Space of modular forms of level 2783, weight 2, and trivial character

• Label: 2783.2.a
• Level: $2783$
• Weight: $2$
• Character orbit: 2783.a
• Rep. character: $\chi_{2783}(1,\cdot)$
• Character field: $\Q$
• Dimension: $201$
• Newform subspaces: $20$
• Sturm bound: $528$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2783 = 11^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2783.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(528\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2783))\).

	Total	New	Old
Modular forms	276	201	75
Cusp forms	253	201	52
Eisenstein series	23	0	23

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
\(+\)	\(+\)	\(+\)		\(60\)	\(42\)	\(18\)		\(55\)	\(42\)	\(13\)		\(5\)	\(0\)	\(5\)
\(+\)	\(-\)	\(-\)		\(78\)	\(60\)	\(18\)		\(72\)	\(60\)	\(12\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)		\(78\)	\(57\)	\(21\)		\(72\)	\(57\)	\(15\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)		\(60\)	\(42\)	\(18\)		\(54\)	\(42\)	\(12\)		\(6\)	\(0\)	\(6\)
Plus space		\(+\)		\(120\)	\(84\)	\(36\)		\(109\)	\(84\)	\(25\)		\(11\)	\(0\)	\(11\)
Minus space		\(-\)		\(156\)	\(117\)	\(39\)		\(144\)	\(117\)	\(27\)		\(12\)	\(0\)	\(12\)

