Space of modular forms of level 4719, weight 2, and trivial character

• Label: 4719.2.a
• Level: $4719$
• Weight: $2$
• Character orbit: 4719.a
• Rep. character: $\chi_{4719}(1,\cdot)$
• Character field: $\Q$
• Dimension: $218$
• Newform subspaces: $44$
• Sturm bound: $1232$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 4719 = 3 \cdot 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4719.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 44 \)
Sturm bound:			\(1232\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4719))\).

	Total	New	Old
Modular forms	640	218	422
Cusp forms	593	218	375
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.

\(3\)	\(11\)	\(13\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(72\)	\(25\)	\(47\)		\(67\)	\(25\)	\(42\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(84\)	\(29\)	\(55\)		\(78\)	\(29\)	\(49\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(86\)	\(30\)	\(56\)		\(80\)	\(30\)	\(50\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(78\)	\(25\)	\(53\)		\(72\)	\(25\)	\(47\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(88\)	\(33\)	\(55\)		\(82\)	\(33\)	\(49\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(76\)	\(21\)	\(55\)		\(70\)	\(21\)	\(49\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(74\)	\(20\)	\(54\)		\(68\)	\(20\)	\(48\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(82\)	\(35\)	\(47\)		\(76\)	\(35\)	\(41\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(300\)	\(91\)	\(209\)		\(277\)	\(91\)	\(186\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(340\)	\(127\)	\(213\)		\(316\)	\(127\)	\(189\)		\(24\)	\(0\)	\(24\)

