Space of modular forms of level 1950, weight 4, and trivial character

• Label: 1950.4.a
• Level: $1950$
• Weight: $4$
• Character orbit: 1950.a
• Rep. character: $\chi_{1950}(1,\cdot)$
• Character field: $\Q$
• Dimension: $114$
• Newform subspaces: $47$
• Sturm bound: $1680$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1950.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 47 \)
Sturm bound:			\(1680\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1950))\).

	Total	New	Old
Modular forms	1284	114	1170
Cusp forms	1236	114	1122
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.

\(2\)	\(3\)	\(5\)	\(13\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(87\)	\(8\)	\(79\)		\(84\)	\(8\)	\(76\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(75\)	\(5\)	\(70\)		\(72\)	\(5\)	\(67\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(77\)	\(7\)	\(70\)		\(74\)	\(7\)	\(67\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(82\)	\(9\)	\(73\)		\(79\)	\(9\)	\(70\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(78\)	\(7\)	\(71\)		\(75\)	\(7\)	\(68\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(81\)	\(7\)	\(74\)		\(78\)	\(7\)	\(71\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(82\)	\(7\)	\(75\)		\(79\)	\(7\)	\(72\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(80\)	\(7\)	\(73\)		\(77\)	\(7\)	\(70\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(81\)	\(7\)	\(74\)		\(78\)	\(7\)	\(71\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(81\)	\(7\)	\(74\)		\(78\)	\(7\)	\(71\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(80\)	\(7\)	\(73\)		\(77\)	\(7\)	\(70\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(79\)	\(7\)	\(72\)		\(76\)	\(7\)	\(69\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(75\)	\(8\)	\(67\)		\(72\)	\(8\)	\(64\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(84\)	\(5\)	\(79\)		\(81\)	\(5\)	\(76\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(82\)	\(7\)	\(75\)		\(79\)	\(7\)	\(72\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(80\)	\(9\)	\(71\)		\(77\)	\(9\)	\(68\)		\(3\)	\(0\)	\(3\)
Plus space				\(+\)		\(648\)	\(62\)	\(586\)		\(624\)	\(62\)	\(562\)		\(24\)	\(0\)	\(24\)
Minus space				\(-\)		\(636\)	\(52\)	\(584\)		\(612\)	\(52\)	\(560\)		\(24\)	\(0\)	\(24\)

Trace form

114 * q + 456 * q^4 + 12 * q^6 - 4 * q^7 + 1026 * q^9 - 112 * q^11 - 26 * q^13 - 40 * q^14 + 1824 * q^16 - 388 * q^17 - 4 * q^19 + 84 * q^21 + 32 * q^22 + 248 * q^23 + 48 * q^24 - 16 * q^28 + 780 * q^29 - 164 * q^31 - 336 * q^33 + 32 * q^34 + 4104 * q^36 - 276 * q^37 + 328 * q^38 - 648 * q^41 - 456 * q^42 - 80 * q^43 - 448 * q^44 - 144 * q^46 - 608 * q^47 + 5306 * q^49 + 576 * q^51 - 104 * q^52 - 1132 * q^53 + 108 * q^54 - 160 * q^56 - 156 * q^57 - 160 * q^58 - 1368 * q^59 - 460 * q^61 + 440 * q^62 - 36 * q^63 + 7296 * q^64 - 240 * q^66 - 532 * q^67 - 1552 * q^68 + 24 * q^69 - 1000 * q^71 + 1788 * q^73 - 272 * q^74 - 16 * q^76 - 2400 * q^77 - 156 * q^78 - 2256 * q^79 + 9234 * q^81 - 936 * q^82 - 1944 * q^83 + 336 * q^84 + 2544 * q^86 - 96 * q^87 + 128 * q^88 + 4224 * q^89 - 260 * q^91 + 992 * q^92 + 684 * q^93 + 1408 * q^94 + 192 * q^96 + 2012 * q^97 - 4000 * q^98 - 1008 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1950))\) 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	5	13
