Space of modular forms of level 6897, weight 2, and trivial character

• Label: 6897.2.a
• Level: $6897$
• Weight: $2$
• Character orbit: 6897.a
• Rep. character: $\chi_{6897}(1,\cdot)$
• Character field: $\Q$
• Dimension: $326$
• Newform subspaces: $43$
• Sturm bound: $1760$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 6897 = 3 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6897.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 43 \)
Sturm bound:			\(1760\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6897))\).

	Total	New	Old
Modular forms	904	326	578
Cusp forms	857	326	531
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.

\(3\)	\(11\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(108\)	\(41\)	\(67\)		\(103\)	\(41\)	\(62\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(114\)	\(37\)	\(77\)		\(108\)	\(37\)	\(71\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(117\)	\(40\)	\(77\)		\(111\)	\(40\)	\(71\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(113\)	\(45\)	\(68\)		\(107\)	\(45\)	\(62\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(118\)	\(45\)	\(73\)		\(112\)	\(45\)	\(67\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(112\)	\(33\)	\(79\)		\(106\)	\(33\)	\(73\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(109\)	\(35\)	\(74\)		\(103\)	\(35\)	\(68\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(113\)	\(50\)	\(63\)		\(107\)	\(50\)	\(57\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(442\)	\(154\)	\(288\)		\(419\)	\(154\)	\(265\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(462\)	\(172\)	\(290\)		\(438\)	\(172\)	\(266\)		\(24\)	\(0\)	\(24\)

