Space of modular forms of level 2205, weight 4, and trivial character

• Label: 2205.4.a
• Level: $2205$
• Weight: $4$
• Character orbit: 2205.a
• Rep. character: $\chi_{2205}(1,\cdot)$
• Character field: $\Q$
• Dimension: $205$
• Newform subspaces: $61$
• Sturm bound: $1344$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2205.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 61 \)
Sturm bound:			\(1344\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2205))\).

	Total	New	Old
Modular forms	1040	205	835
Cusp forms	976	205	771
Eisenstein series	64	0	64

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

\(3\)	\(5\)	\(7\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(136\)	\(20\)	\(116\)		\(128\)	\(20\)	\(108\)		\(8\)	\(0\)	\(8\)
\(+\)	\(+\)	\(-\)	\(-\)		\(126\)	\(21\)	\(105\)		\(118\)	\(21\)	\(97\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)		\(128\)	\(20\)	\(108\)		\(120\)	\(20\)	\(100\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(-\)	\(+\)		\(130\)	\(21\)	\(109\)		\(122\)	\(21\)	\(101\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(+\)	\(-\)		\(128\)	\(29\)	\(99\)		\(120\)	\(29\)	\(91\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(-\)	\(+\)		\(132\)	\(33\)	\(99\)		\(124\)	\(33\)	\(91\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(+\)	\(+\)		\(128\)	\(31\)	\(97\)		\(120\)	\(31\)	\(89\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)		\(132\)	\(30\)	\(102\)		\(124\)	\(30\)	\(94\)		\(8\)	\(0\)	\(8\)
Plus space			\(+\)		\(526\)	\(105\)	\(421\)		\(494\)	\(105\)	\(389\)		\(32\)	\(0\)	\(32\)
Minus space			\(-\)		\(514\)	\(100\)	\(414\)		\(482\)	\(100\)	\(382\)		\(32\)	\(0\)	\(32\)

Trace form

205 * q + 4 * q^2 + 816 * q^4 - 5 * q^5 - 20 * q^10 - 80 * q^11 - 34 * q^13 + 3240 * q^16 - 194 * q^17 - 64 * q^19 - 80 * q^20 - 512 * q^22 - 130 * q^23 + 5125 * q^25 - 72 * q^26 + 422 * q^29 + 412 * q^31 + 104 * q^32 - 552 * q^34 + 1050 * q^37 - 1540 * q^38 - 180 * q^40 + 830 * q^41 - 246 * q^43 - 2464 * q^44 - 236 * q^46 - 554 * q^47 + 100 * q^50 + 416 * q^52 + 1286 * q^53 - 80 * q^55 + 724 * q^58 - 1652 * q^59 + 2158 * q^61 - 936 * q^62 + 12568 * q^64 + 290 * q^65 + 926 * q^67 - 244 * q^68 + 28 * q^71 + 618 * q^73 - 648 * q^74 - 1548 * q^76 - 1192 * q^79 - 2320 * q^80 + 1492 * q^82 + 1166 * q^83 - 210 * q^85 - 7800 * q^86 - 11072 * q^88 - 3030 * q^89 - 2324 * q^92 + 2916 * q^94 + 500 * q^95 + 2170 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2205))\) 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	5	7
2205.4.a.a	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				45.4.a.a	$1$	$1$	\(-5\)	\(0\)	\(-5\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{2}+17q^{4}-5q^{5}-45q^{8}+5^{2}q^{10}+\cdots\)
2205.4.a.b	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				105.4.a.b	$1$	$1$	\(-5\)	\(0\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{2}+17q^{4}+5q^{5}-45q^{8}-5^{2}q^{10}+\cdots\)
2205.4.a.c	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				15.4.a.b	$1$	$0$	\(-3\)	\(0\)	\(-5\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}+q^{4}-5q^{5}+21q^{8}+15q^{10}+\cdots\)
2205.4.a.d	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				105.4.i.a	$1$	$0$	\(-3\)	\(0\)	\(-5\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}+q^{4}-5q^{5}+21q^{8}+15q^{10}+\cdots\)
