Space of modular forms of level 20339, weight 2, and trivial character

• Label: 20339.2.a
• Level: $20339$
• Weight: $2$
• Character orbit: 20339.a
• Rep. character: $\chi_{20339}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1504$
• Newform subspaces: $32$
• Sturm bound: $3784$

Defining parameters

Level:	\( N \)	\(=\)	\( 20339 = 11 \cdot 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	20339.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 32 \)
Sturm bound:			\(3784\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(20339))\).

	Total	New	Old
Modular forms	1936	1504	432
Cusp forms	1849	1504	345
Eisenstein series	87	0	87

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

\(11\)	\(43\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(462\)	\(359\)	\(103\)		\(441\)	\(359\)	\(82\)		\(21\)	\(0\)	\(21\)
\(+\)	\(-\)	\(-\)		\(506\)	\(392\)	\(114\)		\(484\)	\(392\)	\(92\)		\(22\)	\(0\)	\(22\)
\(-\)	\(+\)	\(-\)		\(506\)	\(403\)	\(103\)		\(484\)	\(403\)	\(81\)		\(22\)	\(0\)	\(22\)
\(-\)	\(-\)	\(+\)		\(462\)	\(350\)	\(112\)		\(440\)	\(350\)	\(90\)		\(22\)	\(0\)	\(22\)
Plus space		\(+\)		\(924\)	\(709\)	\(215\)		\(881\)	\(709\)	\(172\)		\(43\)	\(0\)	\(43\)
Minus space		\(-\)		\(1012\)	\(795\)	\(217\)		\(968\)	\(795\)	\(173\)		\(44\)	\(0\)	\(44\)

