Space of modular forms of level 2002, weight 2, and Character 2002.g

• Label: 2002.2.g
• Level: $2002$
• Weight: $2$
• Character orbit: 2002.g
• Rep. character: $\chi_{2002}(155,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $4$
• Sturm bound: $672$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2002 = 2 \cdot 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2002.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(672\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2002, [\chi])\).

	Total	New	Old
Modular forms	344	68	276
Cusp forms	328	68	260
Eisenstein series	16	0	16

Trace form

\( 68 q - 68 q^{4} + 60 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2002, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2002.2.g.a	$2002$	$2$	2002.g	13.b	$2$	$12$	$12$	$15.986$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}+\beta _{10}q^{3}-q^{4}+(-\beta _{3}-\beta _{7}+\cdots)q^{5}+\cdots\)
2002.2.g.b	$2002$	$2$	2002.g	13.b	$2$	$18$	$18$	$15.986$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-\beta _{2}q^{3}-q^{4}-\beta _{9}q^{5}+\beta _{1}q^{6}+\cdots\)
2002.2.g.c	$2002$	$2$	2002.g	13.b	$2$	$18$	$18$	$15.986$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{2}-\beta _{3}q^{3}-q^{4}+(\beta _{6}+\beta _{8})q^{5}+\cdots\)
2002.2.g.d	$2002$	$2$	2002.g	13.b	$2$	$20$	$20$	$15.986$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{11}q^{2}+\beta _{6}q^{3}-q^{4}+\beta _{14}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2002, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2002, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)