Space of modular forms of level 2640, weight 2, and trivial character

• Label: 2640.2.a
• Level: $2640$
• Weight: $2$
• Character orbit: 2640.a
• Rep. character: $\chi_{2640}(1,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $31$
• Sturm bound: $1152$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2640.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 31 \)
Sturm bound:			\(1152\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2640))\).

	Total	New	Old
Modular forms	600	40	560
Cusp forms	553	40	513
Eisenstein series	47	0	47

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

\(2\)	\(3\)	\(5\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(2\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(1\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(2\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(4\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(4\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(4\)
Plus space				\(+\)	\(16\)
Minus space				\(-\)	\(24\)

Trace form

\( 40 q + 4 q^{3} + 8 q^{7} + 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2640))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	5	11
2640.2.a.a	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}-q^{11}+q^{15}+\cdots\)
2640.2.a.b	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
2640.2.a.c	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}-q^{11}+q^{15}+\cdots\)
2640.2.a.d	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
2640.2.a.e	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}+q^{15}+\cdots\)
2640.2.a.f	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+4q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
2640.2.a.g	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+q^{11}-2q^{13}-q^{15}+\cdots\)
2640.2.a.h	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+q^{11}-2q^{13}-q^{15}+\cdots\)
2640.2.a.i	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+4q^{7}+q^{9}-q^{11}-6q^{13}+\cdots\)
2640.2.a.j	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-4q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
2640.2.a.k	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-4q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
2640.2.a.l	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
2640.2.a.m	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-q^{11}-4q^{13}-q^{15}+\cdots\)
2640.2.a.n	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-q^{11}+2q^{13}-q^{15}+\cdots\)
2640.2.a.o	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
2640.2.a.p	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
2640.2.a.q	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
2640.2.a.r	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-4q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
2640.2.a.s	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-q^{11}-6q^{13}+q^{15}+\cdots\)
2640.2.a.t	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-q^{11}+6q^{13}+q^{15}+\cdots\)
2640.2.a.u	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+q^{11}-2q^{13}+q^{15}+\cdots\)
2640.2.a.v	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+4q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
2640.2.a.w	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+4q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
2640.2.a.x	$2640$	$2$	2640.a	1.a	$1$	$2$	$2$	$21.081$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}+q^{11}+(2+\cdots)q^{13}+\cdots\)
2640.2.a.y	$2640$	$2$	2640.a	1.a	$1$	$2$	$2$	$21.081$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-1-\beta )q^{7}+q^{9}+q^{11}+\cdots\)
2640.2.a.z	$2640$	$2$	2640.a	1.a	$1$	$2$	$2$	$21.081$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+\beta q^{7}+q^{9}-q^{11}+(2+\cdots)q^{13}+\cdots\)
2640.2.a.ba	$2640$	$2$	2640.a	1.a	$1$	$2$	$2$	$21.081$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}-q^{11}+\cdots\)
2640.2.a.bb	$2640$	$2$	2640.a	1.a	$1$	$2$	$2$	$21.081$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(4\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(2+\beta )q^{7}+q^{9}+q^{11}+\cdots\)
2640.2.a.bc	$2640$	$2$	2640.a	1.a	$1$	$2$	$2$	$21.081$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(-1-\beta )q^{7}+q^{9}-q^{11}+\cdots\)
2640.2.a.bd	$2640$	$2$	2640.a	1.a	$1$	$2$	$2$	$21.081$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+\beta q^{7}+q^{9}+q^{11}+(2+\cdots)q^{13}+\cdots\)
2640.2.a.be	$2640$	$2$	2640.a	1.a	$1$	$3$	$3$	$21.081$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-\beta _{2}q^{7}+q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2640))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2640)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(660))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(880))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1320))\)\(^{\oplus 2}\)