Space of modular forms of level 2664, weight 2, and trivial character

• Label: 2664.2.a
• Level: $2664$
• Weight: $2$
• Character orbit: 2664.a
• Rep. character: $\chi_{2664}(1,\cdot)$
• Character field: $\Q$
• Dimension: $45$
• Newform subspaces: $20$
• Sturm bound: $912$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2664 = 2^{3} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2664.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(912\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2664))\).

	Total	New	Old
Modular forms	472	45	427
Cusp forms	441	45	396
Eisenstein series	31	0	31

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

\(2\)	\(3\)	\(37\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(54\)	\(4\)	\(50\)		\(51\)	\(4\)	\(47\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)		\(64\)	\(5\)	\(59\)		\(60\)	\(5\)	\(55\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)		\(59\)	\(8\)	\(51\)		\(55\)	\(8\)	\(47\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)		\(59\)	\(5\)	\(54\)		\(55\)	\(5\)	\(50\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)		\(64\)	\(4\)	\(60\)		\(60\)	\(4\)	\(56\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)		\(54\)	\(5\)	\(49\)		\(50\)	\(5\)	\(45\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)		\(59\)	\(6\)	\(53\)		\(55\)	\(6\)	\(49\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)		\(59\)	\(8\)	\(51\)		\(55\)	\(8\)	\(47\)		\(4\)	\(0\)	\(4\)
Plus space			\(+\)		\(226\)	\(20\)	\(206\)		\(211\)	\(20\)	\(191\)		\(15\)	\(0\)	\(15\)
Minus space			\(-\)		\(246\)	\(25\)	\(221\)		\(230\)	\(25\)	\(205\)		\(16\)	\(0\)	\(16\)

Trace form

45 * q - 2 * q^5 - 4 * q^7 - 2 * q^11 + 2 * q^13 + 6 * q^17 - 16 * q^23 + 57 * q^25 + 10 * q^29 + q^37 + 4 * q^41 - 8 * q^43 - 8 * q^47 + 73 * q^49 - 18 * q^53 + 16 * q^55 - 8 * q^59 - 2 * q^61 + 24 * q^65 + 6 * q^67 + 28 * q^71 - 28 * q^73 + 16 * q^77 - 4 * q^79 - 16 * q^83 - 28 * q^85 - 6 * q^89 - 28 * q^91 + 20 * q^95 - 10 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2664))\) 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	37
2664.2.a.a	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	\(\Q\)	None	✓				888.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+2q^{13}+6q^{23}+11q^{25}+\cdots\)
2664.2.a.b	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	\(\Q\)	None	✓	✓			2664.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}-5q^{11}+3q^{13}-q^{17}+\cdots\)
2664.2.a.c	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	\(\Q\)	None	✓				296.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}+3q^{11}-2q^{17}-2q^{19}+6q^{23}+\cdots\)
2664.2.a.d	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	\(\Q\)	None	✓				888.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-6q^{13}+4q^{17}+4q^{19}-6q^{23}+\cdots\)
2664.2.a.e	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	\(\Q\)	None	✓				888.2.a.c	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{11}-2q^{13}+6q^{17}+4q^{23}+\cdots\)
2664.2.a.f	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	\(\Q\)	None	✓				296.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}-q^{11}-6q^{13}+4q^{17}+\cdots\)
2664.2.a.g	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	\(\Q\)	None	✓	✓			2664.2.a.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}+5q^{11}+3q^{13}+q^{17}+\cdots\)
2664.2.a.h	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	\(\Q\)	None	✓				888.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-q^{7}+3q^{11}-5q^{13}-7q^{17}+\cdots\)
2664.2.a.i	$2664$	$2$	2664.a	1.a	$1$	$2$	$2$	$21.272$	\(\Q(\sqrt{3}) \)	None	✓				888.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}-2q^{7}+(2-2\beta )q^{11}+\cdots\)
2664.2.a.j	$2664$	$2$	2664.a	1.a	$1$	$2$	$2$	$21.272$	\(\Q(\sqrt{5}) \)	None	✓				888.2.a.f	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(8\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+4q^{7}+(-2-2\beta )q^{11}+\cdots\)
2664.2.a.k	$2664$	$2$	2664.a	1.a	$1$	$2$	$2$	$21.272$	\(\Q(\sqrt{41}) \)	None	✓		✓		888.2.a.h	$1$	$1$	\(0\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{7}+(-1-\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
2664.2.a.l	$2664$	$2$	2664.a	1.a	$1$	$2$	$2$	$21.272$	\(\Q(\sqrt{2}) \)	None	✓				888.2.a.g	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{5}+(-2+2\beta )q^{7}+2\beta q^{11}+\cdots\)
2664.2.a.m	$2664$	$2$	2664.a	1.a	$1$	$3$	$3$	$21.272$	3.3.316.1	None	✓				888.2.a.i	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}+\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots\)
2664.2.a.n	$2664$	$2$	2664.a	1.a	$1$	$3$	$3$	$21.272$	3.3.148.1	None	✓	✓	✓		2664.2.a.n	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{5}+(2-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2664.2.a.o	$2664$	$2$	2664.a	1.a	$1$	$3$	$3$	$21.272$	3.3.568.1	None	✓		✓		888.2.a.j	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(-2+\beta _{2})q^{11}+\cdots\)
2664.2.a.p	$2664$	$2$	2664.a	1.a	$1$	$3$	$3$	$21.272$	3.3.229.1	None	✓				296.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+(2+\beta _{1}-\beta _{2})q^{7}+3\beta _{1}q^{11}+\cdots\)
2664.2.a.q	$2664$	$2$	2664.a	1.a	$1$	$3$	$3$	$21.272$	3.3.148.1	None	✓	✓	✓		2664.2.a.n	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{5}+(2-\beta _{1}-\beta _{2})q^{7}-2q^{13}+\cdots\)
2664.2.a.r	$2664$	$2$	2664.a	1.a	$1$	$4$	$4$	$21.272$	4.4.48389.1	None	✓		✓		296.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{5}+(-\beta _{2}+\beta _{3})q^{7}+(-1+\cdots)q^{11}+\cdots\)
2664.2.a.s	$2664$	$2$	2664.a	1.a	$1$	$5$	$5$	$21.272$	5.5.935504.1	None	✓	✓	✓	✓	2664.2.a.s	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-7\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+(-1+\beta _{4})q^{7}+(-1-\beta _{2}+\cdots)q^{11}+\cdots\)
2664.2.a.t	$2664$	$2$	2664.a	1.a	$1$	$5$	$5$	$21.272$	5.5.935504.1	None	✓	✓	✓	✓	2664.2.a.s	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-7\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+(-1+\beta _{4})q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2664))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2664)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(222))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(333))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(444))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(666))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(888))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1332))\)\(^{\oplus 2}\)