Space of modular forms of level 2667, weight 2, and trivial character

• Label: 2667.2.a
• Level: $2667$
• Weight: $2$
• Character orbit: 2667.a
• Rep. character: $\chi_{2667}(1,\cdot)$
• Character field: $\Q$
• Dimension: $127$
• Newform subspaces: $17$
• Sturm bound: $682$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(682\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2667))\).

	Total	New	Old
Modular forms	344	127	217
Cusp forms	337	127	210
Eisenstein series	7	0	7

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

\(3\)	\(7\)	\(127\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(38\)	\(14\)	\(24\)		\(38\)	\(14\)	\(24\)		\(0\)	\(0\)	\(0\)
\(+\)	\(+\)	\(-\)	\(-\)		\(47\)	\(19\)	\(28\)		\(46\)	\(19\)	\(27\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)		\(42\)	\(13\)	\(29\)		\(41\)	\(13\)	\(28\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)		\(43\)	\(18\)	\(25\)		\(42\)	\(18\)	\(24\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)		\(48\)	\(17\)	\(31\)		\(47\)	\(17\)	\(30\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(39\)	\(14\)	\(25\)		\(38\)	\(14\)	\(24\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(44\)	\(10\)	\(34\)		\(43\)	\(10\)	\(33\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(43\)	\(22\)	\(21\)		\(42\)	\(22\)	\(20\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(164\)	\(56\)	\(108\)		\(161\)	\(56\)	\(105\)		\(3\)	\(0\)	\(3\)
Minus space			\(-\)		\(180\)	\(71\)	\(109\)		\(176\)	\(71\)	\(105\)		\(4\)	\(0\)	\(4\)

