Space of modular forms of level 1872, weight 4, and trivial character

• Label: 1872.4.a
• Level: $1872$
• Weight: $4$
• Character orbit: 1872.a
• Rep. character: $\chi_{1872}(1,\cdot)$
• Character field: $\Q$
• Dimension: $90$
• Newform subspaces: $45$
• Sturm bound: $1344$
• Trace bound: $7$

Defining parameters

Level:	$N$	$=$	$1872 = 2^{4} \cdot 3^{2} \cdot 13$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1872.a (trivial)
Character field:			$\Q$
Newform subspaces:			$45$
Sturm bound:			$1344$
Trace bound:			$7$
Distinguishing $T_p$:			$5$, $7$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(\Gamma_0(1872))$.

	Total	New	Old
Modular forms	1032	90	942
Cusp forms	984	90	894
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.

$2$	$3$	$13$	Fricke	Dim
$+$	$+$	$+$	$+$	$10$
$+$	$+$	$-$	$-$	$8$
$+$	$-$	$+$	$-$	$13$
$+$	$-$	$-$	$+$	$14$
$-$	$+$	$+$	$-$	$8$
$-$	$+$	$-$	$+$	$10$
$-$	$-$	$+$	$+$	$14$
$-$	$-$	$-$	$-$	$13$
Plus space			$+$	$48$
Minus space			$-$	$42$

Trace form

90 * q + 14 * q^7 + 46 * q^11 + 76 * q^17 - 138 * q^19 - 248 * q^23 + 2082 * q^25 - 144 * q^29 + 450 * q^31 + 576 * q^35 - 8 * q^37 + 20 * q^41 - 620 * q^43 - 1838 * q^47 + 4818 * q^49 + 572 * q^53 + 1140 * q^55 + 1062 * q^59 + 1012 * q^61 - 1122 * q^67 - 2394 * q^71 + 1812 * q^73 + 860 * q^77 + 1476 * q^79 + 4562 * q^83 - 1536 * q^85 + 1364 * q^89 - 546 * q^91 - 4644 * q^95 + 708 * q^97

