Space of modular forms of level 5819, weight 2, and trivial character

• Label: 5819.2.a
• Level: $5819$
• Weight: $2$
• Character orbit: 5819.a
• Rep. character: $\chi_{5819}(1,\cdot)$
• Character field: $\Q$
• Dimension: $422$
• Newform subspaces: $21$
• Sturm bound: $1104$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 5819 = 11 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5819.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 21 \)
Sturm bound:			\(1104\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5819))\).

	Total	New	Old
Modular forms	576	422	154
Cusp forms	529	422	107
Eisenstein series	47	0	47

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

\(11\)	\(23\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(132\)	\(98\)	\(34\)		\(121\)	\(98\)	\(23\)		\(11\)	\(0\)	\(11\)
\(+\)	\(-\)	\(-\)		\(154\)	\(114\)	\(40\)		\(142\)	\(114\)	\(28\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(-\)		\(156\)	\(118\)	\(38\)		\(144\)	\(118\)	\(26\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(+\)		\(134\)	\(92\)	\(42\)		\(122\)	\(92\)	\(30\)		\(12\)	\(0\)	\(12\)
Plus space		\(+\)		\(266\)	\(190\)	\(76\)		\(243\)	\(190\)	\(53\)		\(23\)	\(0\)	\(23\)
Minus space		\(-\)		\(310\)	\(232\)	\(78\)		\(286\)	\(232\)	\(54\)		\(24\)	\(0\)	\(24\)