1950.4.a.a	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				78.4.a.f	$1$	$1$	\(-2\)	\(-3\)	\(0\)	\(-4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}-4q^{7}+\cdots\)
1950.4.a.b	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				390.4.a.k	$1$	$0$	\(-2\)	\(-3\)	\(0\)	\(28\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+28q^{7}+\cdots\)
1950.4.a.c	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				78.4.a.e	$1$	$1$	\(-2\)	\(3\)	\(0\)	\(-20\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}-20q^{7}+\cdots\)
1950.4.a.d	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				390.4.a.h	$1$	$0$	\(-2\)	\(3\)	\(0\)	\(-8\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}-8q^{7}+\cdots\)
1950.4.a.e	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				390.4.a.i	$1$	$1$	\(-2\)	\(3\)	\(0\)	\(-8\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}-8q^{7}+\cdots\)
1950.4.a.f	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				390.4.a.j	$1$	$1$	\(-2\)	\(3\)	\(0\)	\(12\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+12q^{7}+\cdots\)
1950.4.a.g	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				390.4.a.g	$1$	$1$	\(-2\)	\(3\)	\(0\)	\(25\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+5^{2}q^{7}+\cdots\)
1950.4.a.h	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				78.4.a.d	$1$	$0$	\(-2\)	\(3\)	\(0\)	\(32\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+2^{5}q^{7}+\cdots\)
1950.4.a.i	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				390.4.a.e	$1$	$1$	\(2\)	\(-3\)	\(0\)	\(-24\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}-24q^{7}+\cdots\)
1950.4.a.j	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				390.4.a.d	$1$	$1$	\(2\)	\(-3\)	\(0\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}-2q^{7}+\cdots\)
1950.4.a.k	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				78.4.a.b	$1$	$0$	\(2\)	\(-3\)	\(0\)	\(8\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+8q^{7}+\cdots\)
1950.4.a.l	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				78.4.a.c	$1$	$1$	\(2\)	\(-3\)	\(0\)	\(8\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+8q^{7}+\cdots\)
1950.4.a.m	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				390.4.a.f	$1$	$1$	\(2\)	\(-3\)	\(0\)	\(13\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+13q^{7}+\cdots\)
1950.4.a.n	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				390.4.a.c	$1$	$0$	\(2\)	\(-3\)	\(0\)	\(15\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+15q^{7}+\cdots\)
1950.4.a.o	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				78.4.a.a	$1$	$1$	\(2\)	\(3\)	\(0\)	\(-28\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}-28q^{7}+\cdots\)
1950.4.a.p	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				390.4.a.b	$1$	$1$	\(2\)	\(3\)	\(0\)	\(-5\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}-5q^{7}+\cdots\)
1950.4.a.q	$1950$	$4$	1950.a	1.a	$1$	$1$	$1$	$115.054$	\(\Q\)	None	✓				390.4.a.a	$1$	$1$	\(2\)	\(3\)	\(0\)	\(14\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+14q^{7}+\cdots\)
1950.4.a.r	$1950$	$4$	1950.a	1.a	$1$	$2$	$2$	$115.054$	\(\Q(\sqrt{2193}) \)	None	✓				390.4.a.p	$1$	$1$	\(-4\)	\(-6\)	\(0\)	\(-25\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(-12+\cdots)q^{7}+\cdots\)
1950.4.a.s	$1950$	$4$	1950.a	1.a	$1$	$2$	$2$	$115.054$	\(\Q(\sqrt{6}) \)	None	✓	✓			1950.4.a.s	$1$	$1$	\(-4\)	\(-6\)	\(0\)	\(14\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(7+\beta )q^{7}+\cdots\)