Trace form

1504 * q + q^2 - q^3 + 1507 * q^4 + 3 * q^5 + 6 * q^6 - 6 * q^7 + 15 * q^8 + 1501 * q^9 + 16 * q^10 + 2 * q^11 + 14 * q^12 - 2 * q^13 + 12 * q^14 + 23 * q^15 + 1509 * q^16 + 16 * q^17 + 15 * q^18 - 4 * q^20 - 22 * q^21 - q^22 + 11 * q^23 + 8 * q^24 + 1513 * q^25 + 10 * q^26 + 5 * q^27 + 12 * q^28 - 10 * q^29 - 26 * q^30 - 5 * q^31 + 31 * q^32 - q^33 + 34 * q^34 - 10 * q^35 + 1505 * q^36 + q^37 + 4 * q^38 + 12 * q^39 + 50 * q^40 - 10 * q^41 - 28 * q^42 + q^44 + 4 * q^45 - 14 * q^46 + 28 * q^47 + 20 * q^48 + 1464 * q^49 - 43 * q^50 - 2 * q^51 - 26 * q^52 + 28 * q^53 + 26 * q^54 - q^55 + 8 * q^56 + 20 * q^57 + 34 * q^58 + q^59 + 6 * q^60 - 2 * q^61 - 38 * q^62 + 64 * q^63 + 1553 * q^64 + 52 * q^65 + 14 * q^66 + 13 * q^67 + 18 * q^68 + 25 * q^69 - 16 * q^70 - 15 * q^71 + 43 * q^72 - 26 * q^73 - 48 * q^74 - 16 * q^75 + 8 * q^76 - 2 * q^77 + 4 * q^78 - 30 * q^79 - 6 * q^80 + 1480 * q^81 + 42 * q^82 + 14 * q^83 - 52 * q^84 + 38 * q^85 - 12 * q^87 + 9 * q^88 - 7 * q^89 - 26 * q^90 - 48 * q^91 - 14 * q^92 - 7 * q^93 + 24 * q^94 - 4 * q^95 - 48 * q^96 + 15 * q^97 + q^98 + 11 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(20339))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11	43
20339.2.a.a	$20339$	$2$	20339.a	1.a	$1$	$1$	$1$	$162.408$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(-1\)	\(1\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
20339.2.a.b	$20339$	$2$	20339.a	1.a	$1$	$1$	$1$	$162.408$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(1\)	\(-3\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
20339.2.a.c	$20339$	$2$	20339.a	1.a	$1$	$1$	$1$	$162.408$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(-1\)	\(3\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}+3q^{5}-q^{6}-q^{7}+\cdots\)
20339.2.a.d	$20339$	$2$	20339.a	1.a	$1$	$1$	$1$	$162.408$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(1\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{7}+\cdots\)
20339.2.a.e	$20339$	$2$	20339.a	1.a	$1$	$1$	$1$	$162.408$	\(\Q\)	None	✓	?				$-1$		\(2\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}-2q^{9}+\cdots\)
20339.2.a.f	$20339$	$2$	20339.a	1.a	$1$	$1$	$1$	$162.408$	\(\Q\)	None	✓	?				$-1$		\(2\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}+2q^{7}+\cdots\)
20339.2.a.g	$20339$	$2$	20339.a	1.a	$1$	$2$	$2$	$162.408$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-1\)	\(2\)	\(-2\)	\(4\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
20339.2.a.h	$20339$	$2$	20339.a	1.a	$1$	$2$	$2$	$162.408$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-1\)	\(4\)	\(-2\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
20339.2.a.i	$20339$	$2$	20339.a	1.a	$1$	$5$	$5$	$162.408$	5.5.38569.1	None	✓	?				$-1$		\(-1\)	\(3\)	\(6\)	\(15\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
20339.2.a.j	$20339$	$2$	20339.a	1.a	$1$	$5$	$5$	$162.408$	5.5.173513.1	None	✓	?				$-1$		\(3\)	\(1\)	\(4\)	\(9\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
20339.2.a.k	$20339$	$2$	20339.a	1.a	$1$	$9$	$9$	$162.408$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(-4\)	\(-5\)	\(0\)	\(-19\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
20339.2.a.l	$20339$	$2$	20339.a	1.a	$1$	$11$	$11$	$162.408$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(1\)	\(-6\)	\(-3\)	\(-17\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
20339.2.a.m	$20339$	$2$	20339.a	1.a	$1$	$16$	$16$	$162.408$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$
20339.2.a.n	$20339$	$2$	20339.a	1.a	$1$	$17$	$17$	$162.408$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-5\)	\(-2\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
20339.2.a.o	$20339$	$2$	20339.a	1.a	$1$	$17$	$17$	$162.408$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-7\)	\(-8\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
20339.2.a.p	$20339$	$2$	20339.a	1.a	$1$	$17$	$17$	$162.408$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(2\)	\(7\)	\(8\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
20339.2.a.q	$20339$	$2$	20339.a	1.a	$1$	$17$	$17$	$162.408$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	?				$-1$		\(2\)	\(0\)	\(5\)	\(2\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
20339.2.a.r	$20339$	$2$	20339.a	1.a	$1$	$20$	$20$	$162.408$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$
20339.2.a.s	$20339$	$2$	20339.a	1.a	$1$	$57$	$57$	$162.408$		None	✓	?				$-1$		\(-3\)	\(-12\)	\(-18\)	\(-9\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
20339.2.a.t	$20339$	$2$	20339.a	1.a	$1$	$57$	$57$	$162.408$		None	✓	?				$-1$		\(-3\)	\(0\)	\(-6\)	\(-15\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
20339.2.a.u	$20339$	$2$	20339.a	1.a	$1$	$57$	$57$	$162.408$		None	✓	?				$-1$		\(3\)	\(0\)	\(6\)	\(15\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
20339.2.a.v	$20339$	$2$	20339.a	1.a	$1$	$57$	$57$	$162.408$		None	✓	?				$-1$		\(3\)	\(12\)	\(18\)	\(9\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
20339.2.a.w	$20339$	$2$	20339.a	1.a	$1$	$75$	$75$	$162.408$		None	✓	?				$-1$		\(-5\)	\(1\)	\(4\)	\(1\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
20339.2.a.x	$20339$	$2$	20339.a	1.a	$1$	$75$	$75$	$162.408$		None	✓	?				$-1$		\(5\)	\(-1\)	\(-4\)	\(-1\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
20339.2.a.y	$20339$	$2$	20339.a	1.a	$1$	$95$	$95$	$162.408$		None	✓	?				$-1$		\(-5\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
20339.2.a.z	$20339$	$2$	20339.a	1.a	$1$	$95$	$95$	$162.408$		None	✓	?				$-1$		\(5\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
20339.2.a.ba	$20339$	$2$	20339.a	1.a	$1$	$108$	$108$	$162.408$		None	✓	?	✓			$-1$		\(-6\)	\(-18\)	\(-36\)	\(-23\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
20339.2.a.bb	$20339$	$2$	20339.a	1.a	$1$	$108$	$108$	$162.408$		None	✓	?				$-1$		\(-6\)	\(-6\)	\(-12\)	\(-25\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
20339.2.a.bc	$20339$	$2$	20339.a	1.a	$1$	$108$	$108$	$162.408$		None	✓	?	✓			$-1$		\(6\)	\(6\)	\(12\)	\(25\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
20339.2.a.bd	$20339$	$2$	20339.a	1.a	$1$	$108$	$108$	$162.408$		None	✓	?				$-1$		\(6\)	\(18\)	\(36\)	\(23\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
20339.2.a.be	$20339$	$2$	20339.a	1.a	$1$	$160$	$160$	$162.408$		not computed	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$
20339.2.a.bf	$20339$	$2$	20339.a	1.a	$1$	$200$	$200$	$162.408$		not computed	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(20339))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(20339)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(473))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1849))\)\(^{\oplus 2}\)