Space of modular forms of level 980, weight 3, and Character 980.h

• Label: 980.3.h
• Level: $980$
• Weight: $3$
• Character orbit: 980.h
• Rep. character: $\chi_{980}(489,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $2$
• Sturm bound: $504$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	980.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(504\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(980, [\chi])\).

	Total	New	Old
Modular forms	360	40	320
Cusp forms	312	40	272
Eisenstein series	48	0	48

Trace form

\( 40 q + 100 q^{9} - 24 q^{11} - 14 q^{15} - 46 q^{25} - 48 q^{29} + 320 q^{39} + 148 q^{51} - 48 q^{65} + 392 q^{71} - 236 q^{79} - 200 q^{81} - 190 q^{85} + 322 q^{95} - 228 q^{99}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(980, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
980.3.h.a	$980$	$3$	980.h	35.c	$2$	$16$	$16$	$26.703$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					140.3.n.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{2}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}-\beta _{8}q^{5}+(2+\beta _{1})q^{9}+\beta _{2}q^{11}+\cdots\)
980.3.h.b	$980$	$3$	980.h	35.c	$2$	$24$	$24$	$26.703$		None		✓	✓		980.3.h.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(980, [\chi])\) into lower level spaces

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