Space of modular forms of level 4165, weight 2, and trivial character

• Label: 4165.2.a
• Level: $4165$
• Weight: $2$
• Character orbit: 4165.a
• Rep. character: $\chi_{4165}(1,\cdot)$
• Character field: $\Q$
• Dimension: $220$
• Newform subspaces: $48$
• Sturm bound: $1008$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 4165 = 5 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4165.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 48 \)
Sturm bound:			\(1008\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(3\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4165))\).

	Total	New	Old
Modular forms	520	220	300
Cusp forms	489	220	269
Eisenstein series	31	0	31

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

\(5\)	\(7\)	\(17\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(62\)	\(28\)	\(34\)		\(59\)	\(28\)	\(31\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)		\(66\)	\(28\)	\(38\)		\(62\)	\(28\)	\(34\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)		\(68\)	\(25\)	\(43\)		\(64\)	\(25\)	\(39\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)		\(64\)	\(28\)	\(36\)		\(60\)	\(28\)	\(32\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)		\(66\)	\(30\)	\(36\)		\(62\)	\(30\)	\(32\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)		\(62\)	\(22\)	\(40\)		\(58\)	\(22\)	\(36\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)		\(64\)	\(25\)	\(39\)		\(60\)	\(25\)	\(35\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)		\(68\)	\(34\)	\(34\)		\(64\)	\(34\)	\(30\)		\(4\)	\(0\)	\(4\)
Plus space			\(+\)		\(252\)	\(103\)	\(149\)		\(237\)	\(103\)	\(134\)		\(15\)	\(0\)	\(15\)
Minus space			\(-\)		\(268\)	\(117\)	\(151\)		\(252\)	\(117\)	\(135\)		\(16\)	\(0\)	\(16\)

