Space of modular forms of level 882, weight 6, and trivial character

• Label: 882.6.a
• Level: $882$
• Weight: $6$
• Character orbit: 882.a
• Rep. character: $\chi_{882}(1,\cdot)$
• Character field: $\Q$
• Dimension: $85$
• Newform subspaces: $50$
• Sturm bound: $1008$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	882.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 50 \)
Sturm bound:			\(1008\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(882))\).

	Total	New	Old
Modular forms	872	85	787
Cusp forms	808	85	723
Eisenstein series	64	0	64

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
\(+\)	\(+\)	\(+\)	\(+\)	\(9\)
\(+\)	\(+\)	\(-\)	\(-\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)	\(13\)
\(+\)	\(-\)	\(-\)	\(+\)	\(13\)
\(-\)	\(+\)	\(+\)	\(-\)	\(9\)
\(-\)	\(+\)	\(-\)	\(+\)	\(8\)
\(-\)	\(-\)	\(+\)	\(+\)	\(11\)
\(-\)	\(-\)	\(-\)	\(-\)	\(14\)
Plus space			\(+\)	\(41\)
Minus space			\(-\)	\(44\)

Trace form

85 * q - 4 * q^2 + 1360 * q^4 + 72 * q^5 - 64 * q^8 - 192 * q^10 - 404 * q^11 - 264 * q^13 + 21760 * q^16 + 822 * q^17 + 4494 * q^19 + 1152 * q^20 + 2384 * q^22 - 8416 * q^23 + 53783 * q^25 + 880 * q^26 - 4558 * q^29 - 12348 * q^31 - 1024 * q^32 - 4776 * q^34 - 46614 * q^37 + 5656 * q^38 - 3072 * q^40 + 12390 * q^41 + 47444 * q^43 - 6464 * q^44 - 9920 * q^46 - 15900 * q^47 + 29524 * q^50 - 4224 * q^52 + 5758 * q^53 - 4032 * q^55 - 66104 * q^58 + 87546 * q^59 - 43932 * q^61 - 41936 * q^62 + 348160 * q^64 + 52272 * q^65 + 188860 * q^67 + 13152 * q^68 - 141984 * q^71 + 10266 * q^73 - 226920 * q^74 + 71904 * q^76 - 82696 * q^79 + 18432 * q^80 + 6936 * q^82 - 174870 * q^83 + 111136 * q^85 + 165136 * q^86 + 38144 * q^88 + 139962 * q^89 - 134656 * q^92 - 157488 * q^94 - 112592 * q^95 + 221814 * q^97