Trace form

201 * q + 204 * q^4 + 4 * q^5 - q^6 + 2 * q^7 + 9 * q^8 + 195 * q^9 + 5 * q^12 + 16 * q^13 + 4 * q^14 - 2 * q^15 + 194 * q^16 + 4 * q^17 + 27 * q^18 + 4 * q^19 + 22 * q^20 + 14 * q^21 + 3 * q^23 - 10 * q^24 + 207 * q^25 - 9 * q^26 + 24 * q^27 + 2 * q^28 - 4 * q^29 + 10 * q^30 + 16 * q^31 + 38 * q^32 - 26 * q^34 + 8 * q^35 + 195 * q^36 + 20 * q^37 - 22 * q^38 - 20 * q^39 - 20 * q^40 - 12 * q^41 - 12 * q^42 - 8 * q^43 - 2 * q^45 - 2 * q^46 + 20 * q^47 + 5 * q^48 + 213 * q^49 + 2 * q^51 + 23 * q^52 - 18 * q^53 - 87 * q^54 - 18 * q^56 - 8 * q^57 - 15 * q^58 - 16 * q^59 - 52 * q^60 + 18 * q^61 - 45 * q^62 + 24 * q^63 + 145 * q^64 + 6 * q^65 + 6 * q^67 + 4 * q^68 + 4 * q^69 - 56 * q^70 - 28 * q^71 + 61 * q^72 + 8 * q^73 - 28 * q^74 + 32 * q^75 + 18 * q^76 - 47 * q^78 + 8 * q^79 + 8 * q^80 + 153 * q^81 + 23 * q^82 + 34 * q^83 + 54 * q^84 + 28 * q^85 + 40 * q^86 + 12 * q^87 - 26 * q^89 + 58 * q^90 + 58 * q^91 + 6 * q^92 + 46 * q^93 - 65 * q^94 - 24 * q^95 - 49 * q^96 + 56 * q^97 - 32 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2783))\) 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
2783.2.a.a	$2783$	$2$	2783.a	1.a	$1$	$2$	$2$	$22.222$	\(\Q(\sqrt{5}) \)	None	✓				253.2.e.a	$1$	$2$	\(-2\)	\(-3\)	\(-5\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1-\beta )q^{3}-q^{4}+(-2-\beta )q^{5}+\cdots\)
2783.2.a.b	$2783$	$2$	2783.a	1.a	$1$	$2$	$2$	$22.222$	\(\Q(\sqrt{3}) \)	None	✓	✓			2783.2.a.b	$2$	$1$	\(0\)	\(4\)	\(-6\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+2q^{3}+q^{4}-3q^{5}+2\beta q^{6}+\cdots\)
2783.2.a.c	$2783$	$2$	2783.a	1.a	$1$	$2$	$2$	$22.222$	\(\Q(\sqrt{5}) \)	None	✓				23.2.a.a	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
2783.2.a.d	$2783$	$2$	2783.a	1.a	$1$	$2$	$2$	$22.222$	\(\Q(\sqrt{5}) \)	None	✓				253.2.e.a	$1$	$1$	\(2\)	\(-3\)	\(-5\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta )q^{3}-q^{4}+(-2-\beta )q^{5}+\cdots\)
2783.2.a.e	$2783$	$2$	2783.a	1.a	$1$	$3$	$3$	$22.222$	\(\Q(\zeta_{18})^+\)	None	✓				253.2.a.b	$1$	$1$	\(-3\)	\(3\)	\(3\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+\cdots\)
2783.2.a.f	$2783$	$2$	2783.a	1.a	$1$	$3$	$3$	$22.222$	3.3.169.1	None	✓				253.2.a.a	$1$	$1$	\(1\)	\(-5\)	\(-5\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{2})q^{2}+(-2+\beta _{1})q^{3}+\cdots\)
2783.2.a.g	$2783$	$2$	2783.a	1.a	$1$	$5$	$5$	$22.222$	5.5.170701.1	None	✓				253.2.a.c	$1$	$0$	\(4\)	\(-5\)	\(-3\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
2783.2.a.h	$2783$	$2$	2783.a	1.a	$1$	$6$	$6$	$22.222$	6.6.8639957.1	None	✓				253.2.a.d	$1$	$0$	\(-3\)	\(7\)	\(3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots\)
2783.2.a.i	$2783$	$2$	2783.a	1.a	$1$	$6$	$6$	$22.222$	6.6.3822093.1	None	✓	✓			2783.2.a.i	$1$	$1$	\(-1\)	\(-5\)	\(-2\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{1})q^{3}+(1+\cdots)q^{4}+\cdots\)
2783.2.a.j	$2783$	$2$	2783.a	1.a	$1$	$6$	$6$	$22.222$	6.6.9139520.1	None	✓	✓			2783.2.a.j	$2$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+\beta _{2}q^{4}-\beta _{2}q^{5}+\cdots\)
2783.2.a.k	$2783$	$2$	2783.a	1.a	$1$	$6$	$6$	$22.222$	6.6.3822093.1	None	✓	✓			2783.2.a.i	$1$	$1$	\(1\)	\(-5\)	\(-2\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{2}+(-1+\beta _{1})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
2783.2.a.l	$2783$	$2$	2783.a	1.a	$1$	$12$	$12$	$22.222$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			2783.2.a.l	$1$	$0$	\(-1\)	\(3\)	\(6\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
2783.2.a.m	$2783$	$2$	2783.a	1.a	$1$	$12$	$12$	$22.222$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			2783.2.a.m	$2$	$1$	\(0\)	\(-10\)	\(-4\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{8}q^{2}+(-1+\beta _{7})q^{3}+(1-\beta _{7}+\beta _{11})q^{4}+\cdots\)
2783.2.a.n	$2783$	$2$	2783.a	1.a	$1$	$12$	$12$	$22.222$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			2783.2.a.n	$2$	$0$	\(0\)	\(6\)	\(6\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{10})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2783.2.a.o	$2783$	$2$	2783.a	1.a	$1$	$12$	$12$	$22.222$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			2783.2.a.l	$1$	$0$	\(1\)	\(3\)	\(6\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
2783.2.a.p	$2783$	$2$	2783.a	1.a	$1$	$20$	$20$	$22.222$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		253.2.e.b	$1$	$1$	\(-8\)	\(2\)	\(5\)	\(-18\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{17}q^{3}+(1+\beta _{2})q^{4}+\beta _{15}q^{5}+\cdots\)
2783.2.a.q	$2783$	$2$	2783.a	1.a	$1$	$20$	$20$	$22.222$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓				253.2.e.b	$1$	$0$	\(8\)	\(2\)	\(5\)	\(18\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{17}q^{3}+(1+\beta _{2})q^{4}+\beta _{15}q^{5}+\cdots\)
2783.2.a.r	$2783$	$2$	2783.a	1.a	$1$	$22$	$22$	$22.222$		None	✓		✓		253.2.e.c	$1$	$1$	\(-2\)	\(-1\)	\(0\)	\(-18\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
2783.2.a.s	$2783$	$2$	2783.a	1.a	$1$	$22$	$22$	$22.222$		None	✓		✓		253.2.e.c	$1$	$0$	\(2\)	\(-1\)	\(0\)	\(18\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2783.2.a.t	$2783$	$2$	2783.a	1.a	$1$	$26$	$26$	$22.222$		None	✓	✓	✓		2783.2.a.t	$2$	$0$	\(0\)	\(10\)	\(6\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2783))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2783)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(253))\)\(^{\oplus 2}\)