Trace form

220 * q + 4 * q^2 + 4 * q^3 + 228 * q^4 + 2 * q^5 - 8 * q^6 + 228 * q^9 + 2 * q^10 + 12 * q^11 + 20 * q^13 + 260 * q^16 + 4 * q^17 + 16 * q^18 + 16 * q^19 + 6 * q^20 + 20 * q^22 - 12 * q^23 - 28 * q^24 + 220 * q^25 - 24 * q^26 - 20 * q^27 + 16 * q^29 - 12 * q^30 + 16 * q^31 + 4 * q^32 - 4 * q^33 + 284 * q^36 - 16 * q^37 + 24 * q^38 - 76 * q^39 + 6 * q^40 + 4 * q^41 - 20 * q^43 + 64 * q^44 + 18 * q^45 + 32 * q^46 - 20 * q^47 + 76 * q^48 + 4 * q^50 + 20 * q^52 + 16 * q^53 + 36 * q^54 - 16 * q^57 - 40 * q^58 - 8 * q^59 + 28 * q^60 + 20 * q^61 + 32 * q^62 + 284 * q^64 + 72 * q^66 + 4 * q^67 + 12 * q^68 + 24 * q^69 + 36 * q^71 + 68 * q^72 + 36 * q^73 + 16 * q^74 + 4 * q^75 + 8 * q^76 + 12 * q^78 - 24 * q^79 - 18 * q^80 + 260 * q^81 - 84 * q^82 - 4 * q^83 - 2 * q^85 - 112 * q^86 - 24 * q^87 - 120 * q^88 + 8 * q^89 + 30 * q^90 - 88 * q^92 - 84 * q^93 - 16 * q^95 - 56 * q^96 + 24 * q^97 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4165))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	7	17
4165.2.a.a	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓				595.2.a.a	$1$	$1$	\(-2\)	\(-2\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-2q^{3}+2q^{4}+q^{5}+4q^{6}+\cdots\)
4165.2.a.b	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓				595.2.i.d	$1$	$1$	\(-2\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{9}+\cdots\)
4165.2.a.c	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓	✓			4165.2.a.c	$1$	$1$	\(-2\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-q^{5}-3q^{9}+2q^{10}+\cdots\)
4165.2.a.d	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓	✓			4165.2.a.c	$1$	$1$	\(-2\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-3q^{9}-2q^{10}+\cdots\)
4165.2.a.e	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓				595.2.i.d	$1$	$0$	\(-2\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-2q^{9}+\cdots\)
4165.2.a.f	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓				595.2.i.c	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+3q^{8}+\cdots\)
4165.2.a.g	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓				595.2.i.b	$1$	$1$	\(-1\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots\)
4165.2.a.h	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓				595.2.i.b	$1$	$0$	\(-1\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+3q^{8}+\cdots\)
4165.2.a.i	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓				595.2.i.c	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots\)
4165.2.a.j	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓				595.2.i.a	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+q^{5}-2q^{9}-6q^{11}+\cdots\)
4165.2.a.k	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓				595.2.i.a	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{5}-2q^{9}-6q^{11}+\cdots\)
4165.2.a.l	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓				85.2.a.a	$1$	$1$	\(1\)	\(-2\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}-q^{4}+q^{5}-2q^{6}-3q^{8}+\cdots\)
4165.2.a.m	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓	✓			4165.2.a.m	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-3q^{8}-3q^{9}-q^{10}+\cdots\)
4165.2.a.n	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓	✓			4165.2.a.m	$1$	$0$	\(1\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-3q^{8}-3q^{9}+q^{10}+\cdots\)
4165.2.a.o	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓				595.2.a.c	$1$	$0$	\(2\)	\(-2\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-2q^{3}+2q^{4}-q^{5}-4q^{6}+\cdots\)
4165.2.a.p	$4165$	$2$	4165.a	1.a	$1$	$1$	$1$	$33.258$	\(\Q\)	None	✓				595.2.a.b	$1$	$0$	\(2\)	\(-2\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots\)
4165.2.a.q	$4165$	$2$	4165.a	1.a	$1$	$2$	$2$	$33.258$	\(\Q(\sqrt{2}) \)	None	✓				85.2.a.b	$1$	$0$	\(-2\)	\(4\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(2+\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
4165.2.a.r	$4165$	$2$	4165.a	1.a	$1$	$2$	$2$	$33.258$	\(\Q(\sqrt{21}) \)	None	✓				595.2.i.g	$1$	$1$	\(-1\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-\beta q^{3}+(3+\beta )q^{4}-q^{5}+(5+\cdots)q^{6}+\cdots\)
4165.2.a.s	$4165$	$2$	4165.a	1.a	$1$	$2$	$2$	$33.258$	\(\Q(\sqrt{21}) \)	None	✓				595.2.i.g	$1$	$0$	\(-1\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+\beta q^{3}+(3+\beta )q^{4}+q^{5}+(-5+\cdots)q^{6}+\cdots\)
4165.2.a.t	$4165$	$2$	4165.a	1.a	$1$	$2$	$2$	$33.258$	\(\Q(\sqrt{3}) \)	None	✓				85.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(3+\cdots)q^{6}+\cdots\)
4165.2.a.u	$4165$	$2$	4165.a	1.a	$1$	$2$	$2$	$33.258$	\(\Q(\sqrt{13}) \)	None	✓				595.2.i.f	$1$	$1$	\(1\)	\(-3\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-2+\beta )q^{3}+(1+\beta )q^{4}-q^{5}+\cdots\)
4165.2.a.v	$4165$	$2$	4165.a	1.a	$1$	$2$	$2$	$33.258$	\(\Q(\sqrt{13}) \)	None	✓				595.2.i.f	$1$	$0$	\(1\)	\(3\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2-\beta )q^{3}+(1+\beta )q^{4}+q^{5}+\cdots\)
4165.2.a.w	$4165$	$2$	4165.a	1.a	$1$	$2$	$2$	$33.258$	\(\Q(\sqrt{7}) \)	None	✓				595.2.i.e	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta q^{3}-q^{4}-q^{5}-\beta q^{6}-3q^{8}+\cdots\)
