$	$2$	4368.a	1.a	$1$	$3$	$3$	$34.879$	3.3.2089.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
4368.2.a.bn	$4368$	$2$	4368.a	1.a	$1$	$3$	$3$	$34.879$	3.3.1373.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(1\)	\(3\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
4368.2.a.bo	$4368$	$2$	4368.a	1.a	$1$	$3$	$3$	$34.879$	3.3.961.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
4368.2.a.bp	$4368$	$2$	4368.a	1.a	$1$	$3$	$3$	$34.879$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(-3\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4368.2.a.bq	$4368$	$2$	4368.a	1.a	$1$	$3$	$3$	$34.879$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{1})q^{5}+q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4368.2.a.br	$4368$	$2$	4368.a	1.a	$1$	$4$	$4$	$34.879$	4.4.17428.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-3\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{2})q^{5}-q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
4368.2.a.bs	$4368$	$2$	4368.a	1.a	$1$	$4$	$4$	$34.879$	4.4.138892.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(2\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{1})q^{5}+q^{7}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4368))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4368)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(546))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1092))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2184))\)\(^{\oplus 2}\)