Space of modular forms of level 4046, weight 2, and trivial character

• Label: 4046.2.a
• Level: $4046$
• Weight: $2$
• Character orbit: 4046.a
• Rep. character: $\chi_{4046}(1,\cdot)$
• Character field: $\Q$
• Dimension: $136$
• Newform subspaces: $41$
• Sturm bound: $1224$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 4046 = 2 \cdot 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4046.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 41 \)
Sturm bound:			\(1224\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(5\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4046))\).

	Total	New	Old
Modular forms	648	136	512
Cusp forms	577	136	441
Eisenstein series	71	0	71

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

\(2\)	\(7\)	\(17\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(72\)	\(13\)	\(59\)		\(64\)	\(13\)	\(51\)		\(8\)	\(0\)	\(8\)
\(+\)	\(+\)	\(-\)	\(-\)		\(90\)	\(20\)	\(70\)		\(81\)	\(20\)	\(61\)		\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(+\)	\(-\)		\(90\)	\(22\)	\(68\)		\(81\)	\(22\)	\(59\)		\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(-\)	\(+\)		\(72\)	\(12\)	\(60\)		\(63\)	\(12\)	\(51\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(+\)	\(-\)		\(81\)	\(19\)	\(62\)		\(72\)	\(19\)	\(53\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(-\)	\(+\)		\(81\)	\(16\)	\(65\)		\(72\)	\(16\)	\(56\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(+\)	\(+\)		\(81\)	\(10\)	\(71\)		\(72\)	\(10\)	\(62\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(-\)	\(-\)		\(81\)	\(24\)	\(57\)		\(72\)	\(24\)	\(48\)		\(9\)	\(0\)	\(9\)
Plus space			\(+\)		\(306\)	\(51\)	\(255\)		\(271\)	\(51\)	\(220\)		\(35\)	\(0\)	\(35\)
Minus space			\(-\)		\(342\)	\(85\)	\(257\)		\(306\)	\(85\)	\(221\)		\(36\)	\(0\)	\(36\)

