Space of modular forms of level 2166, weight 2, and trivial character

• Label: 2166.2.a
• Level: $2166$
• Weight: $2$
• Character orbit: 2166.a
• Rep. character: $\chi_{2166}(1,\cdot)$
• Character field: $\Q$
• Dimension: $57$
• Newform subspaces: $25$
• Sturm bound: $760$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 25 \)
Sturm bound:			\(760\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\), \(13\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2166))\).

	Total	New	Old
Modular forms	420	57	363
Cusp forms	341	57	284
Eisenstein series	79	0	79

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

\(2\)	\(3\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(45\)	\(4\)	\(41\)		\(36\)	\(4\)	\(32\)		\(9\)	\(0\)	\(9\)
\(+\)	\(+\)	\(-\)	\(-\)		\(59\)	\(10\)	\(49\)		\(49\)	\(10\)	\(39\)		\(10\)	\(0\)	\(10\)
\(+\)	\(-\)	\(+\)	\(-\)		\(55\)	\(8\)	\(47\)		\(45\)	\(8\)	\(37\)		\(10\)	\(0\)	\(10\)
\(+\)	\(-\)	\(-\)	\(+\)		\(50\)	\(7\)	\(43\)		\(40\)	\(7\)	\(33\)		\(10\)	\(0\)	\(10\)
\(-\)	\(+\)	\(+\)	\(-\)		\(55\)	\(9\)	\(46\)		\(45\)	\(9\)	\(36\)		\(10\)	\(0\)	\(10\)
\(-\)	\(+\)	\(-\)	\(+\)		\(50\)	\(5\)	\(45\)		\(40\)	\(5\)	\(35\)		\(10\)	\(0\)	\(10\)
\(-\)	\(-\)	\(+\)	\(+\)		\(55\)	\(3\)	\(52\)		\(45\)	\(3\)	\(42\)		\(10\)	\(0\)	\(10\)
\(-\)	\(-\)	\(-\)	\(-\)		\(51\)	\(11\)	\(40\)		\(41\)	\(11\)	\(30\)		\(10\)	\(0\)	\(10\)
Plus space			\(+\)		\(200\)	\(19\)	\(181\)		\(161\)	\(19\)	\(142\)		\(39\)	\(0\)	\(39\)
Minus space			\(-\)		\(220\)	\(38\)	\(182\)		\(180\)	\(38\)	\(142\)		\(40\)	\(0\)	\(40\)