2205.4.a.e	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				35.4.e.a	$1$	$1$	\(-3\)	\(0\)	\(-5\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}+q^{4}-5q^{5}+21q^{8}+15q^{10}+\cdots\)
2205.4.a.f	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				315.4.a.b	$1$	$2$	\(-3\)	\(0\)	\(5\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}+q^{4}+5q^{5}+21q^{8}-15q^{10}+\cdots\)
2205.4.a.g	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				35.4.e.a	$1$	$1$	\(-3\)	\(0\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}+q^{4}+5q^{5}+21q^{8}-15q^{10}+\cdots\)
2205.4.a.h	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				105.4.i.a	$1$	$0$	\(-3\)	\(0\)	\(5\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}+q^{4}+5q^{5}+21q^{8}-15q^{10}+\cdots\)
2205.4.a.i	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				35.4.a.a	$1$	$0$	\(-1\)	\(0\)	\(-5\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-7q^{4}-5q^{5}+15q^{8}+5q^{10}+\cdots\)
2205.4.a.j	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				735.4.a.d	$1$	$0$	\(-1\)	\(0\)	\(-5\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-7q^{4}-5q^{5}+15q^{8}+5q^{10}+\cdots\)
2205.4.a.k	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				245.4.a.b	$1$	$0$	\(-1\)	\(0\)	\(-5\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-7q^{4}-5q^{5}+15q^{8}+5q^{10}+\cdots\)
2205.4.a.l	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				15.4.a.a	$1$	$1$	\(-1\)	\(0\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-7q^{4}+5q^{5}+15q^{8}-5q^{10}+\cdots\)
2205.4.a.m	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				735.4.a.d	$1$	$1$	\(-1\)	\(0\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-7q^{4}+5q^{5}+15q^{8}-5q^{10}+\cdots\)
2205.4.a.n	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				245.4.a.b	$1$	$1$	\(-1\)	\(0\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-7q^{4}+5q^{5}+15q^{8}-5q^{10}+\cdots\)
2205.4.a.o	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				105.4.a.a	$1$	$1$	\(0\)	\(0\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-8q^{4}+5q^{5}-42q^{11}-20q^{13}+\cdots\)
2205.4.a.p	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				315.4.a.b	$1$	$1$	\(3\)	\(0\)	\(-5\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}+q^{4}-5q^{5}-21q^{8}-15q^{10}+\cdots\)
2205.4.a.q	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				5.4.a.a	$1$	$0$	\(4\)	\(0\)	\(-5\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+8q^{4}-5q^{5}-20q^{10}-2^{5}q^{11}+\cdots\)
2205.4.a.r	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				735.4.a.a	$1$	$0$	\(4\)	\(0\)	\(-5\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+8q^{4}-5q^{5}-20q^{10}+10q^{11}+\cdots\)
2205.4.a.s	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				735.4.a.a	$1$	$1$	\(4\)	\(0\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+8q^{4}+5q^{5}+20q^{10}+10q^{11}+\cdots\)
2205.4.a.t	$2205$	$4$	2205.a	1.a	$1$	$1$	$1$	$130.099$	\(\Q\)	None	✓				45.4.a.a	$1$	$0$	\(5\)	\(0\)	\(5\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+5q^{2}+17q^{4}+5q^{5}+45q^{8}+5^{2}q^{10}+\cdots\)
2205.4.a.u	$2205$	$4$	2205.a	1.a	$1$	$2$	$2$	$130.099$	\(\Q(\sqrt{2}) \)	None	✓				35.4.a.b	$1$	$0$	\(-8\)	\(0\)	\(-10\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-4+\beta )q^{2}+(10-8\beta )q^{4}-5q^{5}+\cdots\)
