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 - 10 * q^10 + 54 * q^16 + 4 * q^19 - 6 * q^22 + 40 * q^25 + 6 * q^31 - 8 * q^34 + 16 * q^37 - 10 * q^40 + 64 * q^43 - 4 * q^46 + 58 * q^55 + 4 * q^58 + 54 * q^64 + 32 * q^67 + 38 * q^73 + 4 * q^76 + 52 * q^79 - 12 * q^82 + 8 * q^85 - 6 * q^88 + 36 * q^94 - 46 * q^97

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}$