Space of modular forms of level 6664, weight 2, and trivial character

• Label: 6664.2.a
• Level: $6664$
• Weight: $2$
• Character orbit: 6664.a
• Rep. character: $\chi_{6664}(1,\cdot)$
• Character field: $\Q$
• Dimension: $164$
• Newform subspaces: $31$
• Sturm bound: $2016$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 6664 = 2^{3} \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6664.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 31 \)
Sturm bound:			\(2016\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6664))\).

	Total	New	Old
Modular forms	1040	164	876
Cusp forms	977	164	813
Eisenstein series	63	0	63

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

\(2\)	\(7\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(18\)
\(+\)	\(+\)	\(-\)	\(-\)	\(22\)
\(+\)	\(-\)	\(+\)	\(-\)	\(24\)
\(+\)	\(-\)	\(-\)	\(+\)	\(18\)
\(-\)	\(+\)	\(+\)	\(-\)	\(20\)
\(-\)	\(+\)	\(-\)	\(+\)	\(20\)
\(-\)	\(-\)	\(+\)	\(+\)	\(21\)
\(-\)	\(-\)	\(-\)	\(-\)	\(21\)
Plus space			\(+\)	\(77\)
Minus space			\(-\)	\(87\)

Trace form

\( 164 q + 2 q^{3} - 2 q^{5} + 160 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6664))\) 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	17
6664.2.a.a	$6664$	$2$	6664.a	1.a	$1$	$1$	$1$	$53.212$	\(\Q\)	None	✓				952.2.q.b	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{5}+6q^{9}+5q^{11}-7q^{13}+\cdots\)
6664.2.a.b	$6664$	$2$	6664.a	1.a	$1$	$1$	$1$	$53.212$	\(\Q\)	None	✓				136.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{9}+2q^{11}+6q^{13}+q^{17}+\cdots\)
6664.2.a.c	$6664$	$2$	6664.a	1.a	$1$	$1$	$1$	$53.212$	\(\Q\)	None	✓				952.2.q.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}+2q^{11}-4q^{13}+q^{17}+\cdots\)
6664.2.a.d	$6664$	$2$	6664.a	1.a	$1$	$1$	$1$	$53.212$	\(\Q\)	None	✓				952.2.q.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}+2q^{11}+4q^{13}-q^{17}+\cdots\)
6664.2.a.e	$6664$	$2$	6664.a	1.a	$1$	$1$	$1$	$53.212$	\(\Q\)	None	✓				136.2.a.a	$1$	$1$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}+q^{9}-6q^{11}-2q^{13}+\cdots\)
6664.2.a.f	$6664$	$2$	6664.a	1.a	$1$	$1$	$1$	$53.212$	\(\Q\)	None	✓				952.2.q.b	$1$	$0$	\(0\)	\(3\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-2q^{5}+6q^{9}+5q^{11}+7q^{13}+\cdots\)
6664.2.a.g	$6664$	$2$	6664.a	1.a	$1$	$2$	$2$	$53.212$	\(\Q(\sqrt{13}) \)	None	✓				952.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1+\beta )q^{5}+\beta q^{9}+(2-2\beta )q^{11}+\cdots\)
6664.2.a.h	$6664$	$2$	6664.a	1.a	$1$	$2$	$2$	$53.212$	\(\Q(\sqrt{5}) \)	None	✓				952.2.a.a	$1$	$0$	\(0\)	\(1\)	\(3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1+\beta )q^{5}+(-2+\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
6664.2.a.i	$6664$	$2$	6664.a	1.a	$1$	$2$	$2$	$53.212$	\(\Q(\sqrt{5}) \)	None	✓				136.2.a.c	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-2q^{5}+(3+2\beta )q^{9}+(1+\cdots)q^{11}+\cdots\)
6664.2.a.j	$6664$	$2$	6664.a	1.a	$1$	$3$	$3$	$53.212$	3.3.229.1	None	✓				952.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+(\beta _{1}-2\beta _{2})q^{9}+\cdots\)
6664.2.a.k	$6664$	$2$	6664.a	1.a	$1$	$3$	$3$	$53.212$	3.3.1229.1	None	✓				952.2.a.e	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(2+\beta _{2})q^{9}+\cdots\)
6664.2.a.l	$6664$	$2$	6664.a	1.a	$1$	$3$	$3$	$53.212$	3.3.229.1	None	✓				952.2.a.d	$1$	$1$	\(0\)	\(3\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+\beta _{2}q^{5}+(1-2\beta _{1}+\beta _{2})q^{9}+\cdots\)
6664.2.a.m	$6664$	$2$	6664.a	1.a	$1$	$3$	$3$	$53.212$	3.3.229.1	None	✓				952.2.a.c	$1$	$0$	\(0\)	\(3\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(2+\beta _{2})q^{5}+(1+2\beta _{1}+\cdots)q^{9}+\cdots\)
6664.2.a.n	$6664$	$2$	6664.a	1.a	$1$	$4$	$4$	$53.212$	4.4.13448.1	None	✓				952.2.a.h	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{3}+(-1+\beta _{2})q^{5}+(2+\cdots)q^{9}+\cdots\)
6664.2.a.o	$6664$	$2$	6664.a	1.a	$1$	$4$	$4$	$53.212$	4.4.5225.1	None	✓				952.2.a.g	$1$	$0$	\(0\)	\(-3\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