2205.4.a.v	$2205$	$4$	2205.a	1.a	$1$	$2$	$2$	$130.099$	\(\Q(\sqrt{41}) \)	None	✓				105.4.a.g	$1$	$0$	\(-3\)	\(0\)	\(-10\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(3+3\beta )q^{4}-5q^{5}+\cdots\)
2205.4.a.w	$2205$	$4$	2205.a	1.a	$1$	$2$	$2$	$130.099$	\(\Q(\sqrt{11}) \)	None	✓				245.4.a.i	$1$	$0$	\(-2\)	\(0\)	\(-10\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(4-2\beta )q^{4}-5q^{5}+\cdots\)
2205.4.a.x	$2205$	$4$	2205.a	1.a	$1$	$2$	$2$	$130.099$	\(\Q(\sqrt{11}) \)	None	✓				245.4.a.i	$1$	$1$	\(-2\)	\(0\)	\(10\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(4-2\beta )q^{4}+5q^{5}+\cdots\)
2205.4.a.y	$2205$	$4$	2205.a	1.a	$1$	$2$	$2$	$130.099$	\(\Q(\sqrt{17}) \)	None	✓				315.4.a.h	$1$	$0$	\(-1\)	\(0\)	\(10\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-4+\beta )q^{4}+5q^{5}+(-4+\cdots)q^{8}+\cdots\)
2205.4.a.z	$2205$	$4$	2205.a	1.a	$1$	$2$	$2$	$130.099$	\(\Q(\sqrt{65}) \)	None	✓				105.4.a.f	$1$	$1$	\(-1\)	\(0\)	\(10\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(8+\beta )q^{4}+5q^{5}+(-2^{4}-\beta )q^{8}+\cdots\)
2205.4.a.ba	$2205$	$4$	2205.a	1.a	$1$	$2$	$2$	$130.099$	\(\Q(\sqrt{17}) \)	None	✓				315.4.a.h	$1$	$1$	\(1\)	\(0\)	\(-10\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-4+\beta )q^{4}-5q^{5}+(4-11\beta )q^{8}+\cdots\)
2205.4.a.bb	$2205$	$4$	2205.a	1.a	$1$	$2$	$2$	$130.099$	\(\Q(\sqrt{2}) \)	None	✓				105.4.a.e	$1$	$1$	\(2\)	\(0\)	\(10\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+5q^{5}+(9+\cdots)q^{8}+\cdots\)
2205.4.a.bc	$2205$	$4$	2205.a	1.a	$1$	$2$	$2$	$130.099$	\(\Q(\sqrt{2}) \)	None	✓				105.4.i.b	$1$	$0$	\(4\)	\(0\)	\(-10\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{2}+(-2+4\beta )q^{4}-5q^{5}+\cdots\)
2205.4.a.bd	$2205$	$4$	2205.a	1.a	$1$	$2$	$2$	$130.099$	\(\Q(\sqrt{2}) \)	None	✓				105.4.i.b	$1$	$0$	\(4\)	\(0\)	\(10\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{2}+(-2+4\beta )q^{4}+5q^{5}+\cdots\)
2205.4.a.be	$2205$	$4$	2205.a	1.a	$1$	$2$	$2$	$130.099$	\(\Q(\sqrt{5}) \)	None	✓				105.4.a.d	$1$	$0$	\(4\)	\(0\)	\(-10\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{2}+(1+4\beta )q^{4}-5q^{5}+(6+\cdots)q^{8}+\cdots\)
2205.4.a.bf	$2205$	$4$	2205.a	1.a	$1$	$2$	$2$	$130.099$	\(\Q(\sqrt{2}) \)	None	✓				35.4.e.b	$1$	$1$	\(6\)	\(0\)	\(-10\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(3+\beta )q^{2}+(3+6\beta )q^{4}-5q^{5}+(-3+\cdots)q^{8}+\cdots\)
2205.4.a.bg	$2205$	$4$	2205.a	1.a	$1$	$2$	$2$	$130.099$	\(\Q(\sqrt{2}) \)	None	✓				35.4.e.b	$1$	$1$	\(6\)	\(0\)	\(10\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(3+\beta )q^{2}+(3+6\beta )q^{4}+5q^{5}+(-3+\cdots)q^{8}+\cdots\)
2205.4.a.bh	$2205$	$4$	2205.a	1.a	$1$	$2$	$2$	$130.099$	\(\Q(\sqrt{17}) \)	None	✓				105.4.a.c	$1$	$0$	\(7\)	\(0\)	\(-10\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(4-\beta )q^{2}+(12-7\beta )q^{4}-5q^{5}+(44+\cdots)q^{8}+\cdots\)
2205.4.a.bi	$2205$	$4$	2205.a	1.a	$1$	$3$	$3$	$130.099$	3.3.4892.1	None	✓				105.4.i.c	$1$	$1$	\(-3\)	\(0\)	\(-15\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}-5q^{5}+\cdots\)
2205.4.a.bj	$2205$	$4$	2205.a	1.a	$1$	$3$	$3$	$130.099$	3.3.4892.1	None	✓				105.4.i.c	$1$	$1$	\(-3\)	\(0\)	\(15\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