Trace form

136 * q + 2 * q^2 - 2 * q^3 + 136 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^8 + 140 * q^9 + 6 * q^10 + 8 * q^11 - 2 * q^12 + 18 * q^13 - 2 * q^14 + 136 * q^16 + 6 * q^18 + 18 * q^19 - 2 * q^20 + 6 * q^21 + 8 * q^22 - 8 * q^23 + 2 * q^24 + 140 * q^25 + 2 * q^26 - 20 * q^27 - 8 * q^29 - 8 * q^30 + 4 * q^31 + 2 * q^32 - 8 * q^33 - 2 * q^35 + 140 * q^36 + 8 * q^37 - 18 * q^38 + 16 * q^39 + 6 * q^40 + 20 * q^41 + 2 * q^42 + 20 * q^43 + 8 * q^44 + 14 * q^45 + 8 * q^46 - 4 * q^47 - 2 * q^48 + 136 * q^49 + 2 * q^50 + 18 * q^52 - 8 * q^53 + 20 * q^54 + 8 * q^55 - 2 * q^56 + 44 * q^57 - 4 * q^58 + 10 * q^59 + 14 * q^61 - 4 * q^62 + 4 * q^63 + 136 * q^64 - 12 * q^65 + 24 * q^67 - 24 * q^69 + 6 * q^70 - 16 * q^71 + 6 * q^72 + 8 * q^73 - 20 * q^74 + 18 * q^75 + 18 * q^76 + 12 * q^77 - 16 * q^78 + 16 * q^79 - 2 * q^80 + 164 * q^81 - 14 * q^83 + 6 * q^84 + 36 * q^86 + 36 * q^87 + 8 * q^88 - 8 * q^89 + 6 * q^90 + 14 * q^91 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 2 * q^96 + 28 * q^97 + 2 * q^98 - 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4046))\) 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	7	17
4046.2.a.a	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓	✓			4046.2.a.a	$1$	$2$	\(-1\)	\(-3\)	\(-2\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}+q^{4}-2q^{5}+3q^{6}-q^{7}+\cdots\)
4046.2.a.b	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓				238.2.a.b	$1$	$1$	\(-1\)	\(-2\)	\(-4\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}-4q^{5}+2q^{6}-q^{7}+\cdots\)
4046.2.a.c	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓	✓			4046.2.a.c	$1$	$1$	\(-1\)	\(-1\)	\(-2\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
4046.2.a.d	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓				238.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
4046.2.a.e	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓	✓			4046.2.a.c	$1$	$1$	\(-1\)	\(1\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{7}+\cdots\)
4046.2.a.f	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓				14.2.a.a	$1$	$1$	\(-1\)	\(2\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
4046.2.a.g	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓	✓			4046.2.a.a	$1$	$0$	\(-1\)	\(3\)	\(2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}+q^{4}+2q^{5}-3q^{6}+q^{7}+\cdots\)
4046.2.a.h	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓	✓			4046.2.a.h	$1$	$0$	\(1\)	\(-3\)	\(-1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
4046.2.a.i	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓				238.2.a.e	$1$	$1$	\(1\)	\(-2\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{7}+q^{8}+\cdots\)
4046.2.a.j	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓	✓			4046.2.a.j	$1$	$0$	\(1\)	\(-1\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
4046.2.a.k	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓	✓			4046.2.a.k	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
4046.2.a.l	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓	✓			4046.2.a.l	$1$	$0$	\(1\)	\(-1\)	\(4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
4046.2.a.m	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓				238.2.a.d	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
4046.2.a.n	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓				238.2.b.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{9}+2q^{13}+\cdots\)
4046.2.a.o	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓				238.2.b.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}+2q^{13}+\cdots\)
4046.2.a.p	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓	✓			4046.2.a.l	$1$	$0$	\(1\)	\(1\)	\(-4\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots\)
4046.2.a.q	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓	✓			4046.2.a.k	$1$	$1$	\(1\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
4046.2.a.r	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓	✓			4046.2.a.j	$1$	$0$	\(1\)	\(1\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots\)
4046.2.a.s	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓				238.2.a.c	$1$	$0$	\(1\)	\(2\)	\(4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}+4q^{5}+2q^{6}-q^{7}+\cdots\)
4046.2.a.t	$4046$	$2$	4046.a	1.a	$1$	$1$	$1$	$32.307$	\(\Q\)	None	✓	✓			4046.2.a.h	$1$	$0$	\(1\)	\(3\)	\(1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}+q^{4}+q^{5}+3q^{6}-q^{7}+\cdots\)
