Space of modular forms of level 2366, weight 2, and trivial character

• Label: 2366.2.a
• Level: $2366$
• Weight: $2$
• Character orbit: 2366.a
• Rep. character: $\chi_{2366}(1,\cdot)$
• Character field: $\Q$
• Dimension: $78$
• Newform subspaces: $34$
• Sturm bound: $728$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 34 \)
Sturm bound:			\(728\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2366))\).

	Total	New	Old
Modular forms	392	78	314
Cusp forms	337	78	259
Eisenstein series	55	0	55

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

\(2\)	\(7\)	\(13\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(42\)	\(8\)	\(34\)		\(36\)	\(8\)	\(28\)		\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)		\(55\)	\(12\)	\(43\)		\(48\)	\(12\)	\(36\)		\(7\)	\(0\)	\(7\)
\(+\)	\(-\)	\(+\)	\(-\)		\(56\)	\(13\)	\(43\)		\(49\)	\(13\)	\(36\)		\(7\)	\(0\)	\(7\)
\(+\)	\(-\)	\(-\)	\(+\)		\(43\)	\(6\)	\(37\)		\(36\)	\(6\)	\(30\)		\(7\)	\(0\)	\(7\)
\(-\)	\(+\)	\(+\)	\(-\)		\(49\)	\(10\)	\(39\)		\(42\)	\(10\)	\(32\)		\(7\)	\(0\)	\(7\)
\(-\)	\(+\)	\(-\)	\(+\)		\(50\)	\(9\)	\(41\)		\(43\)	\(9\)	\(34\)		\(7\)	\(0\)	\(7\)
\(-\)	\(-\)	\(+\)	\(+\)		\(49\)	\(5\)	\(44\)		\(42\)	\(5\)	\(37\)		\(7\)	\(0\)	\(7\)
\(-\)	\(-\)	\(-\)	\(-\)		\(48\)	\(15\)	\(33\)		\(41\)	\(15\)	\(26\)		\(7\)	\(0\)	\(7\)
Plus space			\(+\)		\(184\)	\(28\)	\(156\)		\(157\)	\(28\)	\(129\)		\(27\)	\(0\)	\(27\)
Minus space			\(-\)		\(208\)	\(50\)	\(158\)		\(180\)	\(50\)	\(130\)		\(28\)	\(0\)	\(28\)