2205.4.a.bk	$2205$	$4$	2205.a	1.a	$1$	$3$	$3$	$130.099$	3.3.22952.1	None	✓				315.4.a.n	$1$	$0$	\(-2\)	\(0\)	\(15\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(5-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
2205.4.a.bl	$2205$	$4$	2205.a	1.a	$1$	$3$	$3$	$130.099$	3.3.22952.1	None	✓				315.4.a.n	$1$	$1$	\(2\)	\(0\)	\(-15\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(5-2\beta _{1}+\beta _{2})q^{4}-5q^{5}+\cdots\)
2205.4.a.bm	$2205$	$4$	2205.a	1.a	$1$	$3$	$3$	$130.099$	3.3.14360.1	None	✓				35.4.a.c	$1$	$1$	\(3\)	\(0\)	\(15\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(4-\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
2205.4.a.bn	$2205$	$4$	2205.a	1.a	$1$	$4$	$4$	$130.099$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				735.4.a.v	$1$	$0$	\(-1\)	\(0\)	\(-20\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(10+\beta _{2})q^{4}-5q^{5}+(-7+\cdots)q^{8}+\cdots\)
2205.4.a.bo	$2205$	$4$	2205.a	1.a	$1$	$4$	$4$	$130.099$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				735.4.a.v	$1$	$1$	\(-1\)	\(0\)	\(20\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(10+\beta _{2})q^{4}+5q^{5}+(-7+\cdots)q^{8}+\cdots\)
2205.4.a.bp	$2205$	$4$	2205.a	1.a	$1$	$4$	$4$	$130.099$	4.4.51264.1	None	✓				735.4.a.t	$1$	$1$	\(6\)	\(0\)	\(-20\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1}-\beta _{2})q^{2}+(6-\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots\)
2205.4.a.bq	$2205$	$4$	2205.a	1.a	$1$	$4$	$4$	$130.099$	4.4.51264.1	None	✓				735.4.a.t	$1$	$0$	\(6\)	\(0\)	\(20\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1}-\beta _{2})q^{2}+(6-\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots\)
2205.4.a.br	$2205$	$4$	2205.a	1.a	$1$	$5$	$5$	$130.099$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				105.4.i.d	$1$	$1$	\(-3\)	\(0\)	\(-25\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(5+\beta _{2})q^{4}-5q^{5}+\cdots\)
2205.4.a.bs	$2205$	$4$	2205.a	1.a	$1$	$5$	$5$	$130.099$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		105.4.i.d	$1$	$1$	\(-3\)	\(0\)	\(25\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(5+\beta _{2})q^{4}+5q^{5}+\cdots\)
2205.4.a.bt	$2205$	$4$	2205.a	1.a	$1$	$5$	$5$	$130.099$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				35.4.e.c	$1$	$0$	\(-1\)	\(0\)	\(-25\)	\(0\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(7+\beta _{3})q^{4}-5q^{5}+(-4+\cdots)q^{8}+\cdots\)
2205.4.a.bu	$2205$	$4$	2205.a	1.a	$1$	$5$	$5$	$130.099$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				35.4.e.c	$1$	$0$	\(-1\)	\(0\)	\(25\)	\(0\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(7+\beta _{3})q^{4}+5q^{5}+(-4+\cdots)q^{8}+\cdots\)
2205.4.a.bv	$2205$	$4$	2205.a	1.a	$1$	$5$	$5$	$130.099$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				105.4.i.e	$1$	$0$	\(1\)	\(0\)	\(-25\)	\(0\)		$-$	$+$	$-$	$+$	$2\cdot 7$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(4+\beta _{1}+\beta _{2})q^{4}-5q^{5}+\cdots\)
2205.4.a.bw	$2205$	$4$	2205.a	1.a	$1$	$5$	$5$	$130.099$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				105.4.i.e	$1$	$0$	\(1\)	\(0\)	\(25\)	\(0\)		$-$	$-$	$+$	$+$	$2\cdot 7$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(4+\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
