Space of modular forms of level 980, weight 2, and Character 980.c

• Label: 980.2.c
• Level: $980$
• Weight: $2$
• Character orbit: 980.c
• Rep. character: $\chi_{980}(979,\cdot)$
• Character field: $\Q$
• Dimension: $112$
• Newform subspaces: $5$
• Sturm bound: $336$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 140 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(336\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(980, [\chi])\).

	Total	New	Old
Modular forms	184	128	56
Cusp forms	152	112	40
Eisenstein series	32	16	16

Trace form

\( 112 q + 4 q^{4} - 88 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(980, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
980.2.c.a	$980$	$2$	980.c	140.c	$2$	$8$	$8$	$7.825$	\(\Q(\zeta_{16})\)	\(\Q(\sqrt{-1}) \)		✓			980.2.c.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$7^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta_{2} q^{2}-2 q^{4}-\beta_{4} q^{5}+2\beta_{2} q^{8}+\cdots\)
980.2.c.b	$980$	$2$	980.c	140.c	$2$	$8$	$8$	$7.825$	8.0.3317760000.3	\(\Q(\sqrt{-5}) \)					140.2.s.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}+2q^{4}+\beta _{6}q^{5}+(-\beta _{5}+\cdots)q^{6}+\cdots\)
980.2.c.c	$980$	$2$	980.c	140.c	$2$	$16$	$16$	$7.825$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			980.2.c.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(-\beta _{8}-\beta _{10}-\beta _{12})q^{3}+\cdots\)
980.2.c.d	$980$	$2$	980.c	140.c	$2$	$32$	$32$	$7.825$		None					140.2.s.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
980.2.c.e	$980$	$2$	980.c	140.c	$2$	$48$	$48$	$7.825$		None		✓	✓		980.2.c.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(980, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(980, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)