Trace form

78 * q - 6 * q^3 + 78 * q^4 - 2 * q^5 - 2 * q^6 + 78 * q^9 + 6 * q^10 + 4 * q^11 - 6 * q^12 + 2 * q^14 + 8 * q^15 + 78 * q^16 + 4 * q^18 - 2 * q^19 - 2 * q^20 + 2 * q^21 - 8 * q^22 + 8 * q^23 - 2 * q^24 + 82 * q^25 - 12 * q^27 + 28 * q^29 + 16 * q^30 - 4 * q^31 + 16 * q^33 + 12 * q^34 + 6 * q^35 + 78 * q^36 - 24 * q^37 + 10 * q^38 + 6 * q^40 + 16 * q^41 + 2 * q^42 + 4 * q^44 + 38 * q^45 + 20 * q^47 - 6 * q^48 + 78 * q^49 - 4 * q^50 + 20 * q^51 + 8 * q^53 + 4 * q^54 + 2 * q^56 + 12 * q^57 + 4 * q^58 + 14 * q^59 + 8 * q^60 - 18 * q^61 - 4 * q^62 - 4 * q^63 + 78 * q^64 - 24 * q^67 + 32 * q^69 - 6 * q^70 - 24 * q^71 + 4 * q^72 - 36 * q^73 + 24 * q^74 - 34 * q^75 - 2 * q^76 + 12 * q^77 + 16 * q^79 - 2 * q^80 + 82 * q^81 + 4 * q^82 + 6 * q^83 + 2 * q^84 - 4 * q^85 - 28 * q^86 + 4 * q^87 - 8 * q^88 + 4 * q^89 + 38 * q^90 + 8 * q^92 - 40 * q^93 - 4 * q^94 - 24 * q^95 - 2 * q^96 - 24 * q^97 + 28 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2366))\) 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	13
2366.2.a.a	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				182.2.g.c	$1$	$2$	\(-1\)	\(-2\)	\(-3\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}+q^{7}+\cdots\)
2366.2.a.b	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				182.2.g.d	$1$	$1$	\(-1\)	\(-2\)	\(1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
2366.2.a.c	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				182.2.d.a	$1$	$1$	\(-1\)	\(-1\)	\(-2\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
2366.2.a.d	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				182.2.a.c	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
2366.2.a.e	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				182.2.a.d	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
2366.2.a.f	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				182.2.g.b	$1$	$0$	\(-1\)	\(1\)	\(3\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots\)
2366.2.a.g	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				182.2.g.a	$1$	$0$	\(-1\)	\(3\)	\(-3\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}+q^{4}-3q^{5}-3q^{6}+q^{7}+\cdots\)
2366.2.a.h	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				182.2.a.e	$1$	$0$	\(-1\)	\(3\)	\(4\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}+q^{4}+4q^{5}-3q^{6}+q^{7}+\cdots\)
2366.2.a.i	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				182.2.g.d	$1$	$1$	\(1\)	\(-2\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{7}+\cdots\)
2366.2.a.j	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				14.2.a.a	$1$	$0$	\(1\)	\(-2\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots\)
2366.2.a.k	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				182.2.g.c	$1$	$0$	\(1\)	\(-2\)	\(3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}-q^{7}+\cdots\)
2366.2.a.l	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				182.2.d.a	$1$	$1$	\(1\)	\(-1\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-q^{7}+\cdots\)
2366.2.a.m	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				182.2.a.a	$1$	$1$	\(1\)	\(1\)	\(-4\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots\)
2366.2.a.n	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				182.2.g.b	$1$	$0$	\(1\)	\(1\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
2366.2.a.o	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				182.2.a.b	$1$	$0$	\(1\)	\(3\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}+q^{4}+3q^{6}-q^{7}+q^{8}+\cdots\)
2366.2.a.p	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	\(\Q\)	None	✓				182.2.g.a	$1$	$0$	\(1\)	\(3\)	\(3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}+q^{4}+3q^{5}+3q^{6}-q^{7}+\cdots\)
2366.2.a.q	$2366$	$2$	2366.a	1.a	$1$	$2$	$2$	$18.893$	\(\Q(\sqrt{3}) \)	None	✓				182.2.m.a	$1$	$1$	\(-2\)	\(-2\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots\)
2366.2.a.r	$2366$	$2$	2366.a	1.a	$1$	$2$	$2$	$18.893$	\(\Q(\sqrt{3}) \)	None	✓				182.2.g.e	$1$	$0$	\(-2\)	\(0\)	\(-4\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}+(-2-\beta )q^{5}-\beta q^{6}+\cdots\)
2366.2.a.s	$2366$	$2$	2366.a	1.a	$1$	$2$	$2$	$18.893$	\(\Q(\sqrt{3}) \)	None	✓				182.2.m.a	$1$	$1$	\(2\)	\(-2\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
2366.2.a.t	$2366$	$2$	2366.a	1.a	$1$	$2$	$2$	$18.893$	\(\Q(\sqrt{3}) \)	None	✓				182.2.g.e	$1$	$0$	\(2\)	\(0\)	\(4\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}+(2+\beta )q^{5}+\beta q^{6}+\cdots\)
2366.2.a.u	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	\(\Q(\zeta_{14})^+\)	None	✓	✓			2366.2.a.u	$1$	$0$	\(-3\)	\(-5\)	\(-2\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-2-\beta _{2})q^{3}+q^{4}-2\beta _{1}q^{5}+\cdots\)
2366.2.a.v	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	\(\Q(\zeta_{14})^+\)	None	✓	✓			2366.2.a.v	$1$	$0$	\(-3\)	\(-4\)	\(-2\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
2366.2.a.w	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	\(\Q(\zeta_{14})^+\)	None	✓	✓			2366.2.a.w	$1$	$0$	\(-3\)	\(0\)	\(8\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}+(3+\beta _{2})q^{5}+\cdots\)
2366.2.a.x	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	3.3.1384.1	None	✓				182.2.d.b	$1$	$0$	\(-3\)	\(1\)	\(-2\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
2366.2.a.y	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	\(\Q(\zeta_{14})^+\)	None	✓	✓	✓		2366.2.a.y	$1$	$1$	\(-3\)	\(2\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots\)
2366.2.a.z	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	\(\Q(\zeta_{14})^+\)	None	✓	✓			2366.2.a.u	$1$	$1$	\(3\)	\(-5\)	\(2\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-2-\beta _{2})q^{3}+q^{4}+2\beta _{1}q^{5}+\cdots\)
2366.2.a.ba	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	\(\Q(\zeta_{14})^+\)	None	✓	✓	✓		2366.2.a.v	$1$	$1$	\(3\)	\(-4\)	\(2\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2366.2.a.bb	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	\(\Q(\zeta_{14})^+\)	None	✓	✓			2366.2.a.w	$1$	$1$	\(3\)	\(0\)	\(-8\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-3+\cdots)q^{5}+\cdots\)
2366.2.a.bc	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	3.3.1384.1	None	✓				182.2.d.b	$1$	$0$	\(3\)	\(1\)	\(2\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{2})q^{5}+\beta _{1}q^{6}+\cdots\)
2366.2.a.bd	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	\(\Q(\zeta_{14})^+\)	None	✓	✓	✓		2366.2.a.y	$1$	$0$	\(3\)	\(2\)	\(0\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
2366.2.a.be	$2366$	$2$	2366.a	1.a	$1$	$6$	$6$	$18.893$	6.6.6052921.1	None	✓	✓	✓		2366.2.a.be	$1$	$1$	\(-6\)	\(1\)	\(-4\)	\(-6\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
2366.2.a.bf	$2366$	$2$	2366.a	1.a	$1$	$6$	$6$	$18.893$	6.6.285686784.1	None	✓		✓		182.2.m.b	$1$	$0$	\(-6\)	\(2\)	\(2\)	\(-6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{1}+\beta _{5})q^{5}+\cdots\)
2366.2.a.bg	$2366$	$2$	2366.a	1.a	$1$	$6$	$6$	$18.893$	6.6.6052921.1	None	✓	✓			2366.2.a.be	$1$	$0$	\(6\)	\(1\)	\(4\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{4})q^{5}+\beta _{1}q^{6}+\cdots\)
2366.2.a.bh	$2366$	$2$	2366.a	1.a	$1$	$6$	$6$	$18.893$	6.6.285686784.1	None	✓				182.2.m.b	$1$	$0$	\(6\)	\(2\)	\(-2\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2366))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2366)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\)\(^{\oplus 2}\)