2205.4.a.bx	$2205$	$4$	2205.a	1.a	$1$	$6$	$6$	$130.099$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			2205.4.a.bx	$2$	$1$	\(0\)	\(0\)	\(-30\)	\(0\)		$+$	$+$	$-$	$-$	$2^{9}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}-5q^{5}+(4\beta _{1}+\cdots)q^{8}+\cdots\)
2205.4.a.by	$2205$	$4$	2205.a	1.a	$1$	$6$	$6$	$130.099$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			2205.4.a.bx	$2$	$0$	\(0\)	\(0\)	\(30\)	\(0\)		$+$	$-$	$-$	$+$	$2^{9}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+5q^{5}+(4\beta _{1}+\cdots)q^{8}+\cdots\)
2205.4.a.bz	$2205$	$4$	2205.a	1.a	$1$	$6$	$6$	$130.099$	6.6.1163891200.1	None	✓				245.4.a.o	$1$	$1$	\(2\)	\(0\)	\(-30\)	\(0\)		$-$	$+$	$+$	$-$	$2\cdot 7$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+3\beta _{1}+2\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
2205.4.a.ca	$2205$	$4$	2205.a	1.a	$1$	$6$	$6$	$130.099$	6.6.1163891200.1	None	✓				245.4.a.o	$1$	$0$	\(2\)	\(0\)	\(30\)	\(0\)		$-$	$-$	$+$	$+$	$2\cdot 7$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+3\beta _{1}+2\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
2205.4.a.cb	$2205$	$4$	2205.a	1.a	$1$	$8$	$8$	$130.099$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		315.4.j.i	$1$	$1$	\(-4\)	\(0\)	\(-40\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(6-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2205.4.a.cc	$2205$	$4$	2205.a	1.a	$1$	$8$	$8$	$130.099$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				315.4.j.i	$1$	$1$	\(-4\)	\(0\)	\(40\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(6-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2205.4.a.cd	$2205$	$4$	2205.a	1.a	$1$	$8$	$8$	$130.099$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		735.4.a.bb	$1$	$1$	\(-2\)	\(0\)	\(-40\)	\(0\)		$-$	$+$	$+$	$-$	$2\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(6+\beta _{1}+\beta _{2})q^{4}-5q^{5}+\cdots\)
2205.4.a.ce	$2205$	$4$	2205.a	1.a	$1$	$8$	$8$	$130.099$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		735.4.a.bb	$1$	$0$	\(-2\)	\(0\)	\(40\)	\(0\)		$-$	$-$	$+$	$+$	$2\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(6+\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
2205.4.a.cf	$2205$	$4$	2205.a	1.a	$1$	$8$	$8$	$130.099$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				315.4.j.i	$1$	$0$	\(4\)	\(0\)	\(-40\)	\(0\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(6-\beta _{1}+\beta _{2})q^{4}-5q^{5}+\cdots\)
2205.4.a.cg	$2205$	$4$	2205.a	1.a	$1$	$8$	$8$	$130.099$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		315.4.j.i	$1$	$0$	\(4\)	\(0\)	\(40\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(6-\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
2205.4.a.ch	$2205$	$4$	2205.a	1.a	$1$	$12$	$12$	$130.099$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		2205.4.a.ch	$2$	$0$	\(0\)	\(0\)	\(-60\)	\(0\)		$+$	$+$	$+$	$+$	$2^{7}\cdot 3^{2}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-5q^{5}+(-\beta _{7}+\cdots)q^{8}+\cdots\)
2205.4.a.ci	$2205$	$4$	2205.a	1.a	$1$	$12$	$12$	$130.099$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		2205.4.a.ch	$2$	$1$	\(0\)	\(0\)	\(60\)	\(0\)		$+$	$-$	$+$	$-$	$2^{7}\cdot 3^{2}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+5q^{5}+(-\beta _{7}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2205))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2205)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(735))\)\(^{\oplus 2}\)