Trace form

422 * q + q^2 + q^3 + 421 * q^4 + q^5 - 14 * q^6 + 6 * q^7 + 3 * q^8 + 421 * q^9 + 8 * q^10 - 2 * q^11 + 6 * q^12 + 18 * q^13 + 12 * q^14 - 11 * q^15 + 423 * q^16 + 12 * q^17 + 15 * q^18 + 24 * q^20 + 2 * q^21 - q^22 - 12 * q^24 + 433 * q^25 - 2 * q^26 + 7 * q^27 - 14 * q^29 + 18 * q^30 + 5 * q^31 + 27 * q^32 - 3 * q^33 - 30 * q^34 + 14 * q^35 + 411 * q^36 + 19 * q^37 - 20 * q^38 - 28 * q^39 - 30 * q^40 - 6 * q^41 - 8 * q^42 - 2 * q^43 - q^44 - 4 * q^45 + 16 * q^47 - 32 * q^48 + 434 * q^49 - 19 * q^50 + 10 * q^51 - 6 * q^52 - 16 * q^53 - 90 * q^54 + q^55 - 4 * q^56 - 8 * q^57 - 6 * q^58 - 13 * q^59 - 26 * q^60 + 10 * q^61 - 22 * q^62 + 24 * q^63 + 399 * q^64 - 4 * q^65 - 14 * q^66 + 7 * q^67 + 10 * q^68 - 48 * q^70 + 7 * q^71 + 31 * q^72 + 10 * q^73 - 28 * q^74 + 48 * q^75 + 20 * q^76 + 6 * q^77 - 52 * q^78 + 14 * q^79 + 46 * q^80 + 366 * q^81 - 22 * q^82 + 18 * q^83 + 60 * q^84 - 6 * q^85 + 52 * q^86 + 9 * q^88 - 49 * q^89 + 66 * q^90 + 16 * q^91 - 57 * q^93 - 88 * q^94 - 20 * q^95 - 76 * q^96 + 13 * q^97 - 27 * q^98 - 11 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5819))\) 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	23
5819.2.a.a	$5819$	$2$	5819.a	1.a	$1$	$1$	$1$	$46.465$	\(\Q\)	None	✓				11.2.a.a	$1$	$0$	\(-2\)	\(-1\)	\(-1\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+2q^{7}+\cdots\)
5819.2.a.b	$5819$	$2$	5819.a	1.a	$1$	$3$	$3$	$46.465$	3.3.169.1	None	✓				253.2.a.a	$1$	$0$	\(-1\)	\(-5\)	\(5\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
5819.2.a.c	$5819$	$2$	5819.a	1.a	$1$	$3$	$3$	$46.465$	\(\Q(\zeta_{18})^+\)	None	✓				253.2.a.b	$1$	$1$	\(3\)	\(3\)	\(-3\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
5819.2.a.d	$5819$	$2$	5819.a	1.a	$1$	$5$	$5$	$46.465$	5.5.170701.1	None	✓				253.2.a.c	$1$	$1$	\(-4\)	\(-5\)	\(3\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
5819.2.a.e	$5819$	$2$	5819.a	1.a	$1$	$6$	$6$	$46.465$	6.6.8639957.1	None	✓				253.2.a.d	$1$	$0$	\(3\)	\(7\)	\(-3\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots\)
5819.2.a.f	$5819$	$2$	5819.a	1.a	$1$	$8$	$8$	$46.465$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			5819.2.a.f	$1$	$1$	\(1\)	\(-2\)	\(-4\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
5819.2.a.g	$5819$	$2$	5819.a	1.a	$1$	$8$	$8$	$46.465$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			5819.2.a.f	$1$	$0$	\(1\)	\(-2\)	\(4\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
5819.2.a.h	$5819$	$2$	5819.a	1.a	$1$	$9$	$9$	$46.465$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓			5819.2.a.h	$1$	$1$	\(-1\)	\(-1\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
5819.2.a.i	$5819$	$2$	5819.a	1.a	$1$	$9$	$9$	$46.465$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓			5819.2.a.h	$1$	$0$	\(-1\)	\(-1\)	\(2\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
5819.2.a.j	$5819$	$2$	5819.a	1.a	$1$	$9$	$9$	$46.465$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓			5819.2.a.j	$1$	$1$	\(-1\)	\(-1\)	\(-6\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{3}+\beta _{4})q^{4}+\cdots\)
5819.2.a.k	$5819$	$2$	5819.a	1.a	$1$	$9$	$9$	$46.465$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓			5819.2.a.j	$1$	$0$	\(-1\)	\(-1\)	\(6\)	\(5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{3}+\beta _{4})q^{4}+\cdots\)
5819.2.a.l	$5819$	$2$	5819.a	1.a	$1$	$18$	$18$	$46.465$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓			5819.2.a.l	$1$	$1$	\(0\)	\(4\)	\(-8\)	\(-8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}+\beta _{14}q^{5}+\cdots\)
5819.2.a.m	$5819$	$2$	5819.a	1.a	$1$	$18$	$18$	$46.465$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓			5819.2.a.l	$1$	$0$	\(0\)	\(4\)	\(8\)	\(8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}-\beta _{14}q^{5}+\cdots\)
5819.2.a.n	$5819$	$2$	5819.a	1.a	$1$	$18$	$18$	$46.465$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓			5819.2.a.n	$1$	$1$	\(2\)	\(-2\)	\(-8\)	\(-10\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
5819.2.a.o	$5819$	$2$	5819.a	1.a	$1$	$18$	$18$	$46.465$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓			5819.2.a.n	$1$	$0$	\(2\)	\(-2\)	\(8\)	\(10\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)
5819.2.a.p	$5819$	$2$	5819.a	1.a	$1$	$40$	$40$	$46.465$		None	✓		✓		253.2.i.a	$1$	$1$	\(-5\)	\(-10\)	\(-11\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
5819.2.a.q	$5819$	$2$	5819.a	1.a	$1$	$40$	$40$	$46.465$		None	✓				253.2.i.a	$1$	$1$	\(-5\)	\(-10\)	\(11\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
5819.2.a.r	$5819$	$2$	5819.a	1.a	$1$	$40$	$40$	$46.465$		None	✓	✓			5819.2.a.r	$1$	$1$	\(0\)	\(4\)	\(-16\)	\(-16\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
5819.2.a.s	$5819$	$2$	5819.a	1.a	$1$	$40$	$40$	$46.465$		None	✓	✓			5819.2.a.r	$1$	$0$	\(0\)	\(4\)	\(16\)	\(16\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
5819.2.a.t	$5819$	$2$	5819.a	1.a	$1$	$60$	$60$	$46.465$		None	✓		✓		253.2.i.b	$1$	$0$	\(5\)	\(9\)	\(-8\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
5819.2.a.u	$5819$	$2$	5819.a	1.a	$1$	$60$	$60$	$46.465$		None	✓		✓		253.2.i.b	$1$	$0$	\(5\)	\(9\)	\(8\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5819))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5819)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(253))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 2}\)