Space of modular forms of level 2671, weight 2, and trivial character

• Label: 2671.2.a
• Level: $2671$
• Weight: $2$
• Character orbit: 2671.a
• Rep. character: $\chi_{2671}(1,\cdot)$
• Character field: $\Q$
• Dimension: $222$
• Newform subspaces: $2$
• Sturm bound: $445$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(445\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2671))\).

	Total	New	Old
Modular forms	223	223	0
Cusp forms	222	222	0
Eisenstein series	1	1	0

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

\(2671\)	Dim
\(+\)	\(100\)
\(-\)	\(122\)

Trace form

\( 222 q - q^{2} - 2 q^{3} + 217 q^{4} - 6 q^{6} - 8 q^{7} - 9 q^{8} + 222 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2671))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2671
2671.2.a.a	$2671$	$2$	2671.a	1.a	$1$	$100$	$100$	$21.328$		None	✓	$1$	$1$	\(-15\)	\(-12\)	\(-33\)	\(-14\)		$+$	$+$		$\mathrm{SU}(2)$
2671.2.a.b	$2671$	$2$	2671.a	1.a	$1$	$122$	$122$	$21.328$		None	✓	$1$	$0$	\(14\)	\(10\)	\(33\)	\(6\)		$-$	$-$		$\mathrm{SU}(2)$