Trace form

218 * q + 4 * q^2 + 218 * q^4 + 4 * q^5 - 2 * q^6 + 12 * q^7 + 218 * q^9 - 8 * q^10 + 4 * q^12 + 2 * q^13 - 4 * q^14 + 222 * q^16 + 4 * q^17 + 4 * q^18 - 4 * q^19 + 4 * q^20 + 4 * q^21 + 16 * q^23 - 6 * q^24 + 238 * q^25 + 12 * q^28 + 4 * q^29 - 4 * q^30 - 20 * q^31 + 4 * q^32 - 24 * q^34 - 32 * q^35 + 218 * q^36 + 28 * q^37 - 4 * q^38 + 4 * q^39 - 20 * q^41 + 12 * q^42 + 4 * q^45 + 32 * q^46 - 4 * q^47 - 8 * q^48 + 250 * q^49 + 44 * q^50 + 10 * q^52 + 20 * q^53 - 2 * q^54 - 4 * q^56 + 20 * q^57 + 8 * q^58 - 28 * q^59 + 20 * q^61 - 36 * q^62 + 12 * q^63 + 250 * q^64 - 4 * q^65 - 20 * q^67 + 44 * q^68 - 8 * q^69 + 32 * q^70 - 20 * q^71 + 12 * q^73 + 56 * q^74 + 8 * q^75 - 36 * q^76 - 2 * q^78 - 16 * q^79 + 116 * q^80 + 218 * q^81 + 88 * q^82 - 28 * q^83 + 44 * q^84 + 48 * q^85 + 64 * q^86 + 36 * q^89 - 8 * q^90 - 4 * q^91 + 88 * q^92 + 20 * q^93 + 52 * q^94 - 64 * q^95 - 34 * q^96 + 20 * q^97 + 20 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4719))\) 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	13
4719.2.a.a	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	\(\Q\)	None	✓	✓			4719.2.a.a	$1$	$0$	\(-2\)	\(-1\)	\(0\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+3q^{7}+\cdots\)
4719.2.a.b	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	\(\Q\)	None	✓	✓			4719.2.a.b	$1$	$1$	\(-2\)	\(1\)	\(-2\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-2q^{5}-2q^{6}+\cdots\)
4719.2.a.c	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	\(\Q\)	None	✓				39.2.a.a	$1$	$0$	\(-1\)	\(-1\)	\(2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
4719.2.a.d	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	\(\Q\)	None	✓	✓			4719.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+2q^{5}-5q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.e	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	\(\Q\)	None	✓	✓			4719.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+2q^{5}-3q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.f	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	\(\Q\)	None	✓	✓			4719.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+2q^{5}+3q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.g	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	\(\Q\)	None	✓	✓			4719.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+2q^{5}+5q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.h	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	\(\Q\)	None	✓	✓			4719.2.a.h	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{7}+q^{9}-2q^{12}+q^{13}+\cdots\)
4719.2.a.i	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	\(\Q\)	None	✓	✓			4719.2.a.h	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{7}+q^{9}-2q^{12}-q^{13}+\cdots\)
4719.2.a.j	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	\(\Q\)	None	✓				429.2.a.a	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
4719.2.a.k	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	\(\Q\)	None	✓				429.2.a.b	$1$	$1$	\(1\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots\)
4719.2.a.l	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	\(\Q\)	None	✓	✓			4719.2.a.a	$1$	$1$	\(2\)	\(-1\)	\(0\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots\)
4719.2.a.m	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	\(\Q\)	None	✓	✓			4719.2.a.b	$1$	$0$	\(2\)	\(1\)	\(-2\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}-2q^{5}+2q^{6}+\cdots\)
4719.2.a.n	$4719$	$2$	4719.a	1.a	$1$	$2$	$2$	$37.681$	\(\Q(\sqrt{3}) \)	None	✓				429.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
4719.2.a.o	$4719$	$2$	4719.a	1.a	$1$	$2$	$2$	$37.681$	\(\Q(\sqrt{2}) \)	None	✓				429.2.a.c	$1$	$0$	\(2\)	\(2\)	\(-4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
4719.2.a.p	$4719$	$2$	4719.a	1.a	$1$	$2$	$2$	$37.681$	\(\Q(\sqrt{2}) \)	None	✓				39.2.a.b	$1$	$0$	\(2\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+2\beta q^{5}+\cdots\)
4719.2.a.q	$4719$	$2$	4719.a	1.a	$1$	$3$	$3$	$37.681$	3.3.148.1	None	✓				429.2.a.g	$1$	$0$	\(-3\)	\(3\)	\(4\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4719.2.a.r	$4719$	$2$	4719.a	1.a	$1$	$3$	$3$	$37.681$	3.3.321.1	None	✓	✓			4719.2.a.r	$1$	$1$	\(-2\)	\(-3\)	\(-5\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}-q^{3}+(3-\beta _{1})q^{4}+\cdots\)
4719.2.a.s	$4719$	$2$	4719.a	1.a	$1$	$3$	$3$	$37.681$	3.3.169.1	None	✓	✓			4719.2.a.s	$1$	$0$	\(-2\)	\(3\)	\(3\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4719.2.a.t	$4719$	$2$	4719.a	1.a	$1$	$3$	$3$	$37.681$	3.3.148.1	None	✓				429.2.a.f	$1$	$1$	\(-1\)	\(3\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots\)
4719.2.a.u	$4719$	$2$	4719.a	1.a	$1$	$3$	$3$	$37.681$	3.3.564.1	None	✓				429.2.a.e	$1$	$1$	\(1\)	\(-3\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
