Space of modular forms of level 8349, weight 2, and trivial character

• Label: 8349.2.a
• Level: $8349$
• Weight: $2$
• Character orbit: 8349.a
• Rep. character: $\chi_{8349}(1,\cdot)$
• Character field: $\Q$
• Dimension: $398$
• Newform subspaces: $41$
• Sturm bound: $2112$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 8349 = 3 \cdot 11^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8349.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 41 \)
Sturm bound:			\(2112\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8349))\).

	Total	New	Old
Modular forms	1080	398	682
Cusp forms	1033	398	635
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.

\(3\)	\(11\)	\(23\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(120\)	\(44\)	\(76\)		\(115\)	\(44\)	\(71\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(150\)	\(56\)	\(94\)		\(144\)	\(56\)	\(88\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(150\)	\(55\)	\(95\)		\(144\)	\(55\)	\(89\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(120\)	\(45\)	\(75\)		\(114\)	\(45\)	\(69\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(132\)	\(52\)	\(80\)		\(126\)	\(52\)	\(74\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(138\)	\(40\)	\(98\)		\(132\)	\(40\)	\(92\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(138\)	\(48\)	\(90\)		\(132\)	\(48\)	\(84\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(132\)	\(58\)	\(74\)		\(126\)	\(58\)	\(68\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(516\)	\(177\)	\(339\)		\(493\)	\(177\)	\(316\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(564\)	\(221\)	\(343\)		\(540\)	\(221\)	\(319\)		\(24\)	\(0\)	\(24\)

