Space of modular forms of level 4416, weight 2, and trivial character

• Label: 4416.2.a
• Level: $4416$
• Weight: $2$
• Character orbit: 4416.a
• Rep. character: $\chi_{4416}(1,\cdot)$
• Character field: $\Q$
• Dimension: $88$
• Newform subspaces: $50$
• Sturm bound: $1536$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 4416 = 2^{6} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4416.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 50 \)
Sturm bound:			\(1536\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4416))\).

	Total	New	Old
Modular forms	792	88	704
Cusp forms	745	88	657
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.

\(2\)	\(3\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(9\)
\(+\)	\(+\)	\(-\)	$-$	\(13\)
\(+\)	\(-\)	\(+\)	$-$	\(12\)
\(+\)	\(-\)	\(-\)	$+$	\(8\)
\(-\)	\(+\)	\(+\)	$-$	\(13\)
\(-\)	\(+\)	\(-\)	$+$	\(9\)
\(-\)	\(-\)	\(+\)	$+$	\(10\)
\(-\)	\(-\)	\(-\)	$-$	\(14\)
Plus space			\(+\)	\(36\)
Minus space			\(-\)	\(52\)

Trace form

\( 88 q + 88 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4416))\) 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	23
4416.2.a.a	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-4\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}-2q^{7}+q^{9}-2q^{13}+\cdots\)
4416.2.a.b	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-4\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+4q^{7}+q^{9}+6q^{11}+\cdots\)
4416.2.a.c	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots\)
4416.2.a.d	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots\)
4416.2.a.e	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
4416.2.a.f	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
4416.2.a.g	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4416.2.a.h	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+2q^{11}+2q^{13}-6q^{17}+\cdots\)
4416.2.a.i	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-2q^{13}-2q^{19}+\cdots\)
4416.2.a.j	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-2q^{13}+8q^{17}+\cdots\)
4416.2.a.k	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-4q^{7}+q^{9}+2q^{13}+\cdots\)
4416.2.a.l	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots\)
4416.2.a.m	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+2q^{7}+q^{9}-6q^{11}+\cdots\)
4416.2.a.n	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
4416.2.a.o	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(1\)	\(-4\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}-4q^{7}+q^{9}-6q^{11}+\cdots\)
4416.2.a.p	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+2q^{7}+q^{9}-2q^{13}+\cdots\)
4416.2.a.q	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
4416.2.a.r	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots\)
4416.2.a.s	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots\)
4416.2.a.t	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-2q^{13}+2q^{19}+\cdots\)
4416.2.a.u	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-2q^{13}+8q^{17}+\cdots\)
4416.2.a.v	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-2q^{11}+2q^{13}-6q^{17}+\cdots\)
4416.2.a.w	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
4416.2.a.x	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
4416.2.a.y	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
4416.2.a.z	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-2q^{7}+q^{9}+6q^{11}+\cdots\)
4416.2.a.ba	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots\)
4416.2.a.bb	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+4q^{7}+q^{9}+2q^{13}+\cdots\)
4416.2.a.bc	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}-\beta q^{7}+q^{9}-4\beta q^{11}+\cdots\)
4416.2.a.bd	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+2q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4416.2.a.be	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+(-2-\beta )q^{7}+q^{9}-4q^{13}+\cdots\)
4416.2.a.bf	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+(-1+\beta )q^{7}+q^{9}+\cdots\)
4416.2.a.bg	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+(-1+\beta )q^{7}+q^{9}+\cdots\)
4416.2.a.bh	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+2\beta q^{7}+q^{9}+(3+\cdots)q^{11}+\cdots\)
4416.2.a.bi	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+\beta )q^{5}+\beta q^{7}+q^{9}+4\beta q^{11}+\cdots\)
4416.2.a.bj	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}-2q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4416.2.a.bk	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+(2+\beta )q^{7}+q^{9}-4q^{13}+\cdots\)
4416.2.a.bl	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}-2\beta q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
4416.2.a.bm	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
4416.2.a.bn	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
4416.2.a.bo	$4416$	$2$	4416.a	1.a	$1$	$3$	$3$	$35.262$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{1})q^{5}+(1-\beta _{2})q^{7}+\cdots\)
4416.2.a.bp	$4416$	$2$	4416.a	1.a	$1$	$3$	$3$	$35.262$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{2}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4416.2.a.bq	$4416$	$2$	4416.a	1.a	$1$	$3$	$3$	$35.262$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(4\)	\(-2\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
4416.2.a.br	$4416$	$2$	4416.a	1.a	$1$	$3$	$3$	$35.262$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
4416.2.a.bs	$4416$	$2$	4416.a	1.a	$1$	$3$	$3$	$35.262$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+q^{9}+\cdots\)
4416.2.a.bt	$4416$	$2$	4416.a	1.a	$1$	$3$	$3$	$35.262$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(4\)	\(2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{1})q^{5}+(1-\beta _{2})q^{7}+q^{9}+\cdots\)
4416.2.a.bu	$4416$	$2$	4416.a	1.a	$1$	$4$	$4$	$35.262$	4.4.19796.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{1})q^{5}-\beta _{3}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4416.2.a.bv	$4416$	$2$	4416.a	1.a	$1$	$4$	$4$	$35.262$	4.4.19796.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{1})q^{5}+\beta _{3}q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4416.2.a.bw	$4416$	$2$	4416.a	1.a	$1$	$5$	$5$	$35.262$	5.5.218524.1	None	✓	$1$	$0$	\(0\)	\(-5\)	\(2\)	\(4\)		$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+(1-\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4416.2.a.bx	$4416$	$2$	4416.a	1.a	$1$	$5$	$5$	$35.262$	5.5.218524.1	None	✓	$1$	$0$	\(0\)	\(5\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4416))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4416)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(552))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(736))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1104))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1472))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2208))\)\(^{\oplus 2}\)