Space of modular forms of level 1008, weight 6, and trivial character

• Label: 1008.6.a
• Level: $1008$
• Weight: $6$
• Character orbit: 1008.a
• Rep. character: $\chi_{1008}(1,\cdot)$
• Character field: $\Q$
• Dimension: $75$
• Newform subspaces: $51$
• Sturm bound: $1152$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1008.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 51 \)
Sturm bound:			\(1152\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(1008))\).

	Total	New	Old
Modular forms	984	75	909
Cusp forms	936	75	861
Eisenstein series	48	0	48

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
\(+\)	\(+\)	\(+\)	$+$	\(8\)
\(+\)	\(+\)	\(-\)	$-$	\(8\)
\(+\)	\(-\)	\(+\)	$-$	\(11\)
\(+\)	\(-\)	\(-\)	$+$	\(11\)
\(-\)	\(+\)	\(+\)	$-$	\(8\)
\(-\)	\(+\)	\(-\)	$+$	\(6\)
\(-\)	\(-\)	\(+\)	$+$	\(11\)
\(-\)	\(-\)	\(-\)	$-$	\(12\)
Plus space			\(+\)	\(36\)
Minus space			\(-\)	\(39\)

Trace form

\( 75 q + 38 q^{5} - 49 q^{7} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(1008))\) 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
1008.6.a.a	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-94\)	\(49\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-94q^{5}+7^{2}q^{7}+52q^{11}-770q^{13}+\cdots\)
1008.6.a.b	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-84\)	\(-49\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-84q^{5}-7^{2}q^{7}-336q^{11}+584q^{13}+\cdots\)
1008.6.a.c	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-78\)	\(-49\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-78q^{5}-7^{2}q^{7}+444q^{11}-442q^{13}+\cdots\)
1008.6.a.d	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-76\)	\(49\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-76q^{5}+7^{2}q^{7}+650q^{11}+762q^{13}+\cdots\)
1008.6.a.e	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-74\)	\(-49\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-74q^{5}-7^{2}q^{7}+6^{3}q^{11}-186q^{13}+\cdots\)
1008.6.a.f	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-54\)	\(-49\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-54q^{5}-7^{2}q^{7}+594q^{11}+26q^{13}+\cdots\)
1008.6.a.g	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-44\)	\(49\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-44q^{5}+7^{2}q^{7}-470q^{11}-1158q^{13}+\cdots\)
1008.6.a.h	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(0\)	\(-32\)	\(-49\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{5}q^{5}-7^{2}q^{7}-624q^{11}-708q^{13}+\cdots\)
1008.6.a.i	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-26\)	\(49\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-26q^{5}+7^{2}q^{7}-470q^{11}+642q^{13}+\cdots\)
1008.6.a.j	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-26\)	\(49\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-26q^{5}+7^{2}q^{7}+664q^{11}+318q^{13}+\cdots\)
1008.6.a.k	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-24\)	\(-49\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-24q^{5}-7^{2}q^{7}+66q^{11}+98q^{13}+\cdots\)
1008.6.a.l	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-16\)	\(49\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{5}+7^{2}q^{7}+8q^{11}+684q^{13}+\cdots\)
1008.6.a.m	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-14\)	\(49\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-14q^{5}+7^{2}q^{7}-700q^{11}+158q^{13}+\cdots\)
1008.6.a.n	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-10\)	\(49\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-10q^{5}+7^{2}q^{7}-340q^{11}-294q^{13}+\cdots\)
1008.6.a.o	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(-49\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-6q^{5}-7^{2}q^{7}-108q^{11}-346q^{13}+\cdots\)
1008.6.a.p	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(-49\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-7^{2}q^{7}-240q^{11}-744q^{13}+\cdots\)
1008.6.a.q	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(49\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+7^{2}q^{7}+370q^{11}+122q^{13}+\cdots\)
1008.6.a.r	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(26\)	\(49\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+26q^{5}+7^{2}q^{7}+470q^{11}+642q^{13}+\cdots\)
1008.6.a.s	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(34\)	\(-49\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+34q^{5}-7^{2}q^{7}-756q^{11}+678q^{13}+\cdots\)
1008.6.a.t	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(34\)	\(49\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+34q^{5}+7^{2}q^{7}-340q^{11}+454q^{13}+\cdots\)
1008.6.a.u	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(34\)	\(49\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+34q^{5}+7^{2}q^{7}-332q^{11}-1026q^{13}+\cdots\)
1008.6.a.v	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(38\)	\(49\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+38q^{5}+7^{2}q^{7}+600q^{11}-674q^{13}+\cdots\)
1008.6.a.w	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(54\)	\(-49\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+54q^{5}-7^{2}q^{7}-594q^{11}+26q^{13}+\cdots\)
1008.6.a.x	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(54\)	\(-49\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+54q^{5}-7^{2}q^{7}+6^{3}q^{11}+998q^{13}+\cdots\)
1008.6.a.y	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(56\)	\(49\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+56q^{5}+7^{2}q^{7}+232q^{11}-140q^{13}+\cdots\)
1008.6.a.z	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(64\)	\(-49\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{6}q^{5}-7^{2}q^{7}-54q^{11}+738q^{13}+\cdots\)
1008.6.a.ba	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(72\)	\(-49\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+72q^{5}-7^{2}q^{7}-414q^{11}-1054q^{13}+\cdots\)
1008.6.a.bb	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(96\)	\(-49\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+96q^{5}-7^{2}q^{7}-720q^{11}+572q^{13}+\cdots\)
