Space of modular forms of level 5376, weight 2, and trivial character

• Label: 5376.2.a
• Level: $5376$
• Weight: $2$
• Character orbit: 5376.a
• Rep. character: $\chi_{5376}(1,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $44$
• Sturm bound: $2048$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 5376 = 2^{8} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5376.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 44 \)
Sturm bound:			\(2048\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5376))\).

	Total	New	Old
Modular forms	1072	96	976
Cusp forms	977	96	881
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
\(+\)	\(+\)	\(+\)	$+$	\(10\)
\(+\)	\(+\)	\(-\)	$-$	\(12\)
\(+\)	\(-\)	\(+\)	$-$	\(14\)
\(+\)	\(-\)	\(-\)	$+$	\(8\)
\(-\)	\(+\)	\(+\)	$-$	\(14\)
\(-\)	\(+\)	\(-\)	$+$	\(12\)
\(-\)	\(-\)	\(+\)	$+$	\(10\)
\(-\)	\(-\)	\(-\)	$-$	\(16\)
Plus space			\(+\)	\(40\)
Minus space			\(-\)	\(56\)

Trace form

\( 96 q + 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5376))\) 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
5376.2.a.a	$5376$	$2$	5376.a	1.a	$1$	$1$	$1$	$42.928$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
5376.2.a.b	$5376$	$2$	5376.a	1.a	$1$	$1$	$1$	$42.928$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
5376.2.a.c	$5376$	$2$	5376.a	1.a	$1$	$1$	$1$	$42.928$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}-2q^{17}+4q^{19}+\cdots\)
5376.2.a.d	$5376$	$2$	5376.a	1.a	$1$	$1$	$1$	$42.928$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}-2q^{17}+4q^{19}+\cdots\)
5376.2.a.e	$5376$	$2$	5376.a	1.a	$1$	$1$	$1$	$42.928$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
5376.2.a.f	$5376$	$2$	5376.a	1.a	$1$	$1$	$1$	$42.928$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
5376.2.a.g	$5376$	$2$	5376.a	1.a	$1$	$1$	$1$	$42.928$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
5376.2.a.h	$5376$	$2$	5376.a	1.a	$1$	$1$	$1$	$42.928$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
5376.2.a.i	$5376$	$2$	5376.a	1.a	$1$	$1$	$1$	$42.928$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}-2q^{17}-4q^{19}+\cdots\)
5376.2.a.j	$5376$	$2$	5376.a	1.a	$1$	$1$	$1$	$42.928$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}-2q^{17}-4q^{19}+\cdots\)
5376.2.a.k	$5376$	$2$	5376.a	1.a	$1$	$1$	$1$	$42.928$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
5376.2.a.l	$5376$	$2$	5376.a	1.a	$1$	$1$	$1$	$42.928$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
5376.2.a.m	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}-q^{7}+q^{9}+\beta q^{11}+\cdots\)
5376.2.a.n	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
5376.2.a.o	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{5}-q^{7}+q^{9}+(3+\cdots)q^{11}+\cdots\)
5376.2.a.p	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
5376.2.a.q	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}-q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
5376.2.a.r	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
5376.2.a.s	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}+(1+3\beta )q^{11}+\cdots\)
5376.2.a.t	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
5376.2.a.u	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+(3+\beta )q^{11}+\cdots\)
5376.2.a.v	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(2+\beta )q^{5}+q^{7}+q^{9}-\beta q^{11}+\cdots\)
5376.2.a.w	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+\beta )q^{5}+q^{7}+q^{9}-\beta q^{11}+\cdots\)
5376.2.a.x	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
5376.2.a.y	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
5376.2.a.z	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
5376.2.a.ba	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
5376.2.a.bb	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
5376.2.a.bc	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
5376.2.a.bd	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
5376.2.a.be	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
5376.2.a.bf	$5376$	$2$	5376.a	1.a	$1$	$2$	$2$	$42.928$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(4\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(2+\beta )q^{5}-q^{7}+q^{9}+\beta q^{11}+\cdots\)
5376.2.a.bg	$5376$	$2$	5376.a	1.a	$1$	$3$	$3$	$42.928$	3.3.1016.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(-3\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{5}-q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
5376.2.a.bh	$5376$	$2$	5376.a	1.a	$1$	$3$	$3$	$42.928$	3.3.1016.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(3\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{2}q^{5}+q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
5376.2.a.bi	$5376$	$2$	5376.a	1.a	$1$	$3$	$3$	$42.928$	3.3.1016.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-3\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{2}q^{5}-q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
5376.2.a.bj	$5376$	$2$	5376.a	1.a	$1$	$3$	$3$	$42.928$	3.3.1016.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
5376.2.a.bk	$5376$	$2$	5376.a	1.a	$1$	$4$	$4$	$42.928$	4.4.7232.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-4\)	\(4\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{1})q^{5}+q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
5376.2.a.bl	$5376$	$2$	5376.a	1.a	$1$	$4$	$4$	$42.928$	4.4.19664.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-2\)	\(4\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{3})q^{5}+q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
5376.2.a.bm	$5376$	$2$	5376.a	1.a	$1$	$4$	$4$	$42.928$	4.4.19664.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(2\)	\(-4\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{3})q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
5376.2.a.bn	$5376$	$2$	5376.a	1.a	$1$	$4$	$4$	$42.928$	4.4.7232.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(4\)	\(-4\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{1})q^{5}-q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
5376.2.a.bo	$5376$	$2$	5376.a	1.a	$1$	$4$	$4$	$42.928$	4.4.7232.1	None	✓	$1$	$1$	\(0\)	\(4\)	\(-4\)	\(-4\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{1})q^{5}-q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
5376.2.a.bp	$5376$	$2$	5376.a	1.a	$1$	$4$	$4$	$42.928$	4.4.19664.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(-2\)	\(-4\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{3})q^{5}-q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
5376.2.a.bq	$5376$	$2$	5376.a	1.a	$1$	$4$	$4$	$42.928$	4.4.19664.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{3})q^{5}+q^{7}+q^{9}+(2+\beta _{2}+\cdots)q^{11}+\cdots\)
5376.2.a.br	$5376$	$2$	5376.a	1.a	$1$	$4$	$4$	$42.928$	4.4.7232.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{1})q^{5}+q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5376))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5376)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(256))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(672))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(768))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(896))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1344))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1792))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2688))\)\(^{\oplus 2}\)