Trace form

127 * q + q^2 - q^3 + 133 * q^4 + 10 * q^5 + 5 * q^6 - q^7 - 3 * q^8 + 127 * q^9 - 2 * q^10 - 12 * q^11 - 7 * q^12 + 2 * q^13 - 3 * q^14 + 2 * q^15 + 133 * q^16 + 14 * q^17 + q^18 - 4 * q^19 + 38 * q^20 + 3 * q^21 + 20 * q^22 - 8 * q^23 + 9 * q^24 + 145 * q^25 + 38 * q^26 - q^27 - 7 * q^28 + 2 * q^29 - 2 * q^30 + 16 * q^31 + 25 * q^32 - 12 * q^33 + 22 * q^34 - 6 * q^35 + 133 * q^36 - 6 * q^37 - 8 * q^38 + 2 * q^39 - 2 * q^40 + 30 * q^41 + q^42 - 28 * q^43 - 64 * q^44 + 10 * q^45 - 8 * q^46 - 24 * q^47 - 31 * q^48 + 127 * q^49 - 25 * q^50 + 6 * q^51 - 38 * q^52 + 10 * q^53 + 5 * q^54 - 32 * q^55 - 15 * q^56 - 12 * q^57 - 34 * q^58 - 36 * q^59 + 6 * q^60 + 10 * q^61 + 28 * q^62 - q^63 + 157 * q^64 + 36 * q^65 - 20 * q^66 - 52 * q^67 - 6 * q^68 + 16 * q^69 + 22 * q^70 - 32 * q^71 - 3 * q^72 + 54 * q^73 + 58 * q^74 - 15 * q^75 + 52 * q^76 - 12 * q^77 + 30 * q^78 + 32 * q^79 + 46 * q^80 + 127 * q^81 - 30 * q^82 + 28 * q^83 + 5 * q^84 + 4 * q^85 - 20 * q^86 - 22 * q^87 + 32 * q^88 + 38 * q^89 - 2 * q^90 - 6 * q^91 - 32 * q^92 + 8 * q^93 - 8 * q^94 + 73 * q^96 - 2 * q^97 + q^98 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2667))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7	127
2667.2.a.a	$2667$	$2$	2667.a	1.a	$1$	$1$	$1$	$21.296$	\(\Q\)	None	✓	✓			2667.2.a.a	$1$	$1$	\(-2\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots\)
2667.2.a.b	$2667$	$2$	2667.a	1.a	$1$	$1$	$1$	$21.296$	\(\Q\)	None	✓	✓			2667.2.a.b	$1$	$0$	\(-1\)	\(-1\)	\(4\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+4q^{5}+q^{6}-q^{7}+\cdots\)
2667.2.a.c	$2667$	$2$	2667.a	1.a	$1$	$1$	$1$	$21.296$	\(\Q\)	None	✓	✓			2667.2.a.c	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{6}+q^{7}+3q^{8}+\cdots\)
2667.2.a.d	$2667$	$2$	2667.a	1.a	$1$	$1$	$1$	$21.296$	\(\Q\)	None	✓	✓			2667.2.a.d	$1$	$0$	\(0\)	\(1\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+3q^{5}+q^{7}+q^{9}+6q^{11}+\cdots\)
2667.2.a.e	$2667$	$2$	2667.a	1.a	$1$	$1$	$1$	$21.296$	\(\Q\)	None	✓	✓			2667.2.a.e	$1$	$0$	\(2\)	\(1\)	\(3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}+3q^{5}+2q^{6}+\cdots\)
2667.2.a.f	$2667$	$2$	2667.a	1.a	$1$	$2$	$2$	$21.296$	\(\Q(\sqrt{17}) \)	None	✓	✓			2667.2.a.f	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+(-1-\beta )q^{5}-q^{7}+q^{9}+\cdots\)
2667.2.a.g	$2667$	$2$	2667.a	1.a	$1$	$2$	$2$	$21.296$	\(\Q(\sqrt{2}) \)	None	✓	✓			2667.2.a.g	$1$	$1$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}-\beta q^{5}+\beta q^{6}+q^{7}-2\beta q^{8}+\cdots\)
2667.2.a.h	$2667$	$2$	2667.a	1.a	$1$	$2$	$2$	$21.296$	\(\Q(\sqrt{6}) \)	None	✓	✓			2667.2.a.h	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+4q^{4}+\beta q^{5}+\beta q^{6}+\cdots\)
2667.2.a.i	$2667$	$2$	2667.a	1.a	$1$	$2$	$2$	$21.296$	\(\Q(\sqrt{17}) \)	None	✓	✓			2667.2.a.i	$1$	$0$	\(1\)	\(-2\)	\(3\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+(2+\beta )q^{4}+(1+\beta )q^{5}+\cdots\)
2667.2.a.j	$2667$	$2$	2667.a	1.a	$1$	$7$	$7$	$21.296$	7.7.118870813.1	None	✓	✓	✓		2667.2.a.j	$1$	$1$	\(-2\)	\(7\)	\(-8\)	\(7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{2}+q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
2667.2.a.k	$2667$	$2$	2667.a	1.a	$1$	$11$	$11$	$21.296$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓	✓		2667.2.a.k	$1$	$1$	\(-2\)	\(11\)	\(1\)	\(-11\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
2667.2.a.l	$2667$	$2$	2667.a	1.a	$1$	$13$	$13$	$21.296$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	✓	✓	✓	2667.2.a.l	$1$	$0$	\(4\)	\(-13\)	\(12\)	\(13\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{10}+\cdots)q^{5}+\cdots\)
2667.2.a.m	$2667$	$2$	2667.a	1.a	$1$	$14$	$14$	$21.296$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓	✓	2667.2.a.m	$1$	$1$	\(-5\)	\(-14\)	\(-4\)	\(-14\)		$+$	$+$	$+$	$+$	$5$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
2667.2.a.n	$2667$	$2$	2667.a	1.a	$1$	$16$	$16$	$21.296$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓		2667.2.a.n	$1$	$0$	\(4\)	\(16\)	\(5\)	\(-16\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)
2667.2.a.o	$2667$	$2$	2667.a	1.a	$1$	$16$	$16$	$21.296$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓		2667.2.a.o	$1$	$0$	\(5\)	\(-16\)	\(-1\)	\(-16\)		$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots\)
2667.2.a.p	$2667$	$2$	2667.a	1.a	$1$	$18$	$18$	$21.296$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓	✓	✓	2667.2.a.p	$1$	$1$	\(-6\)	\(-18\)	\(-10\)	\(18\)		$+$	$-$	$-$	$+$	$2\cdot 5$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{12}+\cdots)q^{5}+\cdots\)
2667.2.a.q	$2667$	$2$	2667.a	1.a	$1$	$19$	$19$	$21.296$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	✓	✓		2667.2.a.q	$1$	$0$	\(4\)	\(19\)	\(5\)	\(19\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2667))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2667)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(127))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(381))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(889))\)\(^{\oplus 2}\)