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(882))\) 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
882.6.a.a	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				6.6.a.a	$1$	$1$	\(-4\)	\(0\)	\(-66\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}-66q^{5}-2^{6}q^{8}+264q^{10}+\cdots\)
882.6.a.b	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				126.6.a.e	$1$	$0$	\(-4\)	\(0\)	\(-54\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}-54q^{5}-2^{6}q^{8}+6^{3}q^{10}+\cdots\)
882.6.a.c	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				126.6.a.d	$1$	$0$	\(-4\)	\(0\)	\(-26\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}-26q^{5}-2^{6}q^{8}+104q^{10}+\cdots\)
882.6.a.d	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				126.6.g.a	$1$	$1$	\(-4\)	\(0\)	\(-12\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}-12q^{5}-2^{6}q^{8}+48q^{10}+\cdots\)
882.6.a.e	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				42.6.e.a	$1$	$1$	\(-4\)	\(0\)	\(-6\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}-6q^{5}-2^{6}q^{8}+24q^{10}+\cdots\)
882.6.a.f	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				42.6.e.a	$1$	$0$	\(-4\)	\(0\)	\(6\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+6q^{5}-2^{6}q^{8}-24q^{10}+\cdots\)
882.6.a.g	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				14.6.a.b	$1$	$1$	\(-4\)	\(0\)	\(10\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+10q^{5}-2^{6}q^{8}-40q^{10}+\cdots\)
882.6.a.h	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				126.6.g.a	$1$	$0$	\(-4\)	\(0\)	\(12\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+12q^{5}-2^{6}q^{8}-48q^{10}+\cdots\)
882.6.a.i	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				42.6.a.f	$1$	$1$	\(-4\)	\(0\)	\(24\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+24q^{5}-2^{6}q^{8}-96q^{10}+\cdots\)
882.6.a.j	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				42.6.a.e	$1$	$1$	\(-4\)	\(0\)	\(76\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+76q^{5}-2^{6}q^{8}-304q^{10}+\cdots\)
882.6.a.k	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				18.6.a.a	$1$	$0$	\(-4\)	\(0\)	\(96\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+96q^{5}-2^{6}q^{8}-384q^{10}+\cdots\)
882.6.a.l	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				18.6.a.a	$1$	$1$	\(4\)	\(0\)	\(-96\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}-96q^{5}+2^{6}q^{8}-384q^{10}+\cdots\)
882.6.a.m	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				42.6.e.b	$1$	$1$	\(4\)	\(0\)	\(-86\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}-86q^{5}+2^{6}q^{8}-344q^{10}+\cdots\)
882.6.a.n	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				42.6.a.c	$1$	$0$	\(4\)	\(0\)	\(-72\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}-72q^{5}+2^{6}q^{8}-288q^{10}+\cdots\)
882.6.a.o	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				42.6.a.a	$1$	$0$	\(4\)	\(0\)	\(-54\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}-54q^{5}+2^{6}q^{8}-6^{3}q^{10}+\cdots\)
882.6.a.p	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				294.6.a.a	$1$	$0$	\(4\)	\(0\)	\(-26\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}-26q^{5}+2^{6}q^{8}-104q^{10}+\cdots\)
882.6.a.q	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				126.6.g.a	$1$	$1$	\(4\)	\(0\)	\(-12\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}-12q^{5}+2^{6}q^{8}-48q^{10}+\cdots\)
882.6.a.r	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				126.6.g.a	$1$	$0$	\(4\)	\(0\)	\(12\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+12q^{5}+2^{6}q^{8}+48q^{10}+\cdots\)
882.6.a.s	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				42.6.a.d	$1$	$0$	\(4\)	\(0\)	\(26\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+26q^{5}+2^{6}q^{8}+104q^{10}+\cdots\)
882.6.a.t	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				294.6.a.a	$1$	$0$	\(4\)	\(0\)	\(26\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+26q^{5}+2^{6}q^{8}+104q^{10}+\cdots\)
882.6.a.u	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				126.6.a.d	$1$	$1$	\(4\)	\(0\)	\(26\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+26q^{5}+2^{6}q^{8}+104q^{10}+\cdots\)
882.6.a.v	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				42.6.a.b	$1$	$0$	\(4\)	\(0\)	\(44\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+44q^{5}+2^{6}q^{8}+176q^{10}+\cdots\)
882.6.a.w	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				126.6.a.e	$1$	$1$	\(4\)	\(0\)	\(54\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+54q^{5}+2^{6}q^{8}+6^{3}q^{10}+\cdots\)
882.6.a.x	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				14.6.a.a	$1$	$0$	\(4\)	\(0\)	\(84\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+84q^{5}+2^{6}q^{8}+336q^{10}+\cdots\)
882.6.a.y	$882$	$6$	882.a	1.a	$1$	$1$	$1$	$141.459$	\(\Q\)	None	✓				42.6.e.b	$1$	$0$	\(4\)	\(0\)	\(86\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+86q^{5}+2^{6}q^{8}+344q^{10}+\cdots\)
882.6.a.z	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{2}) \)	None	✓				294.6.a.t	$1$	$0$	\(-8\)	\(0\)	\(-108\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+(-54+5\beta )q^{5}-2^{6}q^{8}+\cdots\)
882.6.a.ba	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{79}) \)	None	✓				14.6.c.a	$1$	$0$	\(-8\)	\(0\)	\(-70\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+(-35+4\beta )q^{5}-2^{6}q^{8}+\cdots\)
