Space of modular forms of level 1936, weight 4, and trivial character

• Label: 1936.4.a
• Level: $1936$
• Weight: $4$
• Character orbit: 1936.a
• Rep. character: $\chi_{1936}(1,\cdot)$
• Character field: $\Q$
• Dimension: $159$
• Newform subspaces: $51$
• Sturm bound: $1056$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1936 = 2^{4} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1936.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 51 \)
Sturm bound:			\(1056\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1936))\).

	Total	New	Old
Modular forms	828	168	660
Cusp forms	756	159	597
Eisenstein series	72	9	63

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(42\)
\(+\)	\(-\)	\(-\)	\(40\)
\(-\)	\(+\)	\(-\)	\(37\)
\(-\)	\(-\)	\(+\)	\(40\)
Plus space		\(+\)	\(82\)
Minus space		\(-\)	\(77\)

Trace form

\( 159 q + 2 q^{3} - 12 q^{7} + 1361 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1936))\) 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	11
1936.4.a.a	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓				121.4.a.a	$2$	$1$	\(0\)	\(-8\)	\(18\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-8q^{3}+18q^{5}+37q^{9}-12^{2}q^{15}+\cdots\)
1936.4.a.b	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	\(\Q\)	None	✓				88.4.a.b	$1$	$1$	\(0\)	\(-7\)	\(9\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-7q^{3}+9q^{5}+2q^{7}+22q^{9}-63q^{15}+\cdots\)
1936.4.a.c	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	\(\Q\)	None	✓				242.4.a.c	$1$	$1$	\(0\)	\(-5\)	\(-15\)	\(-36\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{3}-15q^{5}-6^{2}q^{7}-2q^{9}-12q^{13}+\cdots\)
1936.4.a.d	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	\(\Q\)	None	✓				242.4.a.c	$1$	$1$	\(0\)	\(-5\)	\(-15\)	\(36\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{3}-15q^{5}+6^{2}q^{7}-2q^{9}+12q^{13}+\cdots\)
1936.4.a.e	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	\(\Q\)	None	✓				242.4.a.b	$1$	$0$	\(0\)	\(-4\)	\(3\)	\(-8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}+3q^{5}-8q^{7}-11q^{9}+83q^{13}+\cdots\)
1936.4.a.f	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	\(\Q\)	None	✓				242.4.a.b	$1$	$0$	\(0\)	\(-4\)	\(3\)	\(8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}+3q^{5}+8q^{7}-11q^{9}-83q^{13}+\cdots\)
1936.4.a.g	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	\(\Q\)	None	✓				22.4.a.b	$1$	$0$	\(0\)	\(-4\)	\(14\)	\(-8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}+14q^{5}-8q^{7}-11q^{9}+50q^{13}+\cdots\)
1936.4.a.h	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	\(\Q\)	None	✓				22.4.a.c	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(-10\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-10q^{7}-26q^{9}+2^{4}q^{13}+\cdots\)
1936.4.a.i	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	\(\Q\)	None	✓				88.4.a.a	$1$	$1$	\(0\)	\(1\)	\(-7\)	\(-6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-7q^{5}-6q^{7}-26q^{9}+40q^{13}+\cdots\)
1936.4.a.j	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	\(\Q\)	None	✓				968.4.a.b	$1$	$1$	\(0\)	\(2\)	\(13\)	\(-10\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+13q^{5}-10q^{7}-23q^{9}-3^{3}q^{13}+\cdots\)
1936.4.a.k	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	\(\Q\)	None	✓				968.4.a.b	$1$	$1$	\(0\)	\(2\)	\(13\)	\(10\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+13q^{5}+10q^{7}-23q^{9}+3^{3}q^{13}+\cdots\)
