Space of modular forms of level 980, weight 4, and Character 980.e

• Label: 980.4.e
• Level: $980$
• Weight: $4$
• Character orbit: 980.e
• Rep. character: $\chi_{980}(589,\cdot)$
• Character field: $\Q$
• Dimension: $62$
• Newform subspaces: $9$
• Sturm bound: $672$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	980.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(672\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(980, [\chi])\).

	Total	New	Old
Modular forms	528	62	466
Cusp forms	480	62	418
Eisenstein series	48	0	48

Trace form

\( 62 q + 6 q^{5} - 578 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(980, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
980.4.e.a	$980$	$4$	980.e	5.b	$2$	$2$	$2$	$57.822$	\(\Q(\sqrt{-19}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-14\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}+(-7+\beta )q^{5}-7^{2}q^{9}+20q^{11}+\cdots\)
980.4.e.b	$980$	$4$	980.e	5.b	$2$	$2$	$2$	$57.822$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+7iq^{3}+(2+11i)q^{5}-22q^{9}-7q^{11}+\cdots\)
980.4.e.c	$980$	$4$	980.e	5.b	$2$	$2$	$2$	$57.822$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5iq^{3}+(10-5i)q^{5}+2q^{9}-65q^{11}+\cdots\)
980.4.e.d	$980$	$4$	980.e	5.b	$2$	$4$	$4$	$57.822$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
980.4.e.e	$980$	$4$	980.e	5.b	$2$	$4$	$4$	$57.822$	\(\Q(\sqrt{-5}, \sqrt{-21})\)	\(\Q(\sqrt{-35}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-2\beta _{1}+\beta _{2})q^{3}-5\beta _{1}q^{5}+(-14+\cdots)q^{9}+\cdots\)
980.4.e.f	$980$	$4$	980.e	5.b	$2$	$4$	$4$	$57.822$	\(\Q(\sqrt{-34}, \sqrt{466})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{1}q^{5}-7q^{9}+24q^{11}+\cdots\)
980.4.e.g	$980$	$4$	980.e	5.b	$2$	$12$	$12$	$57.822$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{9}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{4}q^{5}+(-9+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
980.4.e.h	$980$	$4$	980.e	5.b	$2$	$12$	$12$	$57.822$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{9}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-9+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
980.4.e.i	$980$	$4$	980.e	5.b	$2$	$20$	$20$	$57.822$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{26}\cdot 5^{2}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{10}q^{3}-\beta _{12}q^{5}+(-11-\beta _{1})q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(980, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(980, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)