882.6.a.bb	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{9601}) \)	None	✓				42.6.e.c	$1$	$1$	\(-8\)	\(0\)	\(-53\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+(-26-\beta )q^{5}-2^{6}q^{8}+\cdots\)
882.6.a.bc	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{4705}) \)	None	✓				294.6.a.s	$1$	$1$	\(-8\)	\(0\)	\(-18\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+(-9-\beta )q^{5}-2^{6}q^{8}+\cdots\)
882.6.a.bd	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{697}) \)	None	✓				126.6.g.f	$1$	$1$	\(-8\)	\(0\)	\(-7\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+(-1-5\beta )q^{5}-2^{6}q^{8}+\cdots\)
882.6.a.be	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{274}) \)	None	✓	✓			882.6.a.be	$2$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+\beta q^{5}-2^{6}q^{8}-4\beta q^{10}+\cdots\)
882.6.a.bf	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{697}) \)	None	✓				126.6.g.f	$1$	$0$	\(-8\)	\(0\)	\(7\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+(1+5\beta )q^{5}-2^{6}q^{8}+\cdots\)
882.6.a.bg	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{4705}) \)	None	✓				294.6.a.s	$1$	$1$	\(-8\)	\(0\)	\(18\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+(9-\beta )q^{5}-2^{6}q^{8}+\cdots\)
882.6.a.bh	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{9601}) \)	None	✓				42.6.e.c	$1$	$0$	\(-8\)	\(0\)	\(53\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+(3^{3}-\beta )q^{5}-2^{6}q^{8}+\cdots\)
882.6.a.bi	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{79}) \)	None	✓				14.6.c.a	$1$	$1$	\(-8\)	\(0\)	\(70\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+(35+4\beta )q^{5}-2^{6}q^{8}+\cdots\)
882.6.a.bj	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{2}) \)	None	✓				294.6.a.t	$1$	$0$	\(-8\)	\(0\)	\(108\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+(54+5\beta )q^{5}-2^{6}q^{8}+\cdots\)
882.6.a.bk	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{2}) \)	None	✓				294.6.a.n	$1$	$1$	\(8\)	\(0\)	\(-108\)	\(0\)		$-$	$-$	$+$	$+$	$7$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+(-54+5\beta )q^{5}+2^{6}q^{8}+\cdots\)
882.6.a.bl	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{130}) \)	None	✓				14.6.c.b	$1$	$0$	\(8\)	\(0\)	\(-42\)	\(0\)		$-$	$-$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}-21q^{5}+2^{6}q^{8}-84q^{10}+\cdots\)
882.6.a.bm	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{505}) \)	None	✓				42.6.e.d	$1$	$1$	\(8\)	\(0\)	\(-17\)	\(0\)		$-$	$-$	$+$	$+$	$7$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+(-9-\beta )q^{5}+2^{6}q^{8}+\cdots\)
882.6.a.bn	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{697}) \)	None	✓				126.6.g.f	$1$	$1$	\(8\)	\(0\)	\(-7\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+(-1-5\beta )q^{5}+2^{6}q^{8}+\cdots\)
882.6.a.bo	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{46}) \)	None	✓				98.6.a.e	$2$	$0$	\(8\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+7\beta q^{5}+2^{6}q^{8}+28\beta q^{10}+\cdots\)
882.6.a.bp	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{2}) \)	None	✓				98.6.a.d	$2$	$1$	\(8\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+7\beta q^{5}+2^{6}q^{8}+28\beta q^{10}+\cdots\)
882.6.a.bq	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{274}) \)	None	✓	✓			882.6.a.be	$2$	$1$	\(8\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+\beta q^{5}+2^{6}q^{8}+4\beta q^{10}+\cdots\)
882.6.a.br	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{697}) \)	None	✓				126.6.g.f	$1$	$0$	\(8\)	\(0\)	\(7\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+(1+5\beta )q^{5}+2^{6}q^{8}+\cdots\)
882.6.a.bs	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{505}) \)	None	✓				42.6.e.d	$1$	$0$	\(8\)	\(0\)	\(17\)	\(0\)		$-$	$-$	$-$	$-$	$7$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+(9+\beta )q^{5}+2^{6}q^{8}+\cdots\)
882.6.a.bt	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{130}) \)	None	✓				14.6.c.b	$1$	$1$	\(8\)	\(0\)	\(42\)	\(0\)		$-$	$-$	$+$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+21q^{5}+2^{6}q^{8}+84q^{10}+\cdots\)
882.6.a.bu	$882$	$6$	882.a	1.a	$1$	$2$	$2$	$141.459$	\(\Q(\sqrt{2}) \)	None	✓				294.6.a.n	$1$	$1$	\(8\)	\(0\)	\(108\)	\(0\)		$-$	$-$	$+$	$+$	$7$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+(54+5\beta )q^{5}+2^{6}q^{8}+\cdots\)
882.6.a.bv	$882$	$6$	882.a	1.a	$1$	$4$	$4$	$141.459$	\(\Q(\sqrt{2}, \sqrt{793})\)	None	✓		✓		98.6.a.i	$2$	$0$	\(-16\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2\cdot 3^{2}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+(3\beta _{1}+\beta _{3})q^{5}-2^{6}q^{8}+\cdots\)
882.6.a.bw	$882$	$6$	882.a	1.a	$1$	$6$	$6$	$141.459$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓		882.6.a.bw	$2$	$1$	\(-24\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2^{4}\cdot 3^{4}\cdot 7^{4}$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+(\beta _{1}+2\beta _{2})q^{5}-2^{6}q^{8}+\cdots\)
882.6.a.bx	$882$	$6$	882.a	1.a	$1$	$6$	$6$	$141.459$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓		882.6.a.bw	$2$	$0$	\(24\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2^{4}\cdot 3^{4}\cdot 7^{4}$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+(\beta _{1}+2\beta _{2})q^{5}+2^{6}q^{8}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(882))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(882)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)