1950.4.a.t	$1950$	$4$	1950.a	1.a	$1$	$2$	$2$	$115.054$	\(\Q(\sqrt{31}) \)	None	✓	✓			1950.4.a.t	$1$	$1$	\(-4\)	\(-6\)	\(0\)	\(24\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(12+\beta )q^{7}+\cdots\)
1950.4.a.u	$1950$	$4$	1950.a	1.a	$1$	$2$	$2$	$115.054$	\(\Q(\sqrt{2081}) \)	None	✓				390.4.a.o	$1$	$0$	\(-4\)	\(6\)	\(0\)	\(-27\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(-13+\cdots)q^{7}+\cdots\)
1950.4.a.v	$1950$	$4$	1950.a	1.a	$1$	$2$	$2$	$115.054$	\(\Q(\sqrt{139}) \)	None	✓				390.4.a.n	$1$	$0$	\(4\)	\(-6\)	\(0\)	\(12\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(6+\beta )q^{7}+\cdots\)
1950.4.a.w	$1950$	$4$	1950.a	1.a	$1$	$2$	$2$	$115.054$	\(\Q(\sqrt{31}) \)	None	✓	✓	✓		1950.4.a.t	$1$	$1$	\(4\)	\(6\)	\(0\)	\(-24\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+(-12+\cdots)q^{7}+\cdots\)
1950.4.a.x	$1950$	$4$	1950.a	1.a	$1$	$2$	$2$	$115.054$	\(\Q(\sqrt{6}) \)	None	✓	✓			1950.4.a.s	$1$	$1$	\(4\)	\(6\)	\(0\)	\(-14\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+(-7+\cdots)q^{7}+\cdots\)
1950.4.a.y	$1950$	$4$	1950.a	1.a	$1$	$2$	$2$	$115.054$	\(\Q(\sqrt{129}) \)	None	✓				390.4.a.m	$1$	$0$	\(4\)	\(6\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+(-2+\cdots)q^{7}+\cdots\)
1950.4.a.z	$1950$	$4$	1950.a	1.a	$1$	$2$	$2$	$115.054$	\(\Q(\sqrt{1249}) \)	None	✓				390.4.a.l	$1$	$0$	\(4\)	\(6\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+\beta q^{7}+\cdots\)
1950.4.a.ba	$1950$	$4$	1950.a	1.a	$1$	$3$	$3$	$115.054$	3.3.2340721.1	None	✓				390.4.a.q	$1$	$0$	\(-6\)	\(-9\)	\(0\)	\(-17\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(-6+\cdots)q^{7}+\cdots\)
1950.4.a.bb	$1950$	$4$	1950.a	1.a	$1$	$3$	$3$	$115.054$	3.3.37940.1	None	✓	✓			1950.4.a.bb	$1$	$1$	\(-6\)	\(9\)	\(0\)	\(-5\)		$+$	$-$	$-$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(-1+\cdots)q^{7}+\cdots\)
1950.4.a.bc	$1950$	$4$	1950.a	1.a	$1$	$3$	$3$	$115.054$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓		1950.4.a.bc	$1$	$0$	\(-6\)	\(9\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(-1+\cdots)q^{7}+\cdots\)
1950.4.a.bd	$1950$	$4$	1950.a	1.a	$1$	$3$	$3$	$115.054$	3.3.1718836.1	None	✓	✓	✓		1950.4.a.bd	$1$	$1$	\(-6\)	\(9\)	\(0\)	\(5\)		$+$	$-$	$+$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(2+\beta _{2})q^{7}+\cdots\)
1950.4.a.be	$1950$	$4$	1950.a	1.a	$1$	$3$	$3$	$115.054$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓			1950.4.a.be	$1$	$0$	\(-6\)	\(9\)	\(0\)	\(12\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(4-\beta _{1}+\cdots)q^{7}+\cdots\)
1950.4.a.bf	$1950$	$4$	1950.a	1.a	$1$	$3$	$3$	$115.054$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓		1950.4.a.be	$1$	$0$	\(6\)	\(-9\)	\(0\)	\(-12\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(-4+\cdots)q^{7}+\cdots\)
1950.4.a.bg	$1950$	$4$	1950.a	1.a	$1$	$3$	$3$	$115.054$	3.3.1718836.1	None	✓	✓			1950.4.a.bd	$1$	$1$	\(6\)	\(-9\)	\(0\)	\(-5\)		$-$	$+$	$-$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(-2+\cdots)q^{7}+\cdots\)
1950.4.a.bh	$1950$	$4$	1950.a	1.a	$1$	$3$	$3$	$115.054$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓			1950.4.a.bc	$1$	$0$	\(6\)	\(-9\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
1950.4.a.bi	$1950$	$4$	1950.a	1.a	$1$	$3$	$3$	$115.054$	3.3.37940.1	None	✓	✓	✓		1950.4.a.bb	$1$	$1$	\(6\)	\(-9\)	\(0\)	\(5\)		$-$	$+$	$+$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
