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

• Label: 980.2.e
• Level: $980$
• Weight: $2$
• Character orbit: 980.e
• Rep. character: $\chi_{980}(589,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $6$
• Sturm bound: $336$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(336\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(11\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	192	20	172
Cusp forms	144	20	124
Eisenstein series	48	0	48

Trace form

20 * q + 2 * q^5 - 20 * q^9 - 4 * q^11 + 10 * q^15 - 8 * q^19 - 6 * q^25 + 4 * q^29 + 20 * q^31 - 30 * q^45 + 28 * q^51 + 12 * q^55 - 28 * q^59 + 12 * q^61 - 36 * q^65 + 12 * q^69 - 40 * q^71 - 24 * q^75 - 20 * q^79 + 4 * q^81 + 10 * q^85 - 4 * q^89 + 34 * q^95 + 48 * q^99

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.e.a	$980$	$2$	980.e	5.b	$2$	$2$	$2$	$7.825$	\(\Q(\sqrt{-1}) \)	None					140.2.e.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta-1)q^{5}+3 q^{9}+2\beta q^{13}+\cdots\)
980.2.e.b	$980$	$2$	980.e	5.b	$2$	$2$	$2$	$7.825$	\(\Q(\sqrt{-1}) \)	None					140.2.e.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}+(i+2)q^{5}-6 q^{9}+3 q^{11}+\cdots\)
980.2.e.c	$980$	$2$	980.e	5.b	$2$	$4$	$4$	$7.825$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None					140.2.q.a	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-2-\beta _{1}-\beta _{3})q^{11}+\cdots\)
980.2.e.d	$980$	$2$	980.e	5.b	$2$	$4$	$4$	$7.825$	\(\Q(\sqrt{-5}, \sqrt{-21})\)	\(\Q(\sqrt{-35}) \)		✓			980.2.e.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-4+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots\)
980.2.e.e	$980$	$2$	980.e	5.b	$2$	$4$	$4$	$7.825$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			980.2.e.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}-q^{11}-\beta _{2}q^{13}+\cdots\)
980.2.e.f	$980$	$2$	980.e	5.b	$2$	$4$	$4$	$7.825$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None					140.2.q.a	$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-2-\beta _{1}-\beta _{3})q^{11}+\cdots\)

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

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