Space of modular forms of level 2012, weight 2, and trivial character

• Label: 2012.2.a
• Level: $2012$
• Weight: $2$
• Character orbit: 2012.a
• Rep. character: $\chi_{2012}(1,\cdot)$
• Character field: $\Q$
• Dimension: $42$
• Newform subspaces: $2$
• Sturm bound: $504$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2012 = 2^{2} \cdot 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2012.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(504\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2012))\).

	Total	New	Old
Modular forms	255	42	213
Cusp forms	250	42	208
Eisenstein series	5	0	5

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

\(2\)	\(503\)	Fricke	Dim
\(-\)	\(+\)	$-$	\(21\)
\(-\)	\(-\)	$+$	\(21\)
Plus space		\(+\)	\(21\)
Minus space		\(-\)	\(21\)

Trace form

\( 42 q - 2 q^{7} + 42 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2012))\) 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	503
2012.2.a.a	$2012$	$2$	2012.a	1.a	$1$	$21$	$21$	$16.066$		None	✓	$1$	$1$	\(0\)	\(-10\)	\(-3\)	\(-15\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
2012.2.a.b	$2012$	$2$	2012.a	1.a	$1$	$21$	$21$	$16.066$		None	✓	$1$	$0$	\(0\)	\(10\)	\(3\)	\(13\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2012))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2012)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(503))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1006))\)\(^{\oplus 2}\)