4046.2.a.u	$4046$	$2$	4046.a	1.a	$1$	$2$	$2$	$32.307$	\(\Q(\sqrt{2}) \)	None	✓	✓			4046.2.a.u	$1$	$0$	\(-2\)	\(-2\)	\(-2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
4046.2.a.v	$4046$	$2$	4046.a	1.a	$1$	$2$	$2$	$32.307$	\(\Q(\sqrt{5}) \)	None	✓				238.2.a.f	$1$	$0$	\(-2\)	\(-2\)	\(-2\)	\(2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots\)
4046.2.a.w	$4046$	$2$	4046.a	1.a	$1$	$2$	$2$	$32.307$	\(\Q(\sqrt{2}) \)	None	✓	✓			4046.2.a.u	$1$	$0$	\(-2\)	\(2\)	\(2\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}+(1-\beta )q^{5}+\cdots\)
4046.2.a.x	$4046$	$2$	4046.a	1.a	$1$	$3$	$3$	$32.307$	3.3.148.1	None	✓				238.2.b.b	$1$	$1$	\(-3\)	\(-2\)	\(2\)	\(-3\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{2})q^{5}+\cdots\)
4046.2.a.y	$4046$	$2$	4046.a	1.a	$1$	$3$	$3$	$32.307$	\(\Q(\zeta_{18})^+\)	None	✓	✓			4046.2.a.y	$1$	$1$	\(-3\)	\(0\)	\(0\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
4046.2.a.z	$4046$	$2$	4046.a	1.a	$1$	$3$	$3$	$32.307$	\(\Q(\zeta_{18})^+\)	None	✓	✓			4046.2.a.y	$1$	$1$	\(-3\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
4046.2.a.ba	$4046$	$2$	4046.a	1.a	$1$	$3$	$3$	$32.307$	3.3.148.1	None	✓				238.2.b.b	$1$	$0$	\(-3\)	\(2\)	\(-2\)	\(3\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
4046.2.a.bb	$4046$	$2$	4046.a	1.a	$1$	$3$	$3$	$32.307$	\(\Q(\zeta_{18})^+\)	None	✓	✓			4046.2.a.bb	$1$	$1$	\(3\)	\(0\)	\(0\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+(2\beta _{1}-\beta _{2})q^{5}+\cdots\)
4046.2.a.bc	$4046$	$2$	4046.a	1.a	$1$	$3$	$3$	$32.307$	\(\Q(\zeta_{18})^+\)	None	✓	✓			4046.2.a.bb	$1$	$1$	\(3\)	\(0\)	\(0\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-2\beta _{1}+\beta _{2})q^{5}+\cdots\)
4046.2.a.bd	$4046$	$2$	4046.a	1.a	$1$	$4$	$4$	$32.307$	\(\Q(\zeta_{16})^+\)	None	✓		✓		238.2.g.a	$1$	$1$	\(-4\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{2}+\beta _{3})q^{5}+\cdots\)
4046.2.a.be	$4046$	$2$	4046.a	1.a	$1$	$4$	$4$	$32.307$	\(\Q(\zeta_{16})^+\)	None	✓				238.2.g.a	$1$	$0$	\(-4\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots\)
4046.2.a.bf	$4046$	$2$	4046.a	1.a	$1$	$4$	$4$	$32.307$	\(\Q(\sqrt{7 +2 \sqrt{2}})\)	None	✓		✓		238.2.g.b	$1$	$1$	\(4\)	\(-4\)	\(-4\)	\(4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
4046.2.a.bg	$4046$	$2$	4046.a	1.a	$1$	$4$	$4$	$32.307$	\(\Q(\sqrt{7 +2 \sqrt{2}})\)	None	✓				238.2.g.b	$1$	$0$	\(4\)	\(4\)	\(4\)	\(-4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
4046.2.a.bh	$4046$	$2$	4046.a	1.a	$1$	$8$	$8$	$32.307$	8.8.6513754112.1	None	✓				238.2.k.a	$1$	$0$	\(-8\)	\(0\)	\(0\)	\(-8\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+(\beta _{4}-\beta _{5})q^{3}+q^{4}+(-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
4046.2.a.bi	$4046$	$2$	4046.a	1.a	$1$	$8$	$8$	$32.307$	8.8.6513754112.1	None	✓		✓		238.2.k.a	$1$	$1$	\(-8\)	\(0\)	\(0\)	\(8\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+(\beta _{2}+\beta _{4})q^{3}+q^{4}+(-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
4046.2.a.bj	$4046$	$2$	4046.a	1.a	$1$	$9$	$9$	$32.307$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓		4046.2.a.bj	$1$	$0$	\(-9\)	\(0\)	\(0\)	\(-9\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{6}+\beta _{7})q^{5}+\cdots\)
4046.2.a.bk	$4046$	$2$	4046.a	1.a	$1$	$9$	$9$	$32.307$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓		4046.2.a.bj	$1$	$0$	\(-9\)	\(0\)	\(0\)	\(9\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{6}-\beta _{7})q^{5}+\cdots\)
4046.2.a.bl	$4046$	$2$	4046.a	1.a	$1$	$9$	$9$	$32.307$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓		4046.2.a.bl	$1$	$0$	\(9\)	\(0\)	\(0\)	\(-9\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
4046.2.a.bm	$4046$	$2$	4046.a	1.a	$1$	$9$	$9$	$32.307$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓			4046.2.a.bl	$1$	$0$	\(9\)	\(0\)	\(0\)	\(9\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
4046.2.a.bn	$4046$	$2$	4046.a	1.a	$1$	$12$	$12$	$32.307$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		238.2.k.b	$1$	$1$	\(12\)	\(-8\)	\(-8\)	\(-12\)		$-$	$+$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{7})q^{3}+q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\)
4046.2.a.bo	$4046$	$2$	4046.a	1.a	$1$	$12$	$12$	$32.307$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		238.2.k.b	$1$	$0$	\(12\)	\(8\)	\(8\)	\(12\)		$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{7})q^{3}+q^{4}+(1-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4046))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4046)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2023))\)\(^{\oplus 2}\)