Trace form

326 * q + 2 * q^2 + 328 * q^4 - 6 * q^5 + 2 * q^6 + 10 * q^7 + 6 * q^8 + 326 * q^9 + 8 * q^10 + 8 * q^12 - 4 * q^13 + 20 * q^14 + 4 * q^15 + 356 * q^16 - 10 * q^17 + 2 * q^18 + 4 * q^19 + 4 * q^20 + 20 * q^23 + 18 * q^24 + 320 * q^25 + 4 * q^26 + 28 * q^28 - 8 * q^29 - 4 * q^30 + 12 * q^31 + 14 * q^32 + 8 * q^34 + 14 * q^35 + 328 * q^36 + 24 * q^37 + 16 * q^39 - 12 * q^40 - 20 * q^41 - 8 * q^42 + 26 * q^43 - 6 * q^45 + 12 * q^46 + 34 * q^47 + 340 * q^49 - 38 * q^50 + 4 * q^51 - 40 * q^52 + 2 * q^54 + 48 * q^56 + 2 * q^57 - 32 * q^58 + 32 * q^59 - 8 * q^60 + 2 * q^61 - 32 * q^62 + 10 * q^63 + 412 * q^64 - 36 * q^65 + 16 * q^67 + 20 * q^68 + 4 * q^69 + 36 * q^70 + 32 * q^71 + 6 * q^72 - 2 * q^73 + 44 * q^74 + 24 * q^75 + 10 * q^76 + 4 * q^78 + 24 * q^79 + 16 * q^80 + 326 * q^81 + 24 * q^82 - 4 * q^83 + 8 * q^84 - 30 * q^85 + 100 * q^86 + 4 * q^87 - 8 * q^89 + 8 * q^90 + 68 * q^91 + 4 * q^92 - 8 * q^93 + 16 * q^94 + 2 * q^95 + 18 * q^96 + 12 * q^97 + 78 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6897))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	11	19
6897.2.a.a	$6897$	$2$	6897.a	1.a	$1$	$1$	$1$	$55.073$	\(\Q\)	None	✓				57.2.a.c	$1$	$0$	\(-1\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}+3q^{8}+\cdots\)
6897.2.a.b	$6897$	$2$	6897.a	1.a	$1$	$1$	$1$	$55.073$	\(\Q\)	None	✓				627.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-2q^{7}+q^{9}-2q^{12}+\cdots\)
6897.2.a.c	$6897$	$2$	6897.a	1.a	$1$	$1$	$1$	$55.073$	\(\Q\)	None	✓	✓			6897.2.a.c	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+2q^{5}+q^{9}-2q^{12}+\cdots\)
6897.2.a.d	$6897$	$2$	6897.a	1.a	$1$	$1$	$1$	$55.073$	\(\Q\)	None	✓	✓			6897.2.a.c	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+2q^{5}+q^{9}-2q^{12}+\cdots\)
6897.2.a.e	$6897$	$2$	6897.a	1.a	$1$	$1$	$1$	$55.073$	\(\Q\)	None	✓				627.2.a.b	$1$	$0$	\(0\)	\(1\)	\(4\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+4q^{5}-2q^{7}+q^{9}-2q^{12}+\cdots\)
6897.2.a.f	$6897$	$2$	6897.a	1.a	$1$	$1$	$1$	$55.073$	\(\Q\)	None	✓				57.2.a.a	$1$	$1$	\(2\)	\(-1\)	\(-3\)	\(5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots\)
6897.2.a.g	$6897$	$2$	6897.a	1.a	$1$	$1$	$1$	$55.073$	\(\Q\)	None	✓				57.2.a.b	$1$	$0$	\(2\)	\(1\)	\(1\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-3q^{7}+\cdots\)
6897.2.a.h	$6897$	$2$	6897.a	1.a	$1$	$2$	$2$	$55.073$	\(\Q(\sqrt{3}) \)	None	✓	✓			6897.2.a.h	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+q^{4}+(-2-\beta )q^{5}+\beta q^{6}+\cdots\)
6897.2.a.i	$6897$	$2$	6897.a	1.a	$1$	$2$	$2$	$55.073$	\(\Q(\sqrt{3}) \)	None	✓	✓			6897.2.a.h	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}+\beta q^{6}+\cdots\)
6897.2.a.j	$6897$	$2$	6897.a	1.a	$1$	$2$	$2$	$55.073$	\(\Q(\sqrt{3}) \)	None	✓	✓			6897.2.a.j	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
6897.2.a.k	$6897$	$2$	6897.a	1.a	$1$	$2$	$2$	$55.073$	\(\Q(\sqrt{3}) \)	None	✓	✓			6897.2.a.j	$1$	$1$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
6897.2.a.l	$6897$	$2$	6897.a	1.a	$1$	$3$	$3$	$55.073$	\(\Q(\zeta_{14})^+\)	None	✓				627.2.a.f	$1$	$1$	\(-2\)	\(-3\)	\(-3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
6897.2.a.m	$6897$	$2$	6897.a	1.a	$1$	$3$	$3$	$55.073$	3.3.169.1	None	✓				627.2.a.g	$1$	$1$	\(-2\)	\(3\)	\(5\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
6897.2.a.n	$6897$	$2$	6897.a	1.a	$1$	$3$	$3$	$55.073$	3.3.169.1	None	✓				627.2.a.c	$1$	$0$	\(2\)	\(-3\)	\(1\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
6897.2.a.o	$6897$	$2$	6897.a	1.a	$1$	$3$	$3$	$55.073$	\(\Q(\zeta_{14})^+\)	None	✓				627.2.a.d	$1$	$1$	\(2\)	\(3\)	\(-7\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
6897.2.a.p	$6897$	$2$	6897.a	1.a	$1$	$3$	$3$	$55.073$	3.3.321.1	None	✓				627.2.a.e	$1$	$0$	\(2\)	\(3\)	\(-3\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
6897.2.a.q	$6897$	$2$	6897.a	1.a	$1$	$4$	$4$	$55.073$	4.4.23377.1	None	✓				627.2.a.h	$1$	$0$	\(-1\)	\(4\)	\(3\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
6897.2.a.r	$6897$	$2$	6897.a	1.a	$1$	$5$	$5$	$55.073$	5.5.2179633.1	None	✓				627.2.a.i	$1$	$0$	\(-1\)	\(-5\)	\(3\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots\)
6897.2.a.s	$6897$	$2$	6897.a	1.a	$1$	$5$	$5$	$55.073$	5.5.1920025.1	None	✓				627.2.a.j	$1$	$1$	\(-1\)	\(-5\)	\(7\)	\(-7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots\)
6897.2.a.t	$6897$	$2$	6897.a	1.a	$1$	$6$	$6$	$55.073$	6.6.65858461.1	None	✓	✓			6897.2.a.t	$1$	$1$	\(-3\)	\(6\)	\(-2\)	\(-12\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(1+\beta _{4}+\beta _{5})q^{4}+\cdots\)
6897.2.a.u	$6897$	$2$	6897.a	1.a	$1$	$6$	$6$	$55.073$	6.6.157752128.1	None	✓	✓			6897.2.a.u	$1$	$1$	\(-2\)	\(6\)	\(-4\)	\(-10\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