4165.2.a.x	$4165$	$2$	4165.a	1.a	$1$	$2$	$2$	$33.258$	\(\Q(\sqrt{7}) \)	None	✓				595.2.i.e	$1$	$0$	\(2\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta q^{3}-q^{4}+q^{5}-\beta q^{6}-3q^{8}+\cdots\)
4165.2.a.y	$4165$	$2$	4165.a	1.a	$1$	$3$	$3$	$33.258$	\(\Q(\zeta_{14})^+\)	None	✓				595.2.a.d	$1$	$1$	\(-4\)	\(2\)	\(-3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
4165.2.a.z	$4165$	$2$	4165.a	1.a	$1$	$3$	$3$	$33.258$	3.3.169.1	None	✓				595.2.a.f	$1$	$1$	\(-2\)	\(2\)	\(3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
4165.2.a.ba	$4165$	$2$	4165.a	1.a	$1$	$3$	$3$	$33.258$	\(\Q(\zeta_{14})^+\)	None	✓				595.2.a.e	$1$	$0$	\(-2\)	\(4\)	\(-3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{3}+\cdots\)
4165.2.a.bb	$4165$	$2$	4165.a	1.a	$1$	$3$	$3$	$33.258$	\(\Q(\zeta_{18})^+\)	None	✓				595.2.a.g	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots\)
4165.2.a.bc	$4165$	$2$	4165.a	1.a	$1$	$3$	$3$	$33.258$	\(\Q(\zeta_{14})^+\)	None	✓				595.2.a.h	$1$	$1$	\(2\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(-1+2\beta _{1}-\beta _{2})q^{3}+\cdots\)
4165.2.a.bd	$4165$	$2$	4165.a	1.a	$1$	$4$	$4$	$33.258$	4.4.10889.1	None	✓				595.2.a.i	$1$	$0$	\(1\)	\(2\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
4165.2.a.be	$4165$	$2$	4165.a	1.a	$1$	$4$	$4$	$33.258$	4.4.2777.1	None	✓				595.2.a.j	$1$	$1$	\(2\)	\(-2\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{2}+(-1-\beta _{2}+\beta _{3})q^{3}+\cdots\)
4165.2.a.bf	$4165$	$2$	4165.a	1.a	$1$	$5$	$5$	$33.258$	5.5.1034856.1	None	✓				595.2.a.k	$1$	$0$	\(2\)	\(2\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\cdots\)
4165.2.a.bg	$4165$	$2$	4165.a	1.a	$1$	$6$	$6$	$33.258$	6.6.37124800.1	None	✓	✓			4165.2.a.bg	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
4165.2.a.bh	$4165$	$2$	4165.a	1.a	$1$	$6$	$6$	$33.258$	6.6.37124800.1	None	✓	✓			4165.2.a.bg	$1$	$1$	\(0\)	\(0\)	\(6\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
4165.2.a.bi	$4165$	$2$	4165.a	1.a	$1$	$6$	$6$	$33.258$	6.6.2703198852.1	None	✓				595.2.i.h	$1$	$1$	\(1\)	\(-1\)	\(-6\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
4165.2.a.bj	$4165$	$2$	4165.a	1.a	$1$	$6$	$6$	$33.258$	6.6.2703198852.1	None	✓				595.2.i.h	$1$	$0$	\(1\)	\(1\)	\(6\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{1}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)
4165.2.a.bk	$4165$	$2$	4165.a	1.a	$1$	$7$	$7$	$33.258$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				595.2.i.i	$1$	$1$	\(-1\)	\(-6\)	\(7\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+\beta _{2}q^{4}+q^{5}+\cdots\)
4165.2.a.bl	$4165$	$2$	4165.a	1.a	$1$	$7$	$7$	$33.258$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				595.2.i.i	$1$	$0$	\(-1\)	\(6\)	\(-7\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+\beta _{2}q^{4}-q^{5}+\cdots\)
4165.2.a.bm	$4165$	$2$	4165.a	1.a	$1$	$8$	$8$	$33.258$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓		4165.2.a.bm	$1$	$0$	\(3\)	\(0\)	\(-8\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
4165.2.a.bn	$4165$	$2$	4165.a	1.a	$1$	$8$	$8$	$33.258$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓		4165.2.a.bm	$1$	$0$	\(3\)	\(0\)	\(8\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)
4165.2.a.bo	$4165$	$2$	4165.a	1.a	$1$	$9$	$9$	$33.258$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		595.2.i.j	$1$	$1$	\(0\)	\(-4\)	\(9\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
4165.2.a.bp	$4165$	$2$	4165.a	1.a	$1$	$9$	$9$	$33.258$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				595.2.i.j	$1$	$0$	\(0\)	\(4\)	\(-9\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
4165.2.a.bq	$4165$	$2$	4165.a	1.a	$1$	$12$	$12$	$33.258$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		595.2.i.k	$1$	$1$	\(-2\)	\(-5\)	\(-12\)	\(0\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
4165.2.a.br	$4165$	$2$	4165.a	1.a	$1$	$12$	$12$	$33.258$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				595.2.i.k	$1$	$0$	\(-2\)	\(5\)	\(12\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
4165.2.a.bs	$4165$	$2$	4165.a	1.a	$1$	$14$	$14$	$33.258$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓		4165.2.a.bs	$1$	$1$	\(-4\)	\(0\)	\(-14\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{13}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
4165.2.a.bt	$4165$	$2$	4165.a	1.a	$1$	$14$	$14$	$33.258$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓		4165.2.a.bs	$1$	$1$	\(-4\)	\(0\)	\(14\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{13}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
4165.2.a.bu	$4165$	$2$	4165.a	1.a	$1$	$18$	$18$	$33.258$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓	✓		4165.2.a.bu	$1$	$0$	\(8\)	\(0\)	\(-18\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
4165.2.a.bv	$4165$	$2$	4165.a	1.a	$1$	$18$	$18$	$33.258$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓	✓		4165.2.a.bu	$1$	$0$	\(8\)	\(0\)	\(18\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4165))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4165)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(595))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(833))\)\(^{\oplus 2}\)