Trace form

398 * q - 2 * q^2 - 2 * q^3 + 394 * q^4 - 8 * q^5 + 2 * q^6 - 18 * q^8 + 398 * q^9 - 4 * q^10 + 2 * q^12 - 12 * q^13 + 12 * q^14 + 4 * q^15 + 410 * q^16 - 8 * q^17 - 2 * q^18 - 8 * q^19 - 16 * q^20 - 12 * q^21 + 18 * q^24 + 386 * q^25 + 4 * q^26 - 2 * q^27 - 12 * q^29 + 8 * q^30 - 16 * q^31 - 18 * q^32 + 36 * q^34 - 16 * q^35 + 394 * q^36 - 4 * q^37 + 44 * q^38 - 4 * q^39 + 28 * q^40 - 20 * q^41 + 16 * q^42 + 8 * q^43 - 8 * q^45 + 4 * q^46 + 2 * q^48 + 390 * q^49 - 6 * q^50 + 4 * q^51 + 12 * q^52 + 16 * q^53 + 2 * q^54 + 20 * q^56 - 12 * q^57 + 4 * q^58 + 40 * q^59 + 36 * q^60 + 4 * q^61 + 466 * q^64 - 24 * q^65 - 8 * q^67 + 32 * q^68 - 4 * q^69 + 88 * q^70 + 32 * q^71 - 18 * q^72 - 20 * q^73 + 28 * q^74 + 10 * q^75 - 24 * q^76 + 44 * q^78 - 32 * q^79 + 24 * q^80 + 398 * q^81 + 20 * q^82 - 16 * q^83 - 12 * q^84 - 24 * q^85 - 28 * q^86 + 12 * q^87 - 4 * q^90 - 40 * q^91 - 80 * q^93 + 80 * q^94 + 16 * q^95 + 58 * q^96 - 60 * q^97 + 46 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8349))\) 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	23
8349.2.a.a	$8349$	$2$	8349.a	1.a	$1$	$1$	$1$	$66.667$	\(\Q\)	None	✓				69.2.a.a	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{6}+2q^{7}+3q^{8}+\cdots\)
8349.2.a.b	$8349$	$2$	8349.a	1.a	$1$	$1$	$1$	$66.667$	\(\Q\)	None	✓	✓			8349.2.a.b	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots\)
8349.2.a.c	$8349$	$2$	8349.a	1.a	$1$	$1$	$1$	$66.667$	\(\Q\)	None	✓				759.2.a.a	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-q^{6}+2q^{7}-3q^{8}+\cdots\)
8349.2.a.d	$8349$	$2$	8349.a	1.a	$1$	$1$	$1$	$66.667$	\(\Q\)	None	✓				759.2.a.b	$1$	$1$	\(1\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots\)
8349.2.a.e	$8349$	$2$	8349.a	1.a	$1$	$1$	$1$	$66.667$	\(\Q\)	None	✓	✓			8349.2.a.b	$1$	$1$	\(1\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-3q^{8}+\cdots\)
8349.2.a.f	$8349$	$2$	8349.a	1.a	$1$	$2$	$2$	$66.667$	\(\Q(\sqrt{2}) \)	None	✓				759.2.a.d	$1$	$0$	\(-2\)	\(2\)	\(4\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+2q^{5}+\cdots\)
8349.2.a.g	$8349$	$2$	8349.a	1.a	$1$	$2$	$2$	$66.667$	\(\Q(\sqrt{3}) \)	None	✓	✓			8349.2.a.g	$2$	$0$	\(0\)	\(-2\)	\(-6\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{4}-3q^{5}-\beta q^{6}+3\beta q^{7}+\cdots\)
8349.2.a.h	$8349$	$2$	8349.a	1.a	$1$	$2$	$2$	$66.667$	\(\Q(\sqrt{3}) \)	None	✓	✓			8349.2.a.h	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}+2\beta q^{7}+\cdots\)
8349.2.a.i	$8349$	$2$	8349.a	1.a	$1$	$2$	$2$	$66.667$	\(\Q(\sqrt{5}) \)	None	✓				69.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+3q^{4}+(-1-\beta )q^{5}+\cdots\)
8349.2.a.j	$8349$	$2$	8349.a	1.a	$1$	$2$	$2$	$66.667$	\(\Q(\sqrt{5}) \)	None	✓				759.2.a.c	$1$	$0$	\(1\)	\(2\)	\(-2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots\)
8349.2.a.k	$8349$	$2$	8349.a	1.a	$1$	$3$	$3$	$66.667$	3.3.148.1	None	✓				759.2.a.e	$1$	$0$	\(1\)	\(-3\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
8349.2.a.l	$8349$	$2$	8349.a	1.a	$1$	$3$	$3$	$66.667$	3.3.148.1	None	✓				759.2.a.f	$1$	$0$	\(1\)	\(3\)	\(-2\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
8349.2.a.m	$8349$	$2$	8349.a	1.a	$1$	$5$	$5$	$66.667$	5.5.1563364.1	None	✓				759.2.a.g	$1$	$0$	\(2\)	\(5\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
8349.2.a.n	$8349$	$2$	8349.a	1.a	$1$	$6$	$6$	$66.667$	6.6.4222000.1	None	✓				759.2.a.h	$1$	$1$	\(-2\)	\(-6\)	\(6\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots\)
8349.2.a.o	$8349$	$2$	8349.a	1.a	$1$	$6$	$6$	$66.667$	6.6.199374400.1	None	✓	✓			8349.2.a.o	$2$	$1$	\(0\)	\(-6\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
8349.2.a.p	$8349$	$2$	8349.a	1.a	$1$	$6$	$6$	$66.667$	6.6.3356224.1	None	✓	✓			8349.2.a.p	$2$	$1$	\(0\)	\(6\)	\(-8\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
8349.2.a.q	$8349$	$2$	8349.a	1.a	$1$	$7$	$7$	$66.667$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			8349.2.a.q	$1$	$1$	\(-2\)	\(7\)	\(-9\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+q^{3}+(1-\beta _{4}-\beta _{6})q^{4}+(-2+\cdots)q^{5}+\cdots\)
8349.2.a.r	$8349$	$2$	8349.a	1.a	$1$	$7$	$7$	$66.667$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			8349.2.a.r	$1$	$1$	\(-1\)	\(-7\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}-\beta _{5}q^{5}+\beta _{1}q^{6}+\cdots\)
8349.2.a.s	$8349$	$2$	8349.a	1.a	$1$	$7$	$7$	$66.667$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			8349.2.a.r	$1$	$1$	\(1\)	\(-7\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}-\beta _{5}q^{5}-\beta _{1}q^{6}+\cdots\)
