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

• Label: 980.2.m
• Level: $980$
• Weight: $2$
• Character orbit: 980.m
• Rep. character: $\chi_{980}(97,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $40$
• Newform subspaces: $2$
• Sturm bound: $336$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(336\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	384	40	344
Cusp forms	288	40	248
Eisenstein series	96	0	96

Trace form

\( 40 q + 16 q^{11} - 20 q^{15} - 16 q^{23} + 20 q^{25} - 4 q^{37} + 44 q^{43} + 8 q^{51} - 4 q^{53} + 44 q^{57} - 4 q^{65} - 48 q^{67} - 8 q^{71} - 40 q^{81} - 64 q^{85} + 28 q^{93} + 60 q^{95}+O(q^{100}) \)

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.m.a	$980$	$2$	980.m	35.f	$4$	$16$	$8$	$7.825$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					140.2.u.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{3}-\beta _{10}q^{5}+(-\beta _{3}-\beta _{4}-2\beta _{7}+\cdots)q^{9}+\cdots\)
980.2.m.b	$980$	$2$	980.m	35.f	$4$	$24$	$12$	$7.825$		None		✓	✓		980.2.m.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(980, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)