1950.4.a.bj	$1950$	$4$	1950.a	1.a	$1$	$4$	$4$	$115.054$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓			1950.4.a.bj	$1$	$0$	\(-8\)	\(-12\)	\(0\)	\(-21\)		$+$	$+$	$-$	$-$	$+$	$3$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(-5+\cdots)q^{7}+\cdots\)
1950.4.a.bk	$1950$	$4$	1950.a	1.a	$1$	$4$	$4$	$115.054$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	✓		1950.4.a.bk	$1$	$0$	\(-8\)	\(-12\)	\(0\)	\(-7\)		$+$	$+$	$+$	$+$	$+$	$3^{3}$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(-2+\cdots)q^{7}+\cdots\)
1950.4.a.bl	$1950$	$4$	1950.a	1.a	$1$	$4$	$4$	$115.054$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓		✓		390.4.e.a	$1$	$1$	\(-8\)	\(12\)	\(0\)	\(-1\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
1950.4.a.bm	$1950$	$4$	1950.a	1.a	$1$	$4$	$4$	$115.054$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓		✓		390.4.e.b	$1$	$0$	\(-8\)	\(12\)	\(0\)	\(15\)		$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(3-\beta _{1}+\cdots)q^{7}+\cdots\)
1950.4.a.bn	$1950$	$4$	1950.a	1.a	$1$	$4$	$4$	$115.054$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓		✓		390.4.e.b	$1$	$1$	\(8\)	\(-12\)	\(0\)	\(-15\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(-3+\cdots)q^{7}+\cdots\)
1950.4.a.bo	$1950$	$4$	1950.a	1.a	$1$	$4$	$4$	$115.054$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓		✓		390.4.e.a	$1$	$0$	\(8\)	\(-12\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(\beta _{2}-\beta _{3})q^{7}+\cdots\)
1950.4.a.bp	$1950$	$4$	1950.a	1.a	$1$	$4$	$4$	$115.054$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓			1950.4.a.bk	$1$	$0$	\(8\)	\(12\)	\(0\)	\(7\)		$-$	$-$	$-$	$-$	$+$	$3^{3}$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
1950.4.a.bq	$1950$	$4$	1950.a	1.a	$1$	$4$	$4$	$115.054$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	✓		1950.4.a.bj	$1$	$0$	\(8\)	\(12\)	\(0\)	\(21\)		$-$	$-$	$+$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+(5+\beta _{1}+\cdots)q^{7}+\cdots\)
1950.4.a.br	$1950$	$4$	1950.a	1.a	$1$	$5$	$5$	$115.054$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		390.4.e.d	$1$	$1$	\(-10\)	\(-15\)	\(0\)	\(-41\)		$+$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(-8+\cdots)q^{7}+\cdots\)
1950.4.a.bs	$1950$	$4$	1950.a	1.a	$1$	$5$	$5$	$115.054$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		390.4.e.c	$1$	$0$	\(-10\)	\(-15\)	\(0\)	\(27\)		$+$	$+$	$-$	$-$	$+$	$2^{2}\cdot 5$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(6-\beta _{1}+\cdots)q^{7}+\cdots\)
1950.4.a.bt	$1950$	$4$	1950.a	1.a	$1$	$5$	$5$	$115.054$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		390.4.e.c	$1$	$1$	\(10\)	\(15\)	\(0\)	\(-27\)		$-$	$-$	$-$	$+$	$-$	$2^{2}\cdot 5$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+(-6+\cdots)q^{7}+\cdots\)
1950.4.a.bu	$1950$	$4$	1950.a	1.a	$1$	$5$	$5$	$115.054$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		390.4.e.d	$1$	$0$	\(10\)	\(15\)	\(0\)	\(41\)		$-$	$-$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+(8-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1950))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1950)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(325))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(390))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(650))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(975))\)\(^{\oplus 2}\)