6664.2.a.p	$6664$	$2$	6664.a	1.a	$1$	$6$	$6$	$53.212$	6.6.13431004.1	None	✓	✓			6664.2.a.p	$1$	$1$	\(0\)	\(-4\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}-\beta _{3}q^{5}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
6664.2.a.q	$6664$	$2$	6664.a	1.a	$1$	$6$	$6$	$53.212$	6.6.15751800.1	None	✓	✓			6664.2.a.q	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{4})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6664.2.a.r	$6664$	$2$	6664.a	1.a	$1$	$6$	$6$	$53.212$	6.6.30091192.1	None	✓				952.2.q.c	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{2}q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
6664.2.a.s	$6664$	$2$	6664.a	1.a	$1$	$6$	$6$	$53.212$	6.6.30091192.1	None	✓				952.2.q.c	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{4}q^{5}+\beta _{2}q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
6664.2.a.t	$6664$	$2$	6664.a	1.a	$1$	$6$	$6$	$53.212$	6.6.15751800.1	None	✓	✓			6664.2.a.q	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(\beta _{2}-\beta _{4})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6664.2.a.u	$6664$	$2$	6664.a	1.a	$1$	$6$	$6$	$53.212$	6.6.13431004.1	None	✓	✓			6664.2.a.p	$1$	$0$	\(0\)	\(4\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+\beta _{3}q^{5}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
6664.2.a.v	$6664$	$2$	6664.a	1.a	$1$	$7$	$7$	$53.212$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				952.2.q.e	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{6}q^{5}+(\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
6664.2.a.w	$6664$	$2$	6664.a	1.a	$1$	$7$	$7$	$53.212$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				952.2.q.d	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{4}q^{5}+\beta _{2}q^{9}+(\beta _{3}+\beta _{6})q^{11}+\cdots\)
6664.2.a.x	$6664$	$2$	6664.a	1.a	$1$	$7$	$7$	$53.212$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		952.2.q.d	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{2}q^{9}+(\beta _{3}+\beta _{6})q^{11}+\cdots\)
6664.2.a.y	$6664$	$2$	6664.a	1.a	$1$	$7$	$7$	$53.212$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		952.2.q.e	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{6}q^{5}+(\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
6664.2.a.z	$6664$	$2$	6664.a	1.a	$1$	$10$	$10$	$53.212$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		952.2.q.f	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{7}q^{5}+(2+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
6664.2.a.ba	$6664$	$2$	6664.a	1.a	$1$	$10$	$10$	$53.212$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				952.2.q.f	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{7}q^{5}+(2+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
6664.2.a.bb	$6664$	$2$	6664.a	1.a	$1$	$12$	$12$	$53.212$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		6664.2.a.bb	$1$	$1$	\(0\)	\(-8\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+\beta _{3}q^{5}+(1-\beta _{1}+\beta _{6}+\cdots)q^{9}+\cdots\)
6664.2.a.bc	$6664$	$2$	6664.a	1.a	$1$	$12$	$12$	$53.212$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		6664.2.a.bc	$1$	$0$	\(0\)	\(-4\)	\(8\)	\(0\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1-\beta _{10})q^{5}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
6664.2.a.bd	$6664$	$2$	6664.a	1.a	$1$	$12$	$12$	$53.212$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		6664.2.a.bc	$1$	$1$	\(0\)	\(4\)	\(-8\)	\(0\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{10})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6664.2.a.be	$6664$	$2$	6664.a	1.a	$1$	$12$	$12$	$53.212$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		6664.2.a.bb	$1$	$0$	\(0\)	\(8\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-\beta _{3}q^{5}+(1-\beta _{1}+\beta _{6}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6664))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6664)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(833))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(952))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1666))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3332))\)\(^{\oplus 2}\)