6897.2.a.v	$6897$	$2$	6897.a	1.a	$1$	$6$	$6$	$55.073$	6.6.162030669.1	None	✓	✓			6897.2.a.v	$1$	$1$	\(-1\)	\(6\)	\(2\)	\(-12\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2}+\beta _{4})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
6897.2.a.w	$6897$	$2$	6897.a	1.a	$1$	$6$	$6$	$55.073$	6.6.162030669.1	None	✓	✓			6897.2.a.v	$1$	$0$	\(1\)	\(6\)	\(2\)	\(12\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2}+\beta _{4})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
6897.2.a.x	$6897$	$2$	6897.a	1.a	$1$	$6$	$6$	$55.073$	6.6.157752128.1	None	✓	✓			6897.2.a.u	$1$	$0$	\(2\)	\(6\)	\(-4\)	\(10\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
6897.2.a.y	$6897$	$2$	6897.a	1.a	$1$	$6$	$6$	$55.073$	6.6.65858461.1	None	✓	✓			6897.2.a.t	$1$	$0$	\(3\)	\(6\)	\(-2\)	\(12\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+q^{3}+(1+\beta _{4}+\beta _{5})q^{4}+\cdots\)
6897.2.a.z	$6897$	$2$	6897.a	1.a	$1$	$7$	$7$	$55.073$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			6897.2.a.z	$1$	$1$	\(-2\)	\(-7\)	\(-2\)	\(-6\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
6897.2.a.ba	$6897$	$2$	6897.a	1.a	$1$	$7$	$7$	$55.073$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			6897.2.a.z	$1$	$0$	\(2\)	\(-7\)	\(-2\)	\(6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
6897.2.a.bb	$6897$	$2$	6897.a	1.a	$1$	$8$	$8$	$55.073$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			6897.2.a.bb	$1$	$1$	\(-3\)	\(-8\)	\(-2\)	\(-6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
6897.2.a.bc	$6897$	$2$	6897.a	1.a	$1$	$8$	$8$	$55.073$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			6897.2.a.bc	$1$	$1$	\(-1\)	\(-8\)	\(-2\)	\(-6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1-\beta _{6}+\beta _{7})q^{4}-\beta _{4}q^{5}+\cdots\)
6897.2.a.bd	$6897$	$2$	6897.a	1.a	$1$	$8$	$8$	$55.073$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			6897.2.a.bc	$1$	$0$	\(1\)	\(-8\)	\(-2\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1-\beta _{6}+\beta _{7})q^{4}-\beta _{4}q^{5}+\cdots\)
6897.2.a.be	$6897$	$2$	6897.a	1.a	$1$	$8$	$8$	$55.073$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			6897.2.a.bb	$1$	$0$	\(3\)	\(-8\)	\(-2\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
6897.2.a.bf	$6897$	$2$	6897.a	1.a	$1$	$12$	$12$	$55.073$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				627.2.j.a	$1$	$1$	\(-1\)	\(12\)	\(-6\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-\beta _{8}q^{5}-\beta _{1}q^{6}+\cdots\)
6897.2.a.bg	$6897$	$2$	6897.a	1.a	$1$	$12$	$12$	$55.073$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		627.2.j.a	$1$	$1$	\(1\)	\(12\)	\(-6\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-\beta _{8}q^{5}+\beta _{1}q^{6}+\cdots\)
6897.2.a.bh	$6897$	$2$	6897.a	1.a	$1$	$14$	$14$	$55.073$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓			6897.2.a.bh	$1$	$1$	\(-4\)	\(-14\)	\(2\)	\(-12\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\)
6897.2.a.bi	$6897$	$2$	6897.a	1.a	$1$	$14$	$14$	$55.073$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓		6897.2.a.bi	$1$	$1$	\(-4\)	\(14\)	\(2\)	\(-20\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)
6897.2.a.bj	$6897$	$2$	6897.a	1.a	$1$	$14$	$14$	$55.073$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓			6897.2.a.bh	$1$	$0$	\(4\)	\(-14\)	\(2\)	\(12\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\)
6897.2.a.bk	$6897$	$2$	6897.a	1.a	$1$	$14$	$14$	$55.073$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓			6897.2.a.bi	$1$	$0$	\(4\)	\(14\)	\(2\)	\(20\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)
6897.2.a.bl	$6897$	$2$	6897.a	1.a	$1$	$16$	$16$	$55.073$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓		✓		627.2.j.b	$1$	$0$	\(-3\)	\(-16\)	\(8\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots\)
6897.2.a.bm	$6897$	$2$	6897.a	1.a	$1$	$16$	$16$	$55.073$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓		✓		627.2.j.b	$1$	$0$	\(3\)	\(-16\)	\(8\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots\)
6897.2.a.bn	$6897$	$2$	6897.a	1.a	$1$	$20$	$20$	$55.073$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		627.2.j.c	$1$	$1$	\(-3\)	\(-20\)	\(-9\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
6897.2.a.bo	$6897$	$2$	6897.a	1.a	$1$	$20$	$20$	$55.073$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		627.2.j.c	$1$	$1$	\(3\)	\(-20\)	\(-9\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
6897.2.a.bp	$6897$	$2$	6897.a	1.a	$1$	$24$	$24$	$55.073$		None	✓		✓		627.2.j.d	$1$	$0$	\(-1\)	\(24\)	\(9\)	\(-3\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
6897.2.a.bq	$6897$	$2$	6897.a	1.a	$1$	$24$	$24$	$55.073$		None	✓		✓		627.2.j.d	$1$	$0$	\(1\)	\(24\)	\(9\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6897))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6897)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(627))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2299))\)\(^{\oplus 2}\)