1936.4.a.l	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	\(\Q\)	None	✓				8.4.a.a	$1$	$1$	\(0\)	\(4\)	\(-2\)	\(24\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{3}-2q^{5}+24q^{7}-11q^{9}-22q^{13}+\cdots\)
1936.4.a.m	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	\(\Q\)	None	✓				44.4.a.a	$1$	$0$	\(0\)	\(5\)	\(-7\)	\(-26\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+5q^{3}-7q^{5}-26q^{7}-2q^{9}-52q^{13}+\cdots\)
1936.4.a.n	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	\(\Q\)	None	✓				22.4.a.a	$1$	$0$	\(0\)	\(7\)	\(-19\)	\(14\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+7q^{3}-19q^{5}+14q^{7}+22q^{9}+72q^{13}+\cdots\)
1936.4.a.o	$1936$	$4$	1936.a	1.a	$1$	$2$	$2$	$114.228$	\(\Q(\sqrt{97}) \)	None	✓				44.4.a.b	$1$	$0$	\(0\)	\(-9\)	\(11\)	\(10\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-4-\beta )q^{3}+(6-\beta )q^{5}+(8-6\beta )q^{7}+\cdots\)
1936.4.a.p	$1936$	$4$	1936.a	1.a	$1$	$2$	$2$	$114.228$	\(\Q(\sqrt{37}) \)	None	✓				242.4.a.j	$1$	$0$	\(0\)	\(-6\)	\(4\)	\(-42\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-3-\beta )q^{3}+(2-3\beta )q^{5}+(-21+\cdots)q^{7}+\cdots\)
1936.4.a.q	$1936$	$4$	1936.a	1.a	$1$	$2$	$2$	$114.228$	\(\Q(\sqrt{37}) \)	None	✓				242.4.a.j	$1$	$0$	\(0\)	\(-6\)	\(4\)	\(42\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-3-\beta )q^{3}+(2-3\beta )q^{5}+(21-\beta )q^{7}+\cdots\)
1936.4.a.r	$1936$	$4$	1936.a	1.a	$1$	$2$	$2$	$114.228$	\(\Q(\sqrt{3}) \)	None	✓				242.4.a.i	$1$	$1$	\(0\)	\(2\)	\(-12\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-6+7\beta )q^{5}+(-3-11\beta )q^{7}+\cdots\)
1936.4.a.s	$1936$	$4$	1936.a	1.a	$1$	$2$	$2$	$114.228$	\(\Q(\sqrt{3}) \)	None	✓				242.4.a.i	$1$	$1$	\(0\)	\(2\)	\(-12\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-6+7\beta )q^{5}+(3+11\beta )q^{7}+\cdots\)
1936.4.a.t	$1936$	$4$	1936.a	1.a	$1$	$2$	$2$	$114.228$	\(\Q(\sqrt{5}) \)	None	✓				88.4.a.c	$1$	$1$	\(0\)	\(2\)	\(-6\)	\(-56\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-3+4\beta )q^{5}+(-28+\cdots)q^{7}+\cdots\)
1936.4.a.u	$1936$	$4$	1936.a	1.a	$1$	$2$	$2$	$114.228$	\(\Q(\sqrt{3}) \)	None	✓				484.4.a.c	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-18\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+3\beta )q^{3}+3\beta q^{5}+(-9+\beta )q^{7}+\cdots\)
1936.4.a.v	$1936$	$4$	1936.a	1.a	$1$	$2$	$2$	$114.228$	\(\Q(\sqrt{3}) \)	None	✓				484.4.a.c	$1$	$1$	\(0\)	\(2\)	\(0\)	\(18\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+3\beta )q^{3}+3\beta q^{5}+(9-\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1936.4.a.w	$1936$	$4$	1936.a	1.a	$1$	$2$	$2$	$114.228$	\(\Q(\sqrt{3}) \)	None	✓				11.4.a.a	$1$	$0$	\(0\)	\(2\)	\(2\)	\(20\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(1+2\beta )q^{5}+(10-\beta )q^{7}+\cdots\)
1936.4.a.x	$1936$	$4$	1936.a	1.a	$1$	$2$	$2$	$114.228$	\(\Q(\sqrt{33}) \)	\(\Q(\sqrt{-11}) \)	✓				484.4.a.b	$2$	$1$	\(0\)	\(8\)	\(-18\)	\(0\)		$-$	$+$	$-$	$2$	$N(\mathrm{U}(1))$	\(q+(4+\beta )q^{3}+(-9-2\beta )q^{5}+(22+8\beta )q^{9}+\cdots\)
1936.4.a.y	$1936$	$4$	1936.a	1.a	$1$	$2$	$2$	$114.228$	\(\Q(\sqrt{3}) \)	None	✓				121.4.a.b	$1$	$0$	\(0\)	\(8\)	\(-10\)	\(-8\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(4+\beta )q^{3}+(-5-\beta )q^{5}+(-4+7\beta )q^{7}+\cdots\)