Decomposition of $S_{4}^{\mathrm{new}}(\Gamma_0(1872))$ 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	13
1872.4.a.a	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				104.4.a.b	$1$	$1$	$0$	$0$	$-19$	$3$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-19q^{5}+3q^{7}-2q^{11}-13q^{13}+\cdots$
1872.4.a.b	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				26.4.a.b	$1$	$1$	$0$	$0$	$-17$	$35$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-17q^{5}+35q^{7}+2q^{11}+13q^{13}+\cdots$
1872.4.a.c	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				26.4.a.a	$1$	$0$	$0$	$0$	$-11$	$-19$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-11q^{5}-19q^{7}-38q^{11}-13q^{13}+\cdots$
1872.4.a.d	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				78.4.a.c	$1$	$1$	$0$	$0$	$-10$	$8$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-10q^{5}+8q^{7}+40q^{11}+13q^{13}+\cdots$
1872.4.a.e	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				78.4.a.e	$1$	$1$	$0$	$0$	$-6$	$-20$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-6q^{5}-20q^{7}+24q^{11}+13q^{13}+\cdots$
1872.4.a.f	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				78.4.a.f	$1$	$0$	$0$	$0$	$-4$	$-4$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-4q^{7}+2q^{11}-13q^{13}+6q^{17}+\cdots$
1872.4.a.g	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				234.4.a.d	$1$	$1$	$0$	$0$	$-2$	$26$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+26q^{7}+52q^{11}-13q^{13}+\cdots$
1872.4.a.h	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				234.4.a.d	$1$	$1$	$0$	$0$	$2$	$26$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+26q^{7}-52q^{11}-13q^{13}+\cdots$
1872.4.a.i	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				156.4.a.b	$1$	$1$	$0$	$0$	$2$	$32$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2^{5}q^{7}-68q^{11}+13q^{13}+\cdots$
1872.4.a.j	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				156.4.a.a	$1$	$1$	$0$	$0$	$6$	$4$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+6q^{5}+4q^{7}+6^{2}q^{11}+13q^{13}+\cdots$
1872.4.a.k	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				13.4.a.a	$1$	$1$	$0$	$0$	$7$	$13$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+7q^{5}+13q^{7}-26q^{11}+13q^{13}+\cdots$
1872.4.a.l	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				104.4.a.a	$1$	$0$	$0$	$0$	$7$	$21$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+7q^{5}+21q^{7}+6q^{11}+13q^{13}+\cdots$
1872.4.a.m	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				39.4.a.a	$1$	$1$	$0$	$0$	$12$	$-2$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+12q^{5}-2q^{7}-6^{2}q^{11}+13q^{13}+\cdots$
1872.4.a.n	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				52.4.a.a	$1$	$0$	$0$	$0$	$13$	$11$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+13q^{5}+11q^{7}-2q^{11}-13q^{13}+\cdots$
1872.4.a.o	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				78.4.a.a	$1$	$0$	$0$	$0$	$16$	$-28$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{5}-28q^{7}+34q^{11}-13q^{13}+\cdots$
1872.4.a.p	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				78.4.a.b	$1$	$0$	$0$	$0$	$16$	$8$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{5}+8q^{7}-38q^{11}-13q^{13}+\cdots$
1872.4.a.q	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				26.4.a.c	$1$	$1$	$0$	$0$	$18$	$-20$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+18q^{5}-20q^{7}-48q^{11}+13q^{13}+\cdots$
1872.4.a.r	$1872$	$4$	1872.a	1.a	$1$	$1$	$1$	$110.452$	$\Q$	None	✓				78.4.a.d	$1$	$0$	$0$	$0$	$20$	$32$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+20q^{5}+2^{5}q^{7}+50q^{11}-13q^{13}+\cdots$
1872.4.a.s	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{10})$	None	✓				156.4.a.d	$1$	$0$	$0$	$0$	$-24$	$-8$		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-12+\beta )q^{5}+(-4-3\beta )q^{7}+(18+\cdots)q^{11}+\cdots$
1872.4.a.t	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{14})$	None	✓				39.4.a.b	$1$	$0$	$0$	$0$	$-24$	$0$		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-12+\beta )q^{5}+\beta q^{7}+(-22-6\beta )q^{11}+\cdots$
1872.4.a.u	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{217})$	None	✓				52.4.a.b	$1$	$1$	$0$	$0$	$-23$	$-27$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-11-\beta )q^{5}+(-13-\beta )q^{7}+(2+\cdots)q^{11}+\cdots$
1872.4.a.v	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{43})$	None	✓				312.4.a.f	$1$	$1$	$0$	$0$	$-12$	$-44$		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-6+\beta )q^{5}+(-22+\beta )q^{7}+26q^{11}+\cdots$
1872.4.a.w	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{22})$	None	✓				234.4.a.l	$1$	$0$	$0$	$0$	$-8$	$-12$		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-4+\beta )q^{5}+(-6+\beta )q^{7}+(22+5\beta )q^{11}+\cdots$
1872.4.a.x	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{113})$	None	✓				312.4.a.c	$1$	$0$	$0$	$0$	$-6$	$10$		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-3-\beta )q^{5}+(5+\beta )q^{7}+(-8-4\beta )q^{11}+\cdots$
1872.4.a.y	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{22})$	None	✓				156.4.a.c	$1$	$0$	$0$	$0$	$0$	$-8$		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-4-3\beta )q^{7}+(-30-2\beta )q^{11}+\cdots$
1872.4.a.z	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{13})$	None	✓				468.4.a.f	$2$	$1$	$0$	$0$	$0$	$4$		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta q^{5}+2q^{7}-4\beta q^{11}-13q^{13}+\cdots$
1872.4.a.ba	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{7})$	None	✓				117.4.a.e	$2$	$0$	$0$	$0$	$0$	$44$		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+2\beta q^{5}+22q^{7}-\beta q^{11}+13q^{13}+\cdots$
1872.4.a.bb	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{17})$	None	✓				13.4.a.b	$1$	$0$	$0$	$0$	$3$	$9$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+(-1+11\beta )q^{7}+(46-12\beta )q^{11}+\cdots$
