Space of modular forms of level 2646, weight 2, and trivial character

• Label: 2646.2.a
• Level: $2646$
• Weight: $2$
• Character orbit: 2646.a
• Rep. character: $\chi_{2646}(1,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $42$
• Sturm bound: $1008$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 42 \)
Sturm bound:			\(1008\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2646))\).

	Total	New	Old
Modular forms	552	54	498
Cusp forms	457	54	403
Eisenstein series	95	0	95

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

\(2\)	\(3\)	\(7\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)	\(7\)
\(+\)	\(-\)	\(-\)	\(+\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)	\(8\)
\(-\)	\(+\)	\(-\)	\(+\)	\(5\)
\(-\)	\(-\)	\(+\)	\(+\)	\(5\)
\(-\)	\(-\)	\(-\)	\(-\)	\(9\)
Plus space			\(+\)	\(22\)
Minus space			\(-\)	\(32\)

Trace form

\( 54 q + 54 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2646))\) 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	7
2646.2.a.a	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				54.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}-3q^{11}+\cdots\)
2646.2.a.b	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.g.a	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}-4q^{13}+\cdots\)
2646.2.a.c	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.g.c	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-5q^{11}+\cdots\)
2646.2.a.d	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓	✓			2646.2.a.d	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+2q^{11}+\cdots\)
2646.2.a.e	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓	✓			2646.2.a.e	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-q^{11}+\cdots\)
2646.2.a.f	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.a.d	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}-5q^{13}+q^{16}+3q^{17}+\cdots\)
2646.2.a.g	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.g.b	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}+6q^{11}-5q^{13}+\cdots\)
2646.2.a.h	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.g.b	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}+6q^{11}+5q^{13}+\cdots\)
2646.2.a.i	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.a.c	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-5q^{11}+\cdots\)
2646.2.a.j	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓	✓			2646.2.a.e	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-q^{11}+\cdots\)
2646.2.a.k	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.g.c	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-5q^{11}+\cdots\)
2646.2.a.l	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓	✓			2646.2.a.d	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+2q^{11}+\cdots\)
2646.2.a.m	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.g.a	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+4q^{13}+\cdots\)
2646.2.a.n	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.a.b	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+3q^{11}+\cdots\)
2646.2.a.o	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+4q^{5}-q^{8}-4q^{10}+4q^{11}+\cdots\)
2646.2.a.p	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.a.a	$1$	$0$	\(1\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}-4q^{11}+\cdots\)
2646.2.a.q	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.a.b	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots\)
2646.2.a.r	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.g.a	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+4q^{13}+\cdots\)
2646.2.a.s	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓	✓			2646.2.a.d	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-2q^{11}+\cdots\)
2646.2.a.t	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.g.c	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+5q^{11}+\cdots\)
2646.2.a.u	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓	✓			2646.2.a.e	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{11}+\cdots\)
2646.2.a.v	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.a.c	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+5q^{11}+\cdots\)
2646.2.a.w	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.g.b	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}-6q^{11}-5q^{13}+\cdots\)
2646.2.a.x	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.g.b	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}-6q^{11}+5q^{13}+\cdots\)
2646.2.a.y	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.a.d	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}-5q^{13}+q^{16}-3q^{17}+\cdots\)
2646.2.a.z	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓	✓			2646.2.a.e	$1$	$0$	\(1\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{11}+\cdots\)
2646.2.a.ba	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓	✓			2646.2.a.d	$1$	$0$	\(1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}-2q^{11}+\cdots\)
2646.2.a.bb	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.g.c	$1$	$0$	\(1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}+5q^{11}+\cdots\)
2646.2.a.bc	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				378.2.g.a	$1$	$0$	\(1\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-4q^{13}+\cdots\)
2646.2.a.bd	$2646$	$2$	2646.a	1.a	$1$	$1$	$1$	$21.128$	\(\Q\)	None	✓				54.2.a.a	$1$	$0$	\(1\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}+3q^{11}+\cdots\)
2646.2.a.be	$2646$	$2$	2646.a	1.a	$1$	$2$	$2$	$21.128$	\(\Q(\sqrt{2}) \)	None	✓	✓			2646.2.a.be	$1$	$1$	\(-2\)	\(0\)	\(-6\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-3+\beta )q^{5}-q^{8}+(3+\cdots)q^{10}+\cdots\)
2646.2.a.bf	$2646$	$2$	2646.a	1.a	$1$	$2$	$2$	$21.128$	\(\Q(\sqrt{7}) \)	None	✓		✓		378.2.g.g	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta )q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
2646.2.a.bg	$2646$	$2$	2646.a	1.a	$1$	$2$	$2$	$21.128$	\(\Q(\sqrt{2}) \)	None	✓	✓			2646.2.a.bg	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+(2+\cdots)q^{11}+\cdots\)
2646.2.a.bh	$2646$	$2$	2646.a	1.a	$1$	$2$	$2$	$21.128$	\(\Q(\sqrt{2}) \)	None	✓	✓			2646.2.a.bg	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+(2+\cdots)q^{11}+\cdots\)
2646.2.a.bi	$2646$	$2$	2646.a	1.a	$1$	$2$	$2$	$21.128$	\(\Q(\sqrt{7}) \)	None	✓				378.2.g.g	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
2646.2.a.bj	$2646$	$2$	2646.a	1.a	$1$	$2$	$2$	$21.128$	\(\Q(\sqrt{2}) \)	None	✓	✓			2646.2.a.be	$1$	$0$	\(-2\)	\(0\)	\(6\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(3+\beta )q^{5}-q^{8}+(-3+\cdots)q^{10}+\cdots\)
2646.2.a.bk	$2646$	$2$	2646.a	1.a	$1$	$2$	$2$	$21.128$	\(\Q(\sqrt{2}) \)	None	✓	✓			2646.2.a.be	$1$	$1$	\(2\)	\(0\)	\(-6\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-3+\beta )q^{5}+q^{8}+(-3+\cdots)q^{10}+\cdots\)
2646.2.a.bl	$2646$	$2$	2646.a	1.a	$1$	$2$	$2$	$21.128$	\(\Q(\sqrt{7}) \)	None	✓				378.2.g.g	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1+\beta )q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots\)
2646.2.a.bm	$2646$	$2$	2646.a	1.a	$1$	$2$	$2$	$21.128$	\(\Q(\sqrt{2}) \)	None	✓	✓			2646.2.a.bg	$1$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+(-2+\cdots)q^{11}+\cdots\)
2646.2.a.bn	$2646$	$2$	2646.a	1.a	$1$	$2$	$2$	$21.128$	\(\Q(\sqrt{2}) \)	None	✓	✓			2646.2.a.bg	$1$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+(-2+\cdots)q^{11}+\cdots\)
2646.2.a.bo	$2646$	$2$	2646.a	1.a	$1$	$2$	$2$	$21.128$	\(\Q(\sqrt{7}) \)	None	✓		✓		378.2.g.g	$1$	$0$	\(2\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1+\beta )q^{5}+q^{8}+(1+\beta )q^{10}+\cdots\)
2646.2.a.bp	$2646$	$2$	2646.a	1.a	$1$	$2$	$2$	$21.128$	\(\Q(\sqrt{2}) \)	None	✓	✓			2646.2.a.be	$1$	$0$	\(2\)	\(0\)	\(6\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(3+\beta )q^{5}+q^{8}+(3+\beta )q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2646))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2646)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(882))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1323))\)\(^{\oplus 2}\)