Trace form

57 * q - q^2 + q^3 + 57 * q^4 + 2 * q^5 - q^6 + 4 * q^7 - q^8 + 57 * q^9 - 2 * q^10 + 4 * q^11 + q^12 + 2 * q^13 + 8 * q^14 + 2 * q^15 + 57 * q^16 + 6 * q^17 - q^18 + 2 * q^20 + 8 * q^21 + 8 * q^22 + 16 * q^23 - q^24 + 75 * q^25 + 2 * q^26 + q^27 + 4 * q^28 + 2 * q^29 + 2 * q^30 - 12 * q^31 - q^32 - 2 * q^34 + 8 * q^35 + 57 * q^36 + 2 * q^37 + 6 * q^39 - 2 * q^40 - 26 * q^41 + 16 * q^43 + 4 * q^44 + 2 * q^45 + 8 * q^46 - 8 * q^47 + q^48 + 53 * q^49 + q^50 - 14 * q^51 + 2 * q^52 + 2 * q^53 - q^54 + 16 * q^55 + 8 * q^56 - 6 * q^58 - 4 * q^59 + 2 * q^60 - 10 * q^61 + 4 * q^63 + 57 * q^64 - 4 * q^65 - 4 * q^66 + 4 * q^67 + 6 * q^68 + 8 * q^71 - q^72 + 2 * q^73 - 14 * q^74 - q^75 - 8 * q^77 + 6 * q^78 + 4 * q^79 + 2 * q^80 + 57 * q^81 - 2 * q^82 + 20 * q^83 + 8 * q^84 + 20 * q^85 - 12 * q^86 - 14 * q^87 + 8 * q^88 + 14 * q^89 - 2 * q^90 - 16 * q^91 + 16 * q^92 + 12 * q^93 + 8 * q^94 - q^96 + 10 * q^97 + 7 * q^98 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2166))\) 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	3	19
2166.2.a.a	$2166$	$2$	2166.a	1.a	$1$	$1$	$1$	$17.296$	\(\Q\)	None	✓				114.2.a.c	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots\)
2166.2.a.b	$2166$	$2$	2166.a	1.a	$1$	$1$	$1$	$17.296$	\(\Q\)	None	✓				114.2.e.b	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
2166.2.a.c	$2166$	$2$	2166.a	1.a	$1$	$1$	$1$	$17.296$	\(\Q\)	None	✓				114.2.e.a	$1$	$1$	\(-1\)	\(1\)	\(-4\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-4q^{5}-q^{6}-3q^{7}+\cdots\)
2166.2.a.d	$2166$	$2$	2166.a	1.a	$1$	$1$	$1$	$17.296$	\(\Q\)	None	✓				114.2.a.b	$1$	$1$	\(-1\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
2166.2.a.e	$2166$	$2$	2166.a	1.a	$1$	$1$	$1$	$17.296$	\(\Q\)	None	✓	✓			2166.2.a.e	$1$	$0$	\(-1\)	\(1\)	\(2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
2166.2.a.f	$2166$	$2$	2166.a	1.a	$1$	$1$	$1$	$17.296$	\(\Q\)	None	✓				114.2.e.a	$1$	$0$	\(1\)	\(-1\)	\(-4\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-3q^{7}+\cdots\)
2166.2.a.g	$2166$	$2$	2166.a	1.a	$1$	$1$	$1$	$17.296$	\(\Q\)	None	✓	✓			2166.2.a.e	$1$	$0$	\(1\)	\(-1\)	\(2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
2166.2.a.h	$2166$	$2$	2166.a	1.a	$1$	$1$	$1$	$17.296$	\(\Q\)	None	✓				114.2.e.b	$1$	$0$	\(1\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
2166.2.a.i	$2166$	$2$	2166.a	1.a	$1$	$1$	$1$	$17.296$	\(\Q\)	None	✓				114.2.a.a	$1$	$0$	\(1\)	\(1\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
2166.2.a.j	$2166$	$2$	2166.a	1.a	$1$	$2$	$2$	$17.296$	\(\Q(\sqrt{5}) \)	None	✓	✓			2166.2.a.j	$1$	$0$	\(-2\)	\(-2\)	\(5\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+(3-\beta )q^{5}+q^{6}+\cdots\)
2166.2.a.k	$2166$	$2$	2166.a	1.a	$1$	$2$	$2$	$17.296$	\(\Q(\sqrt{5}) \)	None	✓	✓			2166.2.a.k	$1$	$1$	\(-2\)	\(2\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{8}+\cdots\)
2166.2.a.l	$2166$	$2$	2166.a	1.a	$1$	$2$	$2$	$17.296$	\(\Q(\sqrt{5}) \)	None	✓	✓			2166.2.a.k	$1$	$1$	\(2\)	\(-2\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{8}+\cdots\)
2166.2.a.m	$2166$	$2$	2166.a	1.a	$1$	$2$	$2$	$17.296$	\(\Q(\sqrt{5}) \)	None	✓	✓			2166.2.a.j	$1$	$0$	\(2\)	\(2\)	\(5\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(3-\beta )q^{5}+q^{6}+\cdots\)
2166.2.a.n	$2166$	$2$	2166.a	1.a	$1$	$3$	$3$	$17.296$	\(\Q(\zeta_{18})^+\)	None	✓				114.2.i.b	$1$	$0$	\(-3\)	\(-3\)	\(-6\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+(-2-\beta _{1})q^{5}+q^{6}+\cdots\)
2166.2.a.o	$2166$	$2$	2166.a	1.a	$1$	$3$	$3$	$17.296$	\(\Q(\zeta_{18})^+\)	None	✓		✓		114.2.i.d	$1$	$1$	\(-3\)	\(-3\)	\(0\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
2166.2.a.p	$2166$	$2$	2166.a	1.a	$1$	$3$	$3$	$17.296$	\(\Q(\zeta_{18})^+\)	None	✓		✓		114.2.i.c	$1$	$1$	\(-3\)	\(3\)	\(-6\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+(-2+\beta _{1})q^{5}-q^{6}+\cdots\)
2166.2.a.q	$2166$	$2$	2166.a	1.a	$1$	$3$	$3$	$17.296$	\(\Q(\zeta_{18})^+\)	None	✓				114.2.i.a	$1$	$0$	\(-3\)	\(3\)	\(0\)	\(-9\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+(-2\beta _{1}+\beta _{2})q^{5}+\cdots\)
2166.2.a.r	$2166$	$2$	2166.a	1.a	$1$	$3$	$3$	$17.296$	\(\Q(\zeta_{18})^+\)	None	✓				114.2.i.c	$1$	$0$	\(3\)	\(-3\)	\(-6\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+(-2+\beta _{1})q^{5}-q^{6}+\cdots\)
2166.2.a.s	$2166$	$2$	2166.a	1.a	$1$	$3$	$3$	$17.296$	\(\Q(\zeta_{18})^+\)	None	✓		✓		114.2.i.a	$1$	$1$	\(3\)	\(-3\)	\(0\)	\(-9\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+(-2\beta _{1}+\beta _{2})q^{5}+\cdots\)
2166.2.a.t	$2166$	$2$	2166.a	1.a	$1$	$3$	$3$	$17.296$	\(\Q(\zeta_{18})^+\)	None	✓		✓	✓	114.2.i.b	$1$	$1$	\(3\)	\(3\)	\(-6\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(-2-\beta _{1})q^{5}+q^{6}+\cdots\)
2166.2.a.u	$2166$	$2$	2166.a	1.a	$1$	$3$	$3$	$17.296$	\(\Q(\zeta_{18})^+\)	None	✓				114.2.i.d	$1$	$0$	\(3\)	\(3\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
2166.2.a.v	$2166$	$2$	2166.a	1.a	$1$	$4$	$4$	$17.296$	\(\Q(\sqrt{41 +4 \sqrt{5}})\)	None	✓	✓	✓		2166.2.a.v	$1$	$0$	\(-4\)	\(-4\)	\(2\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)
2166.2.a.w	$2166$	$2$	2166.a	1.a	$1$	$4$	$4$	$17.296$	\(\Q(\zeta_{20})^+\)	None	✓	✓	✓		2166.2.a.w	$1$	$0$	\(-4\)	\(4\)	\(8\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+(2+\beta _{1})q^{5}-q^{6}+\cdots\)
2166.2.a.x	$2166$	$2$	2166.a	1.a	$1$	$4$	$4$	$17.296$	\(\Q(\zeta_{20})^+\)	None	✓	✓	✓		2166.2.a.w	$1$	$0$	\(4\)	\(-4\)	\(8\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+(2+\beta _{1})q^{5}-q^{6}+\cdots\)
2166.2.a.y	$2166$	$2$	2166.a	1.a	$1$	$4$	$4$	$17.296$	\(\Q(\sqrt{41 +4 \sqrt{5}})\)	None	✓	✓	✓		2166.2.a.v	$1$	$0$	\(4\)	\(4\)	\(2\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2166))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2166)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\)\(^{\oplus 2}\)