1872.4.a.bc	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{73})$	None	✓				104.4.a.c	$1$	$1$	$0$	$0$	$3$	$25$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3\beta q^{5}+(12+\beta )q^{7}+(-30+4\beta )q^{11}+\cdots$
1872.4.a.bd	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{55})$	None	✓				312.4.a.b	$1$	$1$	$0$	$0$	$4$	$-20$		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(-10+\beta )q^{7}+(-10+\cdots)q^{11}+\cdots$
1872.4.a.be	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{3})$	None	✓				312.4.a.a	$1$	$1$	$0$	$0$	$4$	$-4$		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(-2-3\beta )q^{7}+(14-6\beta )q^{11}+\cdots$
1872.4.a.bf	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{7})$	None	✓				312.4.a.e	$1$	$1$	$0$	$0$	$4$	$20$		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(10-3\beta )q^{7}+(-30-4\beta )q^{11}+\cdots$
1872.4.a.bg	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{22})$	None	✓				234.4.a.l	$1$	$0$	$0$	$0$	$8$	$-12$		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(4+\beta )q^{5}+(-6-\beta )q^{7}+(-22+5\beta )q^{11}+\cdots$
1872.4.a.bh	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{321})$	None	✓				104.4.a.d	$1$	$1$	$0$	$0$	$11$	$-1$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(6-\beta )q^{5}+(-2+3\beta )q^{7}+58q^{11}+\cdots$
1872.4.a.bi	$1872$	$4$	1872.a	1.a	$1$	$2$	$2$	$110.452$	$\Q(\sqrt{17})$	None	✓				312.4.a.d	$1$	$0$	$0$	$0$	$18$	$10$		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(9-\beta )q^{5}+(5+5\beta )q^{7}+(2+14\beta )q^{11}+\cdots$
1872.4.a.bj	$1872$	$4$	1872.a	1.a	$1$	$3$	$3$	$110.452$	3.3.36248.1	None	✓				312.4.a.g	$1$	$0$	$0$	$0$	$-16$	$22$		$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-5-\beta _{2})q^{5}+(8-\beta _{1}-\beta _{2})q^{7}+\cdots$
1872.4.a.bk	$1872$	$4$	1872.a	1.a	$1$	$3$	$3$	$110.452$	3.3.3144.1	None	✓		✓		39.4.a.c	$1$	$1$	$0$	$0$	$-4$	$-30$		$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}+(-11-3\beta _{1})q^{7}+\cdots$
1872.4.a.bl	$1872$	$4$	1872.a	1.a	$1$	$3$	$3$	$110.452$	3.3.13916.1	None	✓				312.4.a.h	$1$	$0$	$0$	$0$	$4$	$-6$		$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{5}+(-2-\beta _{1}-\beta _{2})q^{7}+\cdots$
1872.4.a.bm	$1872$	$4$	1872.a	1.a	$1$	$3$	$3$	$110.452$	3.3.18257.1	None	✓				104.4.a.e	$1$	$0$	$0$	$0$	$8$	$-36$		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(3+2\beta _{1}+\beta _{2})q^{5}+(-12-\beta _{1})q^{7}+\cdots$
1872.4.a.bn	$1872$	$4$	1872.a	1.a	$1$	$4$	$4$	$110.452$	4.4.6390848.1	None	✓				936.4.a.n	$1$	$1$	$0$	$0$	$-8$	$-24$		$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+(-2-\beta _{1})q^{5}+(-6-\beta _{2})q^{7}+(2^{4}+\cdots)q^{11}+\cdots$
1872.4.a.bo	$1872$	$4$	1872.a	1.a	$1$	$4$	$4$	$110.452$	4.4.1520092.1	None	✓		✓		117.4.a.g	$2$	$1$	$0$	$0$	$0$	$-36$		$-$	$+$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{5}+(-9-\beta _{1})q^{7}+(-\beta _{2}-\beta _{3})q^{11}+\cdots$
1872.4.a.bp	$1872$	$4$	1872.a	1.a	$1$	$4$	$4$	$110.452$	4.4.5126992.1	None	✓		✓		468.4.a.h	$2$	$0$	$0$	$0$	$0$	$0$		$-$	$+$	$-$	$+$	$2^{5}\cdot 3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+\beta _{3}q^{7}+(-\beta _{1}+\beta _{2})q^{11}+\cdots$
1872.4.a.bq	$1872$	$4$	1872.a	1.a	$1$	$4$	$4$	$110.452$	4.4.6390848.1	None	✓				936.4.a.n	$1$	$1$	$0$	$0$	$8$	$-24$		$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+(2+\beta _{1})q^{5}+(-6-\beta _{2})q^{7}+(-2^{4}+\cdots)q^{11}+\cdots$
1872.4.a.br	$1872$	$4$	1872.a	1.a	$1$	$5$	$5$	$110.452$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓				936.4.a.p	$1$	$0$	$0$	$0$	$-2$	$18$		$+$	$+$	$+$	$+$	$2^{8}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+(4+\beta _{1})q^{7}+(-5-\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots$
1872.4.a.bs	$1872$	$4$	1872.a	1.a	$1$	$5$	$5$	$110.452$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓				936.4.a.p	$1$	$0$	$0$	$0$	$2$	$18$		$+$	$+$	$+$	$+$	$2^{8}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}+(4+\beta _{1})q^{7}+(5+\beta _{1}+2\beta _{2}+\cdots)q^{11}+\cdots$

Decomposition of $S_{4}^{\mathrm{old}}(\Gamma_0(1872))$ into lower level spaces

$S_{4}^{\mathrm{old}}(\Gamma_0(1872)) \simeq$ $S_{4}^{\mathrm{new}}(\Gamma_0(6))$$^{\oplus 16}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(8))$$^{\oplus 12}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(9))$$^{\oplus 10}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(12))$$^{\oplus 12}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(13))$$^{\oplus 15}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(16))$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(18))$$^{\oplus 8}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(24))$$^{\oplus 8}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(26))$$^{\oplus 12}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(36))$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(39))$$^{\oplus 10}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(48))$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(52))$$^{\oplus 9}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(72))$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(78))$$^{\oplus 8}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(104))$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(117))$$^{\oplus 5}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(144))$$^{\oplus 2}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(156))$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(208))$$^{\oplus 3}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(234))$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(312))$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(468))$$^{\oplus 3}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(624))$$^{\oplus 2}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_0(936))$$^{\oplus 2}$