Space of modular forms of level 2682, weight 2, and trivial character

• Label: 2682.2.a
• Level: $2682$
• Weight: $2$
• Character orbit: 2682.a
• Rep. character: $\chi_{2682}(1,\cdot)$
• Character field: $\Q$
• Dimension: $63$
• Newform subspaces: $29$
• Sturm bound: $900$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2682 = 2 \cdot 3^{2} \cdot 149 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2682.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 29 \)
Sturm bound:			\(900\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2682))\).

	Total	New	Old
Modular forms	458	63	395
Cusp forms	443	63	380
Eisenstein series	15	0	15

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

\(2\)	\(3\)	\(149\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(5\)
\(+\)	\(+\)	\(-\)	$-$	\(8\)
\(+\)	\(-\)	\(+\)	$-$	\(8\)
\(+\)	\(-\)	\(-\)	$+$	\(10\)
\(-\)	\(+\)	\(+\)	$-$	\(8\)
\(-\)	\(+\)	\(-\)	$+$	\(5\)
\(-\)	\(-\)	\(+\)	$+$	\(7\)
\(-\)	\(-\)	\(-\)	$-$	\(12\)
Plus space			\(+\)	\(27\)
Minus space			\(-\)	\(36\)

Trace form

\( 63 q + q^{2} + 63 q^{4} + 4 q^{5} + q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2682))\) 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	149
2682.2.a.a	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}+2q^{7}-q^{8}+3q^{10}+\cdots\)
2682.2.a.b	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}+4q^{7}-q^{8}+2q^{10}+\cdots\)
2682.2.a.c	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots\)
2682.2.a.d	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-4q^{7}-q^{8}+2q^{11}+q^{13}+\cdots\)
2682.2.a.e	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
2682.2.a.f	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-2q^{10}+\cdots\)
2682.2.a.g	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(3\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-4q^{7}-q^{8}-3q^{10}+\cdots\)
2682.2.a.h	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}+2q^{7}-q^{8}-3q^{10}+\cdots\)
2682.2.a.i	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+2q^{7}+q^{8}-3q^{10}+\cdots\)
2682.2.a.j	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
2682.2.a.k	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
2682.2.a.l	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}+2q^{11}-q^{13}+q^{16}+\cdots\)
2682.2.a.m	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots\)
2682.2.a.n	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+4q^{7}+q^{8}+2q^{10}+\cdots\)
2682.2.a.o	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-q^{11}+\cdots\)
2682.2.a.p	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(3\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+2q^{7}+q^{8}+3q^{10}+\cdots\)
2682.2.a.q	$2682$	$2$	2682.a	1.a	$1$	$1$	$1$	$21.416$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+4q^{5}+4q^{7}+q^{8}+4q^{10}+\cdots\)
2682.2.a.r	$2682$	$2$	2682.a	1.a	$1$	$2$	$2$	$21.416$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(1\)	\(8\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}+4q^{7}-q^{8}-\beta q^{10}+\cdots\)
2682.2.a.s	$2682$	$2$	2682.a	1.a	$1$	$2$	$2$	$21.416$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1+\beta )q^{5}+(1-\beta )q^{7}+\cdots\)
2682.2.a.t	$2682$	$2$	2682.a	1.a	$1$	$3$	$3$	$21.416$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(-3\)	\(0\)	\(-3\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
2682.2.a.u	$2682$	$2$	2682.a	1.a	$1$	$3$	$3$	$21.416$	3.3.169.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(-1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{1}q^{5}+(-2-2\beta _{2})q^{7}+\cdots\)
2682.2.a.v	$2682$	$2$	2682.a	1.a	$1$	$4$	$4$	$21.416$	4.4.15529.1	None	✓	$1$	$1$	\(-4\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-\beta _{2}+\beta _{3})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
2682.2.a.w	$2682$	$2$	2682.a	1.a	$1$	$4$	$4$	$21.416$	4.4.10273.1	None	✓	$1$	$1$	\(-4\)	\(0\)	\(6\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1+\beta _{1})q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
2682.2.a.x	$2682$	$2$	2682.a	1.a	$1$	$4$	$4$	$21.416$	4.4.10273.1	None	✓	$1$	$1$	\(4\)	\(0\)	\(-6\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1-\beta _{1})q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
2682.2.a.y	$2682$	$2$	2682.a	1.a	$1$	$4$	$4$	$21.416$	4.4.6809.1	None	✓	$1$	$1$	\(4\)	\(0\)	\(-2\)	\(-7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
2682.2.a.z	$2682$	$2$	2682.a	1.a	$1$	$5$	$5$	$21.416$	5.5.617176.1	None	✓	$1$	$1$	\(-5\)	\(0\)	\(-5\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1-\beta _{1})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
2682.2.a.ba	$2682$	$2$	2682.a	1.a	$1$	$5$	$5$	$21.416$	5.5.3668908.1	None	✓	$1$	$0$	\(-5\)	\(0\)	\(1\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{4}q^{5}+(1+\beta _{3})q^{7}-q^{8}+\cdots\)
2682.2.a.bb	$2682$	$2$	2682.a	1.a	$1$	$5$	$5$	$21.416$	5.5.3668908.1	None	✓	$1$	$0$	\(5\)	\(0\)	\(-1\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{4}q^{5}+(1+\beta _{3})q^{7}+q^{8}+\cdots\)
2682.2.a.bc	$2682$	$2$	2682.a	1.a	$1$	$5$	$5$	$21.416$	5.5.5444689.1	None	✓	$1$	$0$	\(5\)	\(0\)	\(5\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1-\beta _{1}-\beta _{4})q^{5}+\beta _{2}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2682))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2682)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(149))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(298))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(447))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(894))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1341))\)\(^{\oplus 2}\)