4719.2.a.v	$4719$	$2$	4719.a	1.a	$1$	$3$	$3$	$37.681$	3.3.321.1	None	✓	✓			4719.2.a.r	$1$	$0$	\(2\)	\(-3\)	\(-5\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}-q^{3}+(3-\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.w	$4719$	$2$	4719.a	1.a	$1$	$3$	$3$	$37.681$	3.3.169.1	None	✓	✓			4719.2.a.s	$1$	$1$	\(2\)	\(3\)	\(3\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4719.2.a.x	$4719$	$2$	4719.a	1.a	$1$	$4$	$4$	$37.681$	4.4.2777.1	None	✓	✓			4719.2.a.x	$1$	$1$	\(-2\)	\(-4\)	\(-3\)	\(5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\cdots\)
4719.2.a.y	$4719$	$2$	4719.a	1.a	$1$	$4$	$4$	$37.681$	4.4.2777.1	None	✓	✓			4719.2.a.x	$1$	$0$	\(2\)	\(-4\)	\(-3\)	\(-5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\cdots\)
4719.2.a.z	$4719$	$2$	4719.a	1.a	$1$	$4$	$4$	$37.681$	4.4.8468.1	None	✓				429.2.a.h	$1$	$0$	\(2\)	\(-4\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-q^{3}+(2-\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots\)
4719.2.a.ba	$4719$	$2$	4719.a	1.a	$1$	$5$	$5$	$37.681$	5.5.210557.1	None	✓	✓			4719.2.a.ba	$1$	$1$	\(-2\)	\(5\)	\(3\)	\(-6\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
4719.2.a.bb	$4719$	$2$	4719.a	1.a	$1$	$5$	$5$	$37.681$	5.5.394064.1	None	✓	✓			4719.2.a.bb	$1$	$1$	\(-1\)	\(-5\)	\(2\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
4719.2.a.bc	$4719$	$2$	4719.a	1.a	$1$	$5$	$5$	$37.681$	5.5.303952.1	None	✓	✓			4719.2.a.bc	$1$	$1$	\(-1\)	\(5\)	\(-2\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bd	$4719$	$2$	4719.a	1.a	$1$	$5$	$5$	$37.681$	5.5.394064.1	None	✓	✓			4719.2.a.bb	$1$	$0$	\(1\)	\(-5\)	\(2\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
4719.2.a.be	$4719$	$2$	4719.a	1.a	$1$	$5$	$5$	$37.681$	5.5.303952.1	None	✓	✓			4719.2.a.bc	$1$	$0$	\(1\)	\(5\)	\(-2\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bf	$4719$	$2$	4719.a	1.a	$1$	$5$	$5$	$37.681$	5.5.210557.1	None	✓	✓			4719.2.a.ba	$1$	$0$	\(2\)	\(5\)	\(3\)	\(6\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
4719.2.a.bg	$4719$	$2$	4719.a	1.a	$1$	$6$	$6$	$37.681$	6.6.966125.1	None	✓				429.2.n.a	$1$	$1$	\(-1\)	\(6\)	\(-6\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(-1+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
4719.2.a.bh	$4719$	$2$	4719.a	1.a	$1$	$6$	$6$	$37.681$	6.6.966125.1	None	✓		✓		429.2.n.a	$1$	$1$	\(1\)	\(6\)	\(-6\)	\(5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
4719.2.a.bi	$4719$	$2$	4719.a	1.a	$1$	$10$	$10$	$37.681$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		429.2.n.b	$1$	$1$	\(-3\)	\(-10\)	\(-8\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bj	$4719$	$2$	4719.a	1.a	$1$	$10$	$10$	$37.681$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			4719.2.a.bj	$1$	$1$	\(-2\)	\(-10\)	\(4\)	\(4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
4719.2.a.bk	$4719$	$2$	4719.a	1.a	$1$	$10$	$10$	$37.681$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓		4719.2.a.bk	$1$	$1$	\(-2\)	\(10\)	\(-4\)	\(-12\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
4719.2.a.bl	$4719$	$2$	4719.a	1.a	$1$	$10$	$10$	$37.681$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			4719.2.a.bj	$1$	$0$	\(2\)	\(-10\)	\(4\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
4719.2.a.bm	$4719$	$2$	4719.a	1.a	$1$	$10$	$10$	$37.681$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			4719.2.a.bk	$1$	$0$	\(2\)	\(10\)	\(-4\)	\(12\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
4719.2.a.bn	$4719$	$2$	4719.a	1.a	$1$	$10$	$10$	$37.681$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				429.2.n.b	$1$	$1$	\(3\)	\(-10\)	\(-8\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bo	$4719$	$2$	4719.a	1.a	$1$	$14$	$14$	$37.681$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓		✓		429.2.n.c	$1$	$0$	\(-3\)	\(-14\)	\(8\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots\)
4719.2.a.bp	$4719$	$2$	4719.a	1.a	$1$	$14$	$14$	$37.681$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓		✓		429.2.n.c	$1$	$0$	\(3\)	\(-14\)	\(8\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots\)
4719.2.a.bq	$4719$	$2$	4719.a	1.a	$1$	$18$	$18$	$37.681$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓		✓		429.2.n.d	$1$	$0$	\(-1\)	\(18\)	\(10\)	\(-7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots\)
4719.2.a.br	$4719$	$2$	4719.a	1.a	$1$	$18$	$18$	$37.681$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓		✓		429.2.n.d	$1$	$0$	\(1\)	\(18\)	\(10\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4719))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4719)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(429))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1573))\)\(^{\oplus 2}\)