1936.4.a.z	$1936$	$4$	1936.a	1.a	$1$	$2$	$2$	$114.228$	\(\Q(\sqrt{3}) \)	None	✓				121.4.a.b	$1$	$0$	\(0\)	\(8\)	\(-10\)	\(8\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(4+\beta )q^{3}+(-5-\beta )q^{5}+(4-7\beta )q^{7}+\cdots\)
1936.4.a.ba	$1936$	$4$	1936.a	1.a	$1$	$2$	$2$	$114.228$	\(\Q(\sqrt{26}) \)	None	✓				121.4.a.d	$2$	$1$	\(0\)	\(10\)	\(10\)	\(0\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+5q^{3}+5q^{5}+\beta q^{7}-2q^{9}-3\beta q^{13}+\cdots\)
1936.4.a.bb	$1936$	$4$	1936.a	1.a	$1$	$2$	$2$	$114.228$	\(\Q(\sqrt{5}) \)	None	✓				22.4.c.a	$1$	$1$	\(0\)	\(13\)	\(-1\)	\(-5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(8-3\beta )q^{3}+(-1+\beta )q^{5}+(-8+11\beta )q^{7}+\cdots\)
1936.4.a.bc	$1936$	$4$	1936.a	1.a	$1$	$2$	$2$	$114.228$	\(\Q(\sqrt{5}) \)	None	✓				22.4.c.a	$1$	$0$	\(0\)	\(13\)	\(-1\)	\(5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(8-3\beta )q^{3}+(-1+\beta )q^{5}+(8-11\beta )q^{7}+\cdots\)
1936.4.a.bd	$1936$	$4$	1936.a	1.a	$1$	$3$	$3$	$114.228$	3.3.3124.1	None	✓				968.4.a.j	$1$	$1$	\(0\)	\(-6\)	\(-21\)	\(-2\)		$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{3}+(-7-\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1936.4.a.be	$1936$	$4$	1936.a	1.a	$1$	$3$	$3$	$114.228$	3.3.3124.1	None	✓				968.4.a.j	$1$	$1$	\(0\)	\(-6\)	\(-21\)	\(2\)		$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{3}+(-7-\beta _{1})q^{5}+(1+\cdots)q^{7}+\cdots\)
1936.4.a.bf	$1936$	$4$	1936.a	1.a	$1$	$3$	$3$	$114.228$	3.3.1556.1	None	✓				968.4.a.g	$1$	$1$	\(0\)	\(-2\)	\(-9\)	\(-6\)		$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(-3+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1936.4.a.bg	$1936$	$4$	1936.a	1.a	$1$	$3$	$3$	$114.228$	3.3.1556.1	None	✓				968.4.a.g	$1$	$1$	\(0\)	\(-2\)	\(-9\)	\(6\)		$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(-3+\beta _{2})q^{5}+(2+\cdots)q^{7}+\cdots\)
1936.4.a.bh	$1936$	$4$	1936.a	1.a	$1$	$3$	$3$	$114.228$	3.3.11109.1	None	✓				88.4.a.d	$1$	$1$	\(0\)	\(-2\)	\(8\)	\(24\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(3+\beta _{2})q^{5}+(8-\beta _{1}+\cdots)q^{7}+\cdots\)
1936.4.a.bi	$1936$	$4$	1936.a	1.a	$1$	$3$	$3$	$114.228$	3.3.3124.1	None	✓				484.4.a.f	$1$	$0$	\(0\)	\(2\)	\(19\)	\(-26\)		$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(6-\beta _{1})q^{5}+(-9+\beta _{1}+\cdots)q^{7}+\cdots\)
1936.4.a.bj	$1936$	$4$	1936.a	1.a	$1$	$3$	$3$	$114.228$	3.3.3124.1	None	✓				484.4.a.f	$1$	$0$	\(0\)	\(2\)	\(19\)	\(26\)		$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(6-\beta _{1})q^{5}+(9-\beta _{1}+\cdots)q^{7}+\cdots\)
1936.4.a.bk	$1936$	$4$	1936.a	1.a	$1$	$4$	$4$	$114.228$	\(\Q(\sqrt{5}, \sqrt{37})\)	None	✓				11.4.c.a	$1$	$1$	\(0\)	\(-6\)	\(-11\)	\(-25\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{3}+(-5+\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
1936.4.a.bl	$1936$	$4$	1936.a	1.a	$1$	$4$	$4$	$114.228$	\(\Q(\sqrt{5}, \sqrt{37})\)	None	✓				11.4.c.a	$1$	$0$	\(0\)	\(-6\)	\(-11\)	\(25\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{3}+(-1-\beta _{1}+\beta _{2}-3\beta _{3})q^{5}+\cdots\)
1936.4.a.bm	$1936$	$4$	1936.a	1.a	$1$	$4$	$4$	$114.228$	4.4.978025.2	None	✓				22.4.c.b	$1$	$0$	\(0\)	\(-4\)	\(25\)	\(-3\)		$-$	$-$	$+$	$11$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(6-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1936.4.a.bn	$1936$	$4$	1936.a	1.a	$1$	$4$	$4$	$114.228$	4.4.978025.2	None	✓				22.4.c.b	$1$	$1$	\(0\)	\(-4\)	\(25\)	\(3\)		$-$	$+$	$-$	$11$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(6-\beta _{2})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
