Space of modular forms of level 2010, weight 2, and Character 2010.d

• Label: 2010.2.d
• Level: $2010$
• Weight: $2$
• Character orbit: 2010.d
• Rep. character: $\chi_{2010}(401,\cdot)$
• Character field: $\Q$
• Dimension: $88$
• Newform subspaces: $6$
• Sturm bound: $816$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2010 = 2 \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2010.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 201 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(816\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(7\), \(11\), \(53\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2010, [\chi])\).

	Total	New	Old
Modular forms	416	88	328
Cusp forms	400	88	312
Eisenstein series	16	0	16

Trace form

\( 88 q + 88 q^{4} - 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2010, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2010.2.d.a	$2010$	$2$	2010.d	201.d	$2$	$2$	$2$	$16.050$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(-1-\beta )q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
2010.2.d.b	$2010$	$2$	2010.d	201.d	$2$	$2$	$2$	$16.050$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(2\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(1-\beta )q^{3}+q^{4}+q^{5}+(1-\beta )q^{6}+\cdots\)
2010.2.d.c	$2010$	$2$	2010.d	201.d	$2$	$20$	$20$	$16.050$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-20\)	\(2\)	\(-20\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
2010.2.d.d	$2010$	$2$	2010.d	201.d	$2$	$20$	$20$	$16.050$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(20\)	\(-2\)	\(20\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{4}q^{3}+q^{4}+q^{5}+\beta _{4}q^{6}+\cdots\)
2010.2.d.e	$2010$	$2$	2010.d	201.d	$2$	$22$	$22$	$16.050$		None		$2$	$0$	\(-22\)	\(0\)	\(22\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
2010.2.d.f	$2010$	$2$	2010.d	201.d	$2$	$22$	$22$	$16.050$		None		$2$	$0$	\(22\)	\(0\)	\(-22\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2010, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2010, [\chi]) \cong \)