8349.2.a.t	$8349$	$2$	8349.a	1.a	$1$	$7$	$7$	$66.667$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			8349.2.a.q	$1$	$1$	\(2\)	\(7\)	\(-9\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+q^{3}+(1-\beta _{4}-\beta _{6})q^{4}+(-2+\cdots)q^{5}+\cdots\)
8349.2.a.u	$8349$	$2$	8349.a	1.a	$1$	$8$	$8$	$66.667$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				759.2.a.i	$1$	$0$	\(-2\)	\(-8\)	\(6\)	\(6\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{4}+\cdots)q^{5}+\cdots\)
8349.2.a.v	$8349$	$2$	8349.a	1.a	$1$	$8$	$8$	$66.667$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				759.2.a.j	$1$	$1$	\(-2\)	\(8\)	\(0\)	\(-6\)		$-$	$-$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)
8349.2.a.w	$8349$	$2$	8349.a	1.a	$1$	$8$	$8$	$66.667$	8.8.\(\cdots\).1	None	✓	✓			8349.2.a.w	$2$	$0$	\(0\)	\(-8\)	\(-10\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots\)
8349.2.a.x	$8349$	$2$	8349.a	1.a	$1$	$10$	$10$	$66.667$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			8349.2.a.x	$2$	$0$	\(0\)	\(10\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$2\cdot 5$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
8349.2.a.y	$8349$	$2$	8349.a	1.a	$1$	$11$	$11$	$66.667$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓			8349.2.a.y	$1$	$0$	\(-1\)	\(-11\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
8349.2.a.z	$8349$	$2$	8349.a	1.a	$1$	$11$	$11$	$66.667$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓			8349.2.a.y	$1$	$0$	\(1\)	\(-11\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
8349.2.a.ba	$8349$	$2$	8349.a	1.a	$1$	$12$	$12$	$66.667$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			8349.2.a.ba	$1$	$0$	\(-1\)	\(12\)	\(4\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
8349.2.a.bb	$8349$	$2$	8349.a	1.a	$1$	$12$	$12$	$66.667$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			8349.2.a.bb	$2$	$0$	\(0\)	\(-12\)	\(14\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{6})q^{2}-q^{3}+(1+\beta _{3}+\beta _{7}+\cdots)q^{4}+\cdots\)
8349.2.a.bc	$8349$	$2$	8349.a	1.a	$1$	$12$	$12$	$66.667$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			8349.2.a.bc	$2$	$0$	\(0\)	\(-12\)	\(-4\)	\(0\)		$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
8349.2.a.bd	$8349$	$2$	8349.a	1.a	$1$	$12$	$12$	$66.667$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			8349.2.a.bd	$2$	$1$	\(0\)	\(12\)	\(-10\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-1-\beta _{6}+\cdots)q^{5}+\cdots\)
8349.2.a.be	$8349$	$2$	8349.a	1.a	$1$	$12$	$12$	$66.667$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			8349.2.a.ba	$1$	$0$	\(1\)	\(12\)	\(4\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
8349.2.a.bf	$8349$	$2$	8349.a	1.a	$1$	$14$	$14$	$66.667$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓			8349.2.a.bf	$2$	$1$	\(0\)	\(-14\)	\(6\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(\beta _{5}-\beta _{6})q^{4}-\beta _{6}q^{5}+\cdots\)
8349.2.a.bg	$8349$	$2$	8349.a	1.a	$1$	$20$	$20$	$66.667$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓			8349.2.a.bg	$2$	$0$	\(0\)	\(20\)	\(14\)	\(0\)		$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots\)
8349.2.a.bh	$8349$	$2$	8349.a	1.a	$1$	$22$	$22$	$66.667$		None	✓		✓		759.2.i.d	$1$	$1$	\(-10\)	\(22\)	\(1\)	\(-7\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
8349.2.a.bi	$8349$	$2$	8349.a	1.a	$1$	$22$	$22$	$66.667$		None	✓		✓		759.2.i.a	$1$	$1$	\(-6\)	\(22\)	\(1\)	\(-9\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
8349.2.a.bj	$8349$	$2$	8349.a	1.a	$1$	$22$	$22$	$66.667$		None	✓		✓		759.2.i.b	$1$	$1$	\(-2\)	\(-22\)	\(-1\)	\(-9\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
8349.2.a.bk	$8349$	$2$	8349.a	1.a	$1$	$22$	$22$	$66.667$		None	✓		✓		759.2.i.c	$1$	$0$	\(-2\)	\(-22\)	\(-1\)	\(7\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
8349.2.a.bl	$8349$	$2$	8349.a	1.a	$1$	$22$	$22$	$66.667$		None	✓		✓		759.2.i.c	$1$	$1$	\(2\)	\(-22\)	\(-1\)	\(-7\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8349.2.a.bm	$8349$	$2$	8349.a	1.a	$1$	$22$	$22$	$66.667$		None	✓		✓		759.2.i.b	$1$	$0$	\(2\)	\(-22\)	\(-1\)	\(9\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8349.2.a.bn	$8349$	$2$	8349.a	1.a	$1$	$22$	$22$	$66.667$		None	✓		✓		759.2.i.a	$1$	$0$	\(6\)	\(22\)	\(1\)	\(9\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
8349.2.a.bo	$8349$	$2$	8349.a	1.a	$1$	$22$	$22$	$66.667$		None	✓		✓		759.2.i.d	$1$	$0$	\(10\)	\(22\)	\(1\)	\(7\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8349))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8349)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(253))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(759))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2783))\)\(^{\oplus 2}\)