1936.4.a.bo	$1936$	$4$	1936.a	1.a	$1$	$4$	$4$	$114.228$	4.4.4166757.2	None	✓				968.4.a.l	$1$	$0$	\(0\)	\(3\)	\(9\)	\(-8\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(2+\beta _{2})q^{5}+(-3-2\beta _{1}+\cdots)q^{7}+\cdots\)
1936.4.a.bp	$1936$	$4$	1936.a	1.a	$1$	$4$	$4$	$114.228$	4.4.4166757.2	None	✓				968.4.a.l	$1$	$0$	\(0\)	\(3\)	\(9\)	\(8\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(2+\beta _{2})q^{5}+(3+2\beta _{1}+\cdots)q^{7}+\cdots\)
1936.4.a.bq	$1936$	$4$	1936.a	1.a	$1$	$6$	$6$	$114.228$	6.6.\(\cdots\).1	None	✓				121.4.a.h	$2$	$1$	\(0\)	\(-8\)	\(14\)	\(0\)		$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{4})q^{3}+(2+\beta _{3}-\beta _{4})q^{5}+\cdots\)
1936.4.a.br	$1936$	$4$	1936.a	1.a	$1$	$6$	$6$	$114.228$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				44.4.e.a	$1$	$1$	\(0\)	\(-3\)	\(-12\)	\(-8\)		$-$	$+$	$-$	$2^{2}\cdot 11$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-2+\beta _{1}-\beta _{4})q^{5}+\cdots\)
1936.4.a.bs	$1936$	$4$	1936.a	1.a	$1$	$6$	$6$	$114.228$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓		✓		44.4.e.a	$1$	$0$	\(0\)	\(-3\)	\(-12\)	\(8\)		$-$	$-$	$+$	$2^{2}\cdot 11$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-2+\beta _{1}-\beta _{4})q^{5}+\cdots\)
1936.4.a.bt	$1936$	$4$	1936.a	1.a	$1$	$8$	$8$	$114.228$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				968.4.a.p	$1$	$0$	\(0\)	\(6\)	\(6\)	\(-50\)		$+$	$+$	$+$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(1-2\beta _{3}+\beta _{7})q^{5}+(-6+\cdots)q^{7}+\cdots\)
1936.4.a.bu	$1936$	$4$	1936.a	1.a	$1$	$8$	$8$	$114.228$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				968.4.a.p	$1$	$0$	\(0\)	\(6\)	\(6\)	\(50\)		$+$	$+$	$+$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(1-2\beta _{3}+\beta _{7})q^{5}+(6+\cdots)q^{7}+\cdots\)
1936.4.a.bv	$1936$	$4$	1936.a	1.a	$1$	$8$	$8$	$114.228$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				88.4.i.a	$1$	$1$	\(0\)	\(8\)	\(-13\)	\(-9\)		$+$	$-$	$-$	$2^{6}\cdot 11$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{3}+(-2-\beta _{5})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1936.4.a.bw	$1936$	$4$	1936.a	1.a	$1$	$8$	$8$	$114.228$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				88.4.i.a	$1$	$0$	\(0\)	\(8\)	\(-13\)	\(9\)		$+$	$+$	$+$	$2^{6}\cdot 11$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{3}+(-2-\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1936.4.a.bx	$1936$	$4$	1936.a	1.a	$1$	$10$	$10$	$114.228$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		88.4.i.b	$1$	$0$	\(0\)	\(-9\)	\(13\)	\(-3\)		$+$	$+$	$+$	$2^{8}\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(1+\beta _{4})q^{5}+\beta _{3}q^{7}+\cdots\)
1936.4.a.by	$1936$	$4$	1936.a	1.a	$1$	$10$	$10$	$114.228$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		88.4.i.b	$1$	$1$	\(0\)	\(-9\)	\(13\)	\(3\)		$+$	$-$	$-$	$2^{8}\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(1+\beta _{4})q^{5}-\beta _{3}q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1936))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1936)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(968))\)\(^{\oplus 2}\)