1008.6.a.bc	$1008$	$6$	1008.a	1.a	$1$	$1$	$1$	$161.667$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(106\)	\(49\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+106q^{5}+7^{2}q^{7}+92q^{11}+670q^{13}+\cdots\)
1008.6.a.bd	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{345}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-82\)	\(98\)		$+$	$-$	$-$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-41-\beta )q^{5}+7^{2}q^{7}+(170+2\beta )q^{11}+\cdots\)
1008.6.a.be	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{429}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-80\)	\(-98\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-40-\beta )q^{5}-7^{2}q^{7}+(6^{3}+3\beta )q^{11}+\cdots\)
1008.6.a.bf	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{505}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-78\)	\(-98\)		$-$	$-$	$+$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-39-\beta )q^{5}-7^{2}q^{7}+(87-5\beta )q^{11}+\cdots\)
1008.6.a.bg	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{106}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-76\)	\(-98\)		$+$	$+$	$+$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-38+\beta )q^{5}-7^{2}q^{7}+(282+5\beta )q^{11}+\cdots\)
1008.6.a.bh	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{37}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-48\)	\(98\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-24-5\beta )q^{5}+7^{2}q^{7}+(184+37\beta )q^{11}+\cdots\)
1008.6.a.bi	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{193}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-42\)	\(98\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-21-5\beta )q^{5}+7^{2}q^{7}+(-358+\cdots)q^{11}+\cdots\)
1008.6.a.bj	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{114}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-28\)	\(98\)		$+$	$+$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-14+\beta )q^{5}+7^{2}q^{7}+(-298+7\beta )q^{11}+\cdots\)
1008.6.a.bk	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{91}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-98\)		$-$	$+$	$+$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-7^{2}q^{7}+9\beta q^{11}-670q^{13}+\cdots\)
1008.6.a.bl	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{7}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(98\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+7\beta q^{5}+7^{2}q^{7}-43\beta q^{11}-518q^{13}+\cdots\)
1008.6.a.bm	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{1099}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(98\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+7^{2}q^{7}-5\beta q^{11}-54q^{13}+\cdots\)
1008.6.a.bn	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{1129}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(98\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta q^{5}+7^{2}q^{7}+(50-\beta )q^{11}+(270+\cdots)q^{13}+\cdots\)
1008.6.a.bo	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{5569}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(6\)	\(98\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(3+\beta )q^{5}+7^{2}q^{7}+(-45+7\beta )q^{11}+\cdots\)
1008.6.a.bp	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{4281}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(10\)	\(-98\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(5-\beta )q^{5}-7^{2}q^{7}+(3^{3}+3\beta )q^{11}+\cdots\)
1008.6.a.bq	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{57}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(18\)	\(-98\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(9+5\beta )q^{5}-7^{2}q^{7}+(198+62\beta )q^{11}+\cdots\)
1008.6.a.br	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{114}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(28\)	\(98\)		$+$	$+$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(14+\beta )q^{5}+7^{2}q^{7}+(298+7\beta )q^{11}+\cdots\)
1008.6.a.bs	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{37}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(48\)	\(98\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(24+5\beta )q^{5}+7^{2}q^{7}+(-184-37\beta )q^{11}+\cdots\)
1008.6.a.bt	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{177}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(62\)	\(-98\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(31-5\beta )q^{5}-7^{2}q^{7}+(486+6\beta )q^{11}+\cdots\)
1008.6.a.bu	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{249}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(64\)	\(-98\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(2^{5}-\beta )q^{5}-7^{2}q^{7}+(270-15\beta )q^{11}+\cdots\)
1008.6.a.bv	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{106}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(76\)	\(-98\)		$+$	$+$	$+$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(38+\beta )q^{5}-7^{2}q^{7}+(-282+5\beta )q^{11}+\cdots\)
1008.6.a.bw	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{193}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(78\)	\(98\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(39-5\beta )q^{5}+7^{2}q^{7}+(-185+37\beta )q^{11}+\cdots\)
1008.6.a.bx	$1008$	$6$	1008.a	1.a	$1$	$2$	$2$	$161.667$	\(\Q(\sqrt{429}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(80\)	\(-98\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(40-\beta )q^{5}-7^{2}q^{7}+(-6^{3}+3\beta )q^{11}+\cdots\)
1008.6.a.by	$1008$	$6$	1008.a	1.a	$1$	$4$	$4$	$161.667$	4.4.358541904.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-196\)		$-$	$+$	$+$	$-$	$2^{9}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}-7^{2}q^{7}+(3\beta _{1}